/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
	/*                                                                           */
	/*                  This file is part of the program and library             */
	/*         SCIP --- Solving Constraint Integer Programs                      */
	/*                                                                           */
	/*    Copyright (C) 2002-2021 Konrad-Zuse-Zentrum                            */
	/*                            fuer Informationstechnik Berlin                */
	/*                                                                           */
	/*  SCIP is distributed under the terms of the ZIB Academic License.         */
	/*                                                                           */
	/*  You should have received a copy of the ZIB Academic License              */
	/*  along with SCIP; see the file COPYING. If not visit scipopt.org.         */
	/*                                                                           */
	/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
	
	/**@file   branch.c
	 * @ingroup OTHER_CFILES
	 * @brief  methods for branching rules and branching candidate storage
	 * @author Tobias Achterberg
	 * @author Timo Berthold
	 * @author Gerald Gamrath
	 * @author Stefan Heinz
	 * @author Michael Winkler
	 * @author Stefan Vigerske
	 */
	
	/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
	
	#include <assert.h>
	#include <string.h>
	
	#include "scip/def.h"
	#include "blockmemshell/memory.h"
	#include "scip/set.h"
	#include "scip/stat.h"
	#include "scip/clock.h"
	#include "scip/paramset.h"
	#include "scip/event.h"
	#include "scip/lp.h"
	#include "scip/var.h"
	#include "scip/prob.h"
	#include "scip/tree.h"
	#include "scip/sepastore.h"
	#include "scip/scip.h"
	#include "scip/branch.h"
	#include "scip/solve.h"
	
	#include "scip/struct_branch.h"
	
	/*
	 * memory growing methods for dynamically allocated arrays
	 */
	
	/** ensures, that lpcands array can store at least num entries */
	static
	SCIP_RETCODE ensureLpcandsSize(
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   int                   num                 /**< minimum number of entries to store */
	   )
	{
	   assert(branchcand->nlpcands <= branchcand->lpcandssize);
	
	   if( num > branchcand->lpcandssize )
	   {
	      int newsize;
	
	      newsize = SCIPsetCalcMemGrowSize(set, num);
	      SCIP_ALLOC( BMSreallocMemoryArray(&branchcand->lpcands, newsize) );
	      SCIP_ALLOC( BMSreallocMemoryArray(&branchcand->lpcandssol, newsize) );
	      SCIP_ALLOC( BMSreallocMemoryArray(&branchcand->lpcandsfrac, newsize) );
	      branchcand->lpcandssize = newsize;
	   }
	   assert(num <= branchcand->lpcandssize);
	
	   return SCIP_OKAY;
	}
	
	/** ensures, that pseudocands array can store at least num entries */
	static
	SCIP_RETCODE ensurePseudocandsSize(
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   int                   num                 /**< minimum number of entries to store */
	   )
	{
	   assert(branchcand->npseudocands <= branchcand->pseudocandssize);
	
	   if( num > branchcand->pseudocandssize )
	   {
	      int newsize;
	
	      newsize = SCIPsetCalcMemGrowSize(set, num);
	      SCIP_ALLOC( BMSreallocMemoryArray(&branchcand->pseudocands, newsize) );
	      branchcand->pseudocandssize = newsize;
	   }
	   assert(num <= branchcand->pseudocandssize);
	
	   return SCIP_OKAY;
	}
	
	/** ensures, that externcands array can store at least num entries */
	static
	SCIP_RETCODE ensureExterncandsSize(
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   int                   num                 /**< minimum number of entries to store */
	   )
	{
	   assert(branchcand->nexterncands <= branchcand->externcandssize);
	
	   if( num > branchcand->externcandssize )
	   {
	      int newsize;
	
	      newsize = SCIPsetCalcMemGrowSize(set, num);
	      SCIP_ALLOC( BMSreallocMemoryArray(&branchcand->externcands, newsize) );
	      SCIP_ALLOC( BMSreallocMemoryArray(&branchcand->externcandsscore, newsize) );
	      SCIP_ALLOC( BMSreallocMemoryArray(&branchcand->externcandssol, newsize) );
	      branchcand->externcandssize = newsize;
	   }
	   assert(num <= branchcand->externcandssize);
	
	   return SCIP_OKAY;
	}
	
	
	
	/*
	 * branching candidate storage methods
	 */
	
	/** creates a branching candidate storage */
	SCIP_RETCODE SCIPbranchcandCreate(
	   SCIP_BRANCHCAND**     branchcand          /**< pointer to store branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   SCIP_ALLOC( BMSallocMemory(branchcand) );
	   (*branchcand)->lpcands = NULL;
	   (*branchcand)->lpcandssol = NULL;
	   (*branchcand)->lpcandsfrac = NULL;
	   (*branchcand)->externcands = NULL;
	   (*branchcand)->externcandssol = NULL;
	   (*branchcand)->externcandsscore = NULL;
	   (*branchcand)->pseudocands = NULL;
	   (*branchcand)->lpcandssize = 0;
	   (*branchcand)->nlpcands = 0;
	   (*branchcand)->nimpllpfracs = 0;
	   (*branchcand)->npriolpcands = 0;
	   (*branchcand)->npriolpbins = 0;
	   (*branchcand)->lpmaxpriority = INT_MIN;
	   (*branchcand)->externcandssize = 0;
	   (*branchcand)->nexterncands = 0;
	   (*branchcand)->nprioexterncands = 0;
	   (*branchcand)->nprioexternbins = 0;
	   (*branchcand)->nprioexternints = 0;
	   (*branchcand)->nprioexternimpls = 0;
	   (*branchcand)->externmaxpriority = INT_MIN;
	   (*branchcand)->pseudocandssize = 0;
	   (*branchcand)->npseudocands = 0;
	   (*branchcand)->npriopseudocands = 0;
	   (*branchcand)->npriopseudobins = 0;
	   (*branchcand)->npriopseudoints = 0;
	   (*branchcand)->pseudomaxpriority = INT_MIN;
	
	   SCIPbranchcandInvalidate(*branchcand);
	
	   return SCIP_OKAY;
	}
	
	/** frees branching candidate storage */
	SCIP_RETCODE SCIPbranchcandFree(
	   SCIP_BRANCHCAND**     branchcand          /**< pointer to store branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   BMSfreeMemoryArrayNull(&(*branchcand)->lpcands);
	   BMSfreeMemoryArrayNull(&(*branchcand)->lpcandssol);
	   BMSfreeMemoryArrayNull(&(*branchcand)->lpcandsfrac);
	   BMSfreeMemoryArrayNull(&(*branchcand)->pseudocands);
	   BMSfreeMemoryArrayNull(&(*branchcand)->externcands);
	   BMSfreeMemoryArrayNull(&(*branchcand)->externcandsscore);
	   BMSfreeMemoryArrayNull(&(*branchcand)->externcandssol);
	   BMSfreeMemory(branchcand);
	
	   return SCIP_OKAY;
	}
	
	/** resets branching candidates storage */
	void SCIPbranchcandInvalidate(
	   SCIP_BRANCHCAND*      branchcand          /**< pointer to store branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   branchcand->validlpcandslp = -1;
	}
	
	/** calculates branching candidates for LP solution branching (fractional variables) */
	static
	SCIP_RETCODE branchcandCalcLPCands(
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_STAT*            stat,               /**< problem statistics */
	   SCIP_LP*              lp                  /**< current LP data */
	   )
	{
	   assert(branchcand != NULL);
	   assert(stat != NULL);
	   assert(branchcand->validlpcandslp <= stat->lpcount);
	   assert(lp != NULL);
	   assert(lp->solved);
	   assert(SCIPlpGetSolstat(lp) == SCIP_LPSOLSTAT_OPTIMAL || SCIPlpGetSolstat(lp) == SCIP_LPSOLSTAT_UNBOUNDEDRAY);
	
	   SCIPsetDebugMsg(set, "calculating LP branching candidates: validlp=%" SCIP_LONGINT_FORMAT ", lpcount=%" SCIP_LONGINT_FORMAT "\n",
	      branchcand->validlpcandslp, stat->lpcount);
	
	   /* check, if the current LP branching candidate array is invalid */
	   if( branchcand->validlpcandslp < stat->lpcount )
	   {
	      SCIP_COL** cols;
	      SCIP_VAR* var;
	      SCIP_COL* col;
	      SCIP_Real primsol;
	      SCIP_Real frac;
	      SCIP_VARTYPE vartype;
	      int branchpriority;
	      int ncols;
	      int c;
	      int insertpos;
	
	      SCIPsetDebugMsg(set, " -> recalculating LP branching candidates\n");
	
	      cols = SCIPlpGetCols(lp);
	      ncols = SCIPlpGetNCols(lp);
	
	      /* construct the LP branching candidate set, moving the candidates with maximal priority to the front */
	      SCIP_CALL( ensureLpcandsSize(branchcand, set, ncols) );
	
	      branchcand->lpmaxpriority = INT_MIN / 2;
	      branchcand->nlpcands = 0;
	      branchcand->nimpllpfracs = 0;
	      branchcand->npriolpcands = 0;
	      branchcand->npriolpbins = 0;
	      for( c = 0; c < ncols; ++c )
	      {
	         col = cols[c];
	         assert(col != NULL);
	         assert(col->lppos == c);
	         assert(col->lpipos >= 0);
	
	         primsol = SCIPcolGetPrimsol(col);
	         assert(primsol < SCIP_INVALID);
	         assert(SCIPsetIsInfinity(set, -col->lb) || SCIPsetIsFeasGE(set, primsol, col->lb));
	         assert(SCIPsetIsInfinity(set, col->ub) || SCIPsetIsFeasLE(set, primsol, col->ub));
	
	         /* count values at infinity as integral */
	         if( SCIPsetIsInfinity(set, REALABS(primsol)) )
	            continue;
	
	         var = col->var;
	         assert(var != NULL);
	         assert(SCIPvarGetStatus(var) == SCIP_VARSTATUS_COLUMN);
	         assert(SCIPvarGetCol(var) == col);
	
	         /* LP branching candidates are fractional binary and integer variables; implicit variables are kept at the end
	          * of the candidates array for some rounding heuristics
	          */
	         vartype = SCIPvarGetType(var);
	         if( vartype == SCIP_VARTYPE_CONTINUOUS )
	            continue;
	
	         /* ignore fixed variables (due to numerics, it is possible, that the LP solution of a fixed integer variable
	          * (with large fixed value) is fractional in terms of absolute feasibility measure)
	          */
	         if( SCIPvarGetLbLocal(var) >= SCIPvarGetUbLocal(var) - 0.5 )
	            continue;
	
	         /* check, if the LP solution value is fractional */
	         frac = SCIPsetFeasFrac(set, primsol);
	
	         /* The fractionality should not be smaller than -feastol, however, if the primsol is large enough
	          * and close to an integer, fixed precision floating point arithmetic might give us values slightly
	          * smaller than -feastol. Originally, the "frac >= -feastol"-check was within SCIPsetIsFeasFracIntegral(),
	          * however, we relaxed it to "frac >= -2*feastol" and have the stricter check here for small-enough primsols.
	          */
	         assert(SCIPsetIsGE(set, frac, -SCIPsetFeastol(set)) || (primsol > 1e14 * SCIPsetFeastol(set)));
	
	         if( SCIPsetIsFeasFracIntegral(set, frac) )
	            continue;
	
	         /* insert candidate in candidate list */
	         branchpriority = SCIPvarGetBranchPriority(var);
	         insertpos = branchcand->nlpcands + branchcand->nimpllpfracs;
	         assert(insertpos < branchcand->lpcandssize);
	
	         if( vartype == SCIP_VARTYPE_IMPLINT )
	            branchpriority = INT_MIN;
	
	         assert(vartype == SCIP_VARTYPE_IMPLINT || branchpriority >= INT_MIN/2);
	         /* ensure that implicit variables are stored at the end of the array */
	         if( vartype != SCIP_VARTYPE_IMPLINT && branchcand->nimpllpfracs > 0 )
	         {
	            assert(branchcand->lpcands[branchcand->nlpcands] != NULL
	                  && SCIPvarGetType(branchcand->lpcands[branchcand->nlpcands]) == SCIP_VARTYPE_IMPLINT );
	
	            branchcand->lpcands[insertpos] = branchcand->lpcands[branchcand->nlpcands];
	            branchcand->lpcandssol[insertpos] = branchcand->lpcandssol[branchcand->nlpcands];
	            branchcand->lpcandsfrac[insertpos] = branchcand->lpcandsfrac[branchcand->nlpcands];
	
	            insertpos = branchcand->nlpcands;
	         }
	
	         if( branchpriority > branchcand->lpmaxpriority )
	         {
	            /* candidate has higher priority than the current maximum:
	             * move it to the front and declare it to be the single best candidate
	             */
	            if( insertpos != 0 )
	            {
	               branchcand->lpcands[insertpos] = branchcand->lpcands[0];
	               branchcand->lpcandssol[insertpos] = branchcand->lpcandssol[0];
	               branchcand->lpcandsfrac[insertpos] = branchcand->lpcandsfrac[0];
	               insertpos = 0;
	            }
	            branchcand->npriolpcands = 1;
	            branchcand->npriolpbins = (vartype == SCIP_VARTYPE_BINARY ? 1 : 0);
	            branchcand->lpmaxpriority = branchpriority;
	         }
	         else if( branchpriority == branchcand->lpmaxpriority )
	         {
	            /* candidate has equal priority as the current maximum:
	             * move away the first non-maximal priority candidate, move the current candidate to the correct
	             * slot (binaries first) and increase the number of maximal priority candidates
	             */
	            if( insertpos != branchcand->npriolpcands )
	            {
	               branchcand->lpcands[insertpos] = branchcand->lpcands[branchcand->npriolpcands];
	               branchcand->lpcandssol[insertpos] = branchcand->lpcandssol[branchcand->npriolpcands];
	               branchcand->lpcandsfrac[insertpos] = branchcand->lpcandsfrac[branchcand->npriolpcands];
	               insertpos = branchcand->npriolpcands;
	            }
	            branchcand->npriolpcands++;
	            if( vartype == SCIP_VARTYPE_BINARY )
	            {
	               if( insertpos != branchcand->npriolpbins )
	               {
	                  branchcand->lpcands[insertpos] = branchcand->lpcands[branchcand->npriolpbins];
	                  branchcand->lpcandssol[insertpos] = branchcand->lpcandssol[branchcand->npriolpbins];
	                  branchcand->lpcandsfrac[insertpos] = branchcand->lpcandsfrac[branchcand->npriolpbins];
	                  insertpos = branchcand->npriolpbins;
	               }
	               branchcand->npriolpbins++;
	            }
	         }
	         /* insert variable at the correct position of the candidates storage */
	         branchcand->lpcands[insertpos] = var;
	         branchcand->lpcandssol[insertpos] = primsol;
	         branchcand->lpcandsfrac[insertpos] = frac;
	
	         /* increase the counter depending on the variable type */
	         if( vartype != SCIP_VARTYPE_IMPLINT )
	            branchcand->nlpcands++;
	         else
	            branchcand->nimpllpfracs++;
	
	         SCIPsetDebugMsg(set, " -> candidate %d: var=<%s>, sol=%g, frac=%g, prio=%d (max: %d) -> pos %d\n",
	            branchcand->nlpcands, SCIPvarGetName(var), primsol, frac, branchpriority, branchcand->lpmaxpriority,
	            insertpos);
	      }
	
	#ifndef NDEBUG
	      /* in debug mode we assert that the variables are positioned correctly (binaries and integers first,
	       * implicit integers last)
	       */
	      for( c = 0; c < branchcand->nlpcands + branchcand->nimpllpfracs; ++c )
	      {
	         assert(c >= branchcand->nlpcands || SCIPvarGetType(branchcand->lpcands[c]) != SCIP_VARTYPE_IMPLINT);
	         assert(c < branchcand->nlpcands || SCIPvarGetType(branchcand->lpcands[c]) == SCIP_VARTYPE_IMPLINT);
	      }
	#endif
	
	      branchcand->validlpcandslp = stat->lpcount;
	   }
	   assert(0 <= branchcand->npriolpcands && branchcand->npriolpcands <= branchcand->nlpcands);
	
	   SCIPsetDebugMsg(set, " -> %d fractional variables (%d of maximal priority)\n", branchcand->nlpcands, branchcand->npriolpcands);
	
	   return SCIP_OKAY;
	}
	
	/** gets branching candidates for LP solution branching (fractional variables) */
	SCIP_RETCODE SCIPbranchcandGetLPCands(
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_STAT*            stat,               /**< problem statistics */
	   SCIP_LP*              lp,                 /**< current LP data */
	   SCIP_VAR***           lpcands,            /**< pointer to store the array of LP branching candidates, or NULL */
	   SCIP_Real**           lpcandssol,         /**< pointer to store the array of LP candidate solution values, or NULL */
	   SCIP_Real**           lpcandsfrac,        /**< pointer to store the array of LP candidate fractionalities, or NULL */
	   int*                  nlpcands,           /**< pointer to store the number of LP branching candidates, or NULL */
	   int*                  npriolpcands,       /**< pointer to store the number of candidates with maximal priority, or NULL */
	   int*                  nfracimplvars       /**< pointer to store the number of implicit fractional variables, or NULL */
	   )
	{
	   /* calculate branching candidates */
	   SCIP_CALL( branchcandCalcLPCands(branchcand, set, stat, lp) );
	
	   /* assign return values */
	   if( lpcands != NULL )
	      *lpcands = branchcand->lpcands;
	   if( lpcandssol != NULL )
	      *lpcandssol = branchcand->lpcandssol;
	   if( lpcandsfrac != NULL )
	      *lpcandsfrac = branchcand->lpcandsfrac;
	   if( nlpcands != NULL )
	      *nlpcands = branchcand->nlpcands;
	   if( npriolpcands != NULL )
	      *npriolpcands = (set->branch_preferbinary && branchcand->npriolpbins > 0 ? branchcand->npriolpbins
	         : branchcand->npriolpcands);
	   if( nfracimplvars != NULL )
	      *nfracimplvars = branchcand->nimpllpfracs;
	
	   return SCIP_OKAY;
	}
	
	/** gets external branching candidates */
	SCIP_RETCODE SCIPbranchcandGetExternCands(
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_VAR***           externcands,        /**< pointer to store the array of external branching candidates, or NULL */
	   SCIP_Real**           externcandssol,     /**< pointer to store the array of external candidate solution values, or NULL */
	   SCIP_Real**           externcandsscore,   /**< pointer to store the array of external candidate scores, or NULL */
	   int*                  nexterncands,       /**< pointer to store the number of external branching candidates, or NULL */
	   int*                  nprioexterncands,   /**< pointer to store the number of candidates with maximal priority, or NULL */
	   int*                  nprioexternbins,    /**< pointer to store the number of binary candidates with maximal priority, or NULL */
	   int*                  nprioexternints,    /**< pointer to store the number of integer candidates with maximal priority, or NULL */
	   int*                  nprioexternimpls    /**< pointer to store the number of implicit integer candidates with maximal priority, 
	                                              *   or NULL */
	   )
	{
	   assert(branchcand != NULL);
	
	   /* assign return values */
	   if( externcands != NULL )
	      *externcands = branchcand->externcands;
	   if( externcandssol != NULL )
	      *externcandssol = branchcand->externcandssol;
	   if( externcandsscore != NULL )
	      *externcandsscore = branchcand->externcandsscore;
	   if( nexterncands != NULL )
	      *nexterncands = branchcand->nexterncands;
	   if( nprioexterncands != NULL )
	      *nprioexterncands = branchcand->nprioexterncands;
	   if( nprioexternbins != NULL )
	      *nprioexternbins = branchcand->nprioexternbins;
	   if( nprioexternints != NULL )
	      *nprioexternints = branchcand->nprioexternints;
	   if( nprioexternimpls != NULL )
	      *nprioexternimpls = branchcand->nprioexternimpls;
	
	   return SCIP_OKAY;
	}
	
	/** gets maximal branching priority of LP branching candidates */
	int SCIPbranchcandGetLPMaxPrio(
	   SCIP_BRANCHCAND*      branchcand          /**< branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   return branchcand->lpmaxpriority;
	}
	
	/** gets number of LP branching candidates with maximal branch priority */
	int SCIPbranchcandGetNPrioLPCands(
	   SCIP_BRANCHCAND*      branchcand          /**< branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   return branchcand->npriolpcands;
	}
	
	/** gets maximal branching priority of external branching candidates */
	int SCIPbranchcandGetExternMaxPrio(
	   SCIP_BRANCHCAND*      branchcand          /**< branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   return branchcand->externmaxpriority;
	}
	
	/** gets number of external branching candidates */
	int SCIPbranchcandGetNExternCands(
	   SCIP_BRANCHCAND*      branchcand          /**< branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   return branchcand->nexterncands;
	}
	
	/** gets number of external branching candidates with maximal branch priority */
	int SCIPbranchcandGetNPrioExternCands(
	   SCIP_BRANCHCAND*      branchcand          /**< branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   return branchcand->nprioexterncands;
	}
	
	/** gets number of binary external branching candidates with maximal branch priority */
	int SCIPbranchcandGetNPrioExternBins(
	   SCIP_BRANCHCAND*      branchcand          /**< branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   return branchcand->nprioexternbins;
	}
	
	/** gets number of integer external branching candidates with maximal branch priority */
	int SCIPbranchcandGetNPrioExternInts(
	   SCIP_BRANCHCAND*      branchcand          /**< branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   return branchcand->nprioexternints;
	}
	
	/** gets number of implicit integer external branching candidates with maximal branch priority */
	int SCIPbranchcandGetNPrioExternImpls(
	   SCIP_BRANCHCAND*      branchcand          /**< branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   return branchcand->nprioexternimpls;
	}
	
	/** gets number of continuous external branching candidates with maximal branch priority */
	int SCIPbranchcandGetNPrioExternConts(
	   SCIP_BRANCHCAND*      branchcand          /**< branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   return branchcand->nprioexterncands - branchcand->nprioexternbins - branchcand->nprioexternints - branchcand->nprioexternimpls;
	}
	
	/** insert variable, its score and its solution value into the external branching candidate storage
	 * the absolute difference of the current lower and upper bounds of the variable must be at least epsilon
	 */
	SCIP_RETCODE SCIPbranchcandAddExternCand(
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_VAR*             var,                /**< variable to insert */
	   SCIP_Real             score,              /**< score of external candidate, e.g. infeasibility */
	   SCIP_Real             solval              /**< value of the variable in the current solution */
	   )
	{
	   SCIP_VARTYPE vartype;
	   int branchpriority;
	   int insertpos;
	
	   assert(branchcand != NULL);
	   assert(var != NULL);
	   assert(!SCIPsetIsEQ(set, SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var))); /* the variable should not be fixed yet */
	   assert(SCIPvarGetType(var) == SCIP_VARTYPE_CONTINUOUS || !SCIPsetIsEQ(set, SCIPsetCeil(set, SCIPvarGetLbLocal(var)), SCIPsetFloor(set, SCIPvarGetUbLocal(var)))); /* a discrete variable should also not be fixed, even after rounding bounds to integral values */
	   assert(SCIPvarGetStatus(var) != SCIP_VARSTATUS_MULTAGGR || !SCIPsetIsEQ(set, SCIPvarGetMultaggrLbLocal(var, set), SCIPvarGetMultaggrUbLocal(var, set))); /* also the current bounds of a multi-aggregated variable should not be fixed yet */
	   assert(branchcand->nprioexterncands <= branchcand->nexterncands);
	   assert(branchcand->nexterncands <= branchcand->externcandssize);
	
	   vartype = SCIPvarGetType(var);
	   branchpriority = SCIPvarGetBranchPriority(var);
	   insertpos = branchcand->nexterncands;
	
	   SCIP_CALL( ensureExterncandsSize(branchcand, set, branchcand->nexterncands+1) );
	
	   SCIPsetDebugMsg(set, "inserting external candidate <%s> of type %d and priority %d into candidate set (maxprio: %d), score = %g, solval = %g\n",
	      SCIPvarGetName(var), vartype, branchpriority, branchcand->externmaxpriority, score, solval);
	
	   /* insert the variable into externcands, making sure, that the highest priority candidates are at the front
	    * and ordered binaries, integers, implicit integers, continuous
	    */
	   if( branchpriority > branchcand->externmaxpriority )
	   {
	      /* candidate has higher priority than the current maximum:
	       * move it to the front and declare it to be the single best candidate
	       */
	      branchcand->externcands[insertpos] = branchcand->externcands[0];
	      branchcand->externcandsscore[insertpos] = branchcand->externcandsscore[0];
	      branchcand->externcandssol[insertpos] = branchcand->externcandssol[0];
	
	      insertpos = 0;
	
	      branchcand->nprioexterncands = 1;
	      branchcand->nprioexternbins = (vartype == SCIP_VARTYPE_BINARY ? 1 : 0);
	      branchcand->nprioexternints = (vartype == SCIP_VARTYPE_INTEGER ? 1 : 0);
	      branchcand->nprioexternimpls = (vartype == SCIP_VARTYPE_IMPLINT ? 1 : 0);
	      branchcand->externmaxpriority = branchpriority;
	   }
	   else if( branchpriority == branchcand->externmaxpriority )
	   {
	      /* candidate has equal priority as the current maximum:
	       * move away the first non-maximal priority candidate, move the current candidate to the correct
	       * slot (binaries first, integers next, implicit integers next, continuous last) and increase the number 
	       * of maximal priority candidates
	       */
	      if( insertpos != branchcand->nprioexterncands )
	      {
	         branchcand->externcands[insertpos] = branchcand->externcands[branchcand->nprioexterncands];
	         branchcand->externcandsscore[insertpos] = branchcand->externcandsscore[branchcand->nprioexterncands];
	         branchcand->externcandssol[insertpos] = branchcand->externcandssol[branchcand->nprioexterncands];
	
	         insertpos = branchcand->nprioexterncands;
	      }
	      branchcand->nprioexterncands++;
	      if( vartype == SCIP_VARTYPE_BINARY || vartype == SCIP_VARTYPE_INTEGER || vartype == SCIP_VARTYPE_IMPLINT )
	      {
	         if( insertpos != branchcand->nprioexternbins + branchcand->nprioexternints + branchcand->nprioexternimpls )
	         {
	            branchcand->externcands[insertpos] =
	               branchcand->externcands[branchcand->nprioexternbins + branchcand->nprioexternints + branchcand->nprioexternimpls];
	            branchcand->externcandsscore[insertpos] =
	               branchcand->externcandsscore[branchcand->nprioexternbins + branchcand->nprioexternints + branchcand->nprioexternimpls];
	            branchcand->externcandssol[insertpos] =
	               branchcand->externcandssol[branchcand->nprioexternbins + branchcand->nprioexternints + branchcand->nprioexternimpls];
	
	            insertpos = branchcand->nprioexternbins + branchcand->nprioexternints + branchcand->nprioexternimpls;
	         }
	         branchcand->nprioexternimpls++;
	
	         if( vartype == SCIP_VARTYPE_BINARY || vartype == SCIP_VARTYPE_INTEGER )
	         {
	            if( insertpos != branchcand->nprioexternbins + branchcand->nprioexternints )
	            {
	               branchcand->externcands[insertpos] = 
	                  branchcand->externcands[branchcand->nprioexternbins + branchcand->nprioexternints];
	               branchcand->externcandsscore[insertpos] = 
	                  branchcand->externcandsscore[branchcand->nprioexternbins + branchcand->nprioexternints];
	               branchcand->externcandssol[insertpos] = 
	                  branchcand->externcandssol[branchcand->nprioexternbins + branchcand->nprioexternints];
	
	               insertpos = branchcand->nprioexternbins + branchcand->nprioexternints;
	            }
	            branchcand->nprioexternints++;
	            branchcand->nprioexternimpls--;
	
	            if( vartype == SCIP_VARTYPE_BINARY )
	            {
	               if( insertpos != branchcand->nprioexternbins )
	               {
	                  branchcand->externcands[insertpos] = branchcand->externcands[branchcand->nprioexternbins];
	                  branchcand->externcandsscore[insertpos] = branchcand->externcandsscore[branchcand->nprioexternbins];
	                  branchcand->externcandssol[insertpos] = branchcand->externcandssol[branchcand->nprioexternbins];
	
	                  insertpos = branchcand->nprioexternbins;
	               }
	               branchcand->nprioexternbins++;
	               branchcand->nprioexternints--;
	            }
	         }
	      }
	   }
	   branchcand->externcands[insertpos] = var;
	   branchcand->externcandsscore[insertpos] = score;
	   branchcand->externcandssol[insertpos] = solval;
	   branchcand->nexterncands++;
	
	   SCIPsetDebugMsg(set, " -> inserted at position %d (nprioexterncands=%d)\n", insertpos, branchcand->nprioexterncands);
	
	   assert(0 <= branchcand->nprioexterncands && branchcand->nprioexterncands <= branchcand->nexterncands);
	   assert(0 <= branchcand->nprioexternbins && branchcand->nprioexternbins <= branchcand->nprioexterncands);
	   assert(0 <= branchcand->nprioexternints && branchcand->nprioexternints <= branchcand->nprioexterncands);
	   assert(0 <= branchcand->nprioexternimpls && branchcand->nprioexternimpls <= branchcand->nprioexterncands);
	
	   return SCIP_OKAY;
	}
	
	/** removes all external candidates from the storage for external branching */
	void SCIPbranchcandClearExternCands(
	   SCIP_BRANCHCAND*      branchcand          /**< branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   branchcand->nexterncands = 0;
	   branchcand->nprioexterncands = 0;
	   branchcand->nprioexternbins = 0;
	   branchcand->nprioexternints = 0;
	   branchcand->nprioexternimpls = 0;
	   branchcand->externmaxpriority = INT_MIN;
	}
	
	/** checks whether the given variable is contained in the candidate storage for external branching */
	SCIP_Bool SCIPbranchcandContainsExternCand(
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_VAR*             var                 /**< variable to look for */
	   )
	{
	   int branchpriority;
	   int i;
	
	   assert(branchcand != NULL);
	   assert(var != NULL);
	   assert(branchcand->nprioexterncands <= branchcand->nexterncands);
	   assert(branchcand->nexterncands <= branchcand->externcandssize);
	
	   branchpriority = SCIPvarGetBranchPriority(var);
	
	   /* look for the variable in the externcands, using the fact, that the highest priority candidates are at the front
	    * and ordered binaries, integers, implicit integers, continuous
	    */
	   if( branchpriority > branchcand->externmaxpriority )
	   {
	      /* the branching priority of the variable is higher than the maximal priority contained in the array;
	       * the variable can thus not be contained */
	      return FALSE;
	   }
	   if( branchpriority == branchcand->externmaxpriority )
	   {
	      SCIP_VARTYPE vartype;
	
	      vartype = SCIPvarGetType(var);
	
	      /* variable has equal priority as the current maximum:
	       * look for it in the correct slot (binaries first, integers next, implicit integers next, continuous last)
	       */
	      if( vartype == SCIP_VARTYPE_BINARY )
	      {
	         /* the variable is binary, look at the first branchcand->nprioexternbins slots */
	         for( i = 0; i < branchcand->nprioexternbins; i++ )
	            if( branchcand->externcands[i] == var )
	               return TRUE;
	         return FALSE;
	      }
	      if( vartype == SCIP_VARTYPE_INTEGER )
	      {
	         /* the variable is integer, look at the slots containing integers */
	         for( i = 0; i < branchcand->nprioexternints; i++ )
	            if( branchcand->externcands[branchcand->nprioexternbins + i] == var )
	               return TRUE;
	         return FALSE;
	      }
	      if( vartype == SCIP_VARTYPE_IMPLINT )
	      {
	         /* the variable is implicit integer, look at the slots containing implicit integers */
	         for( i = 0; i < branchcand->nprioexternimpls; i++ )
	            if( branchcand->externcands[branchcand->nprioexternbins + branchcand->nprioexternints + i] == var )
	               return TRUE;
	         return FALSE;
	      }
	      /* the variable is continuous, look at the slots containing continuous variables */
	      assert(vartype == SCIP_VARTYPE_CONTINUOUS);
	      for( i = branchcand->nprioexternbins + branchcand->nprioexternints + branchcand->nprioexternimpls; 
	           i < branchcand->nprioexterncands; i++ )
	         if( branchcand->externcands[i] == var )
	            return TRUE;
	      return FALSE;
	   }
	   /* the branching priority of the variable is lower than the maximal priority contained in the array;
	    * look for the variable in the candidates which do not have maximal priority */
	   assert(branchpriority < branchcand->externmaxpriority);
	
	   for( i = branchcand->nprioexterncands; i < branchcand->nexterncands; i++ )
	      if( branchcand->externcands[i] == var )
	         return TRUE;
	   return FALSE;
	}
	
	/** gets branching candidates for pseudo solution branching (non-fixed variables) */
	SCIP_RETCODE SCIPbranchcandGetPseudoCands(
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_PROB*            prob,               /**< problem data */
	   SCIP_VAR***           pseudocands,        /**< pointer to store the array of pseudo branching candidates, or NULL */
	   int*                  npseudocands,       /**< pointer to store the number of pseudo branching candidates, or NULL */
	   int*                  npriopseudocands    /**< pointer to store the number of candidates with maximal priority, or NULL */
	   )
	{
	   assert(branchcand != NULL);
	
	#ifndef NDEBUG
	   /* check, if the current pseudo branching candidate array is correct */
	   {
	      SCIP_VAR* var;
	      int npcs;
	      int v;
	
	      assert(prob != NULL);
	
	      /* pseudo branching candidates are non-fixed binary, integer, and implicit integer variables */
	      npcs = 0;
	      for( v = 0; v < prob->nbinvars + prob->nintvars + prob->nimplvars; ++v )
	      {
	         var = prob->vars[v];
	         assert(var != NULL);
	         assert(SCIPvarGetStatus(var) == SCIP_VARSTATUS_LOOSE || SCIPvarGetStatus(var) == SCIP_VARSTATUS_COLUMN);
	         assert(SCIPvarGetType(var) == SCIP_VARTYPE_BINARY
	            || SCIPvarGetType(var) == SCIP_VARTYPE_INTEGER
	            || SCIPvarGetType(var) == SCIP_VARTYPE_IMPLINT);
	         assert(SCIPsetIsFeasIntegral(set, SCIPvarGetLbLocal(var)));
	         assert(SCIPsetIsFeasIntegral(set, SCIPvarGetUbLocal(var)));
	         assert(SCIPsetIsLE(set, SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var)));
	
	         if( SCIPsetIsLT(set, SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var)) )
	         {
	            assert(0 <= var->pseudocandindex && var->pseudocandindex < branchcand->npseudocands);
	            assert(branchcand->pseudocands[var->pseudocandindex] == var);
	            npcs++;
	         }
	         else
	         {
	            assert(var->pseudocandindex == -1);
	         }
	      }
	      assert(branchcand->npseudocands == npcs);
	      for (v = 0; v < branchcand->npriopseudocands; ++v)
	         assert( branchcand->pseudocands[v]->branchpriority == branchcand->pseudomaxpriority );
	   }
	#endif
	
	   /* assign return values */
	   if( pseudocands != NULL )
	      *pseudocands = branchcand->pseudocands;
	   if( npseudocands != NULL )
	      *npseudocands = branchcand->npseudocands;
	   if( npriopseudocands != NULL )
	      *npriopseudocands = (set->branch_preferbinary && branchcand->npriopseudobins > 0 ? branchcand->npriopseudobins
	         : branchcand->npriopseudocands);
	
	   return SCIP_OKAY;
	}
	
	/** gets number of branching candidates for pseudo solution branching (non-fixed variables) */
	int SCIPbranchcandGetNPseudoCands(
	   SCIP_BRANCHCAND*      branchcand          /**< branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   return branchcand->npseudocands;
	}
	
	/** gets number of branching candidates with maximal branch priority for pseudo solution branching */
	int SCIPbranchcandGetNPrioPseudoCands(
	   SCIP_BRANCHCAND*      branchcand          /**< branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   return branchcand->npriopseudocands;
	}
	
	/** gets number of binary branching candidates with maximal branch priority for pseudo solution branching */
	int SCIPbranchcandGetNPrioPseudoBins(
	   SCIP_BRANCHCAND*      branchcand          /**< branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   return branchcand->npriopseudobins;
	}
	
	/** gets number of integer branching candidates with maximal branch priority for pseudo solution branching */
	int SCIPbranchcandGetNPrioPseudoInts(
	   SCIP_BRANCHCAND*      branchcand          /**< branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   return branchcand->npriopseudoints;
	}
	
	/** gets number of implicit integer branching candidates with maximal branch priority for pseudo solution branching */
	int SCIPbranchcandGetNPrioPseudoImpls(
	   SCIP_BRANCHCAND*      branchcand          /**< branching candidate storage */
	   )
	{
	   assert(branchcand != NULL);
	
	   return branchcand->npriopseudocands - branchcand->npriopseudobins - branchcand->npriopseudoints;
	}
	
	/** insert pseudocand at given position, or to the first positions of the maximal priority candidates, using the
	 *  given position as free slot for the other candidates
	 */
	static
	void branchcandInsertPseudoCand(
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_VAR*             var,                /**< variable to insert */
	   int                   insertpos           /**< free position to insert the variable */
	   )
	{
	   SCIP_VARTYPE vartype;
	   int branchpriority;
	
	   assert(branchcand != NULL);
	   assert(var != NULL);
	   assert(branchcand->npriopseudocands <= insertpos && insertpos < branchcand->npseudocands);
	   assert(branchcand->npseudocands <= branchcand->pseudocandssize);
	
	   vartype = SCIPvarGetType(var);
	   branchpriority = SCIPvarGetBranchPriority(var);
	
	   SCIPdebugMessage("inserting pseudo candidate <%s> of type %d and priority %d into candidate set at position %d (maxprio: %d)\n",
	      SCIPvarGetName(var), vartype, branchpriority, insertpos, branchcand->pseudomaxpriority);
	
	   /* insert the variable into pseudocands, making sure, that the highest priority candidates are at the front
	    * and ordered binaries, integers, implicit integers
	    */
	   if( branchpriority > branchcand->pseudomaxpriority )
	   {
	      /* candidate has higher priority than the current maximum:
	       * move it to the front and declare it to be the single best candidate
	       */
	      if( insertpos != 0 )
	      {
	         branchcand->pseudocands[insertpos] = branchcand->pseudocands[0];
	         branchcand->pseudocands[insertpos]->pseudocandindex = insertpos;
	         insertpos = 0;
	      }
	      branchcand->npriopseudocands = 1;
	      branchcand->npriopseudobins = (vartype == SCIP_VARTYPE_BINARY ? 1 : 0);
	      branchcand->npriopseudoints = (vartype == SCIP_VARTYPE_INTEGER ? 1 : 0);
	      branchcand->pseudomaxpriority = branchpriority;
	   }
	   else if( branchpriority == branchcand->pseudomaxpriority )
	   {
	      /* candidate has equal priority as the current maximum:
	       * move away the first non-maximal priority candidate, move the current candidate to the correct
	       * slot (binaries first, integers next, implicit integers last) and increase the number of maximal priority candidates
	       */
	      if( insertpos != branchcand->npriopseudocands )
	      {
	         branchcand->pseudocands[insertpos] = branchcand->pseudocands[branchcand->npriopseudocands];
	         branchcand->pseudocands[insertpos]->pseudocandindex = insertpos;
	         insertpos = branchcand->npriopseudocands;
	      }
	      branchcand->npriopseudocands++;
	      if( vartype == SCIP_VARTYPE_BINARY || vartype == SCIP_VARTYPE_INTEGER )
	      {
	         if( insertpos != branchcand->npriopseudobins + branchcand->npriopseudoints )
	         {
	            branchcand->pseudocands[insertpos] =
	               branchcand->pseudocands[branchcand->npriopseudobins + branchcand->npriopseudoints];
	            branchcand->pseudocands[insertpos]->pseudocandindex = insertpos;
	            insertpos = branchcand->npriopseudobins + branchcand->npriopseudoints;
	         }
	         branchcand->npriopseudoints++;
	
	         if( vartype == SCIP_VARTYPE_BINARY )
	         {
	            if( insertpos != branchcand->npriopseudobins )
	            {
	               branchcand->pseudocands[insertpos] = branchcand->pseudocands[branchcand->npriopseudobins];
	               branchcand->pseudocands[insertpos]->pseudocandindex = insertpos;
	               insertpos = branchcand->npriopseudobins;
	            }
	            branchcand->npriopseudobins++;
	            branchcand->npriopseudoints--;
	         }
	      }
	   }
	   branchcand->pseudocands[insertpos] = var;
	   var->pseudocandindex = insertpos;
	
	   SCIPdebugMessage(" -> inserted at position %d (npriopseudocands=%d)\n", insertpos, branchcand->npriopseudocands);
	
	   assert(0 <= branchcand->npriopseudocands && branchcand->npriopseudocands <= branchcand->npseudocands);
	   assert(0 <= branchcand->npriopseudobins && branchcand->npriopseudobins <= branchcand->npriopseudocands);
	   assert(0 <= branchcand->npriopseudoints && branchcand->npriopseudoints <= branchcand->npriopseudocands);
	}
	
	/** sorts the pseudo branching candidates, such that the candidates of maximal priority are at the front,
	 *  ordered by binaries, integers, implicit integers
	 */
	static
	void branchcandSortPseudoCands(
	   SCIP_BRANCHCAND*      branchcand          /**< branching candidate storage */
	   )
	{
	   SCIP_VAR* var;
	   int i;
	
	   assert(branchcand != NULL);
	   assert(branchcand->npriopseudocands == 0); /* is only be called after removal of last maximal candidate */
	   assert(branchcand->npriopseudobins == 0);
	   assert(branchcand->npriopseudoints == 0);
	
	   SCIPdebugMessage("resorting pseudo candidates\n");
	
	   branchcand->pseudomaxpriority = INT_MIN;
	
	   for( i = 0; i < branchcand->npseudocands; ++i )
	   {
	      var = branchcand->pseudocands[i];
	      assert(var->pseudocandindex == i);
	
	      if( SCIPvarGetBranchPriority(var) >= branchcand->pseudomaxpriority )
	         branchcandInsertPseudoCand(branchcand, var, i);
	   }
	
	   assert(0 <= branchcand->npriopseudocands && branchcand->npriopseudocands <= branchcand->npseudocands);
	   assert(0 <= branchcand->npriopseudobins && branchcand->npriopseudobins <= branchcand->npriopseudocands);
	   assert(0 <= branchcand->npriopseudoints && branchcand->npriopseudoints <= branchcand->npriopseudocands);
	#ifndef NDEBUG
	   {
	      for (i = 0; i < branchcand->npriopseudocands; ++i)
	         assert( branchcand->pseudocands[i]->branchpriority == branchcand->pseudomaxpriority );
	   }
	#endif
	}
	
	/** removes pseudo candidate from pseudocands array
	 */
	static
	void branchcandRemovePseudoCand(
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_VAR*             var                 /**< variable to remove */
	   )
	{
	   int freepos;
	
	   assert(branchcand != NULL);
	   assert(var != NULL);
	   assert(var->pseudocandindex < branchcand->npseudocands);
	   assert(branchcand->pseudocands[var->pseudocandindex] == var);
	   assert(branchcand->pseudocands[branchcand->npseudocands-1] != NULL);
	
	   /* Note that the branching priority of the variable to be removed is not necessarily equal to pseudomaxpriority, since
	    * the status of the variable might have changed, leading to a change in the branching priority. Moreover, if the
	    * variable was part of an aggregation, even other variables might at this point have different priorities. */
	   SCIPdebugMessage("removing pseudo candidate <%s> of type %d and priority %d at %d from candidate set (maxprio: %d)\n",
	      SCIPvarGetName(var), SCIPvarGetType(var), SCIPvarGetBranchPriority(var), var->pseudocandindex,
	      branchcand->pseudomaxpriority);
	
	   /* delete the variable from pseudocands, making sure, that the highest priority candidates are at the front
	    * and ordered binaries, integers, implicit integers
	    */
	   freepos = var->pseudocandindex;
	   var->pseudocandindex = -1;
	   assert(0 <= freepos && freepos < branchcand->npseudocands);
	
	   if( freepos < branchcand->npriopseudobins )
	   {
	      /* a binary candidate of maximal priority was removed */
	      assert(SCIPvarGetType(var) == SCIP_VARTYPE_BINARY);
	      if( freepos != branchcand->npriopseudobins - 1 )
	      {
	         branchcand->pseudocands[freepos] = branchcand->pseudocands[branchcand->npriopseudobins - 1];
	         branchcand->pseudocands[freepos]->pseudocandindex = freepos;
	         freepos = branchcand->npriopseudobins - 1;
	      }
	      branchcand->npriopseudobins--;
	      branchcand->npriopseudoints++;
	   }
	
	   if( freepos < branchcand->npriopseudobins + branchcand->npriopseudoints )
	   {
	      /* a binary or integer candidate of maximal priority was removed */
	      assert(SCIPvarGetType(var) == SCIP_VARTYPE_BINARY || SCIPvarGetType(var) == SCIP_VARTYPE_INTEGER);
	      if( freepos != branchcand->npriopseudobins + branchcand->npriopseudoints - 1 )
	      {
	         branchcand->pseudocands[freepos] =
	            branchcand->pseudocands[branchcand->npriopseudobins + branchcand->npriopseudoints - 1];
	         branchcand->pseudocands[freepos]->pseudocandindex = freepos;
	         freepos = branchcand->npriopseudobins + branchcand->npriopseudoints - 1;
	      }
	      branchcand->npriopseudoints--;
	   }
	
	   if( freepos < branchcand->npriopseudocands )
	   {
	      /* a candidate of maximal priority was removed */
	      if( freepos != branchcand->npriopseudocands - 1 )
	      {
	         branchcand->pseudocands[freepos] = branchcand->pseudocands[branchcand->npriopseudocands - 1];
	         branchcand->pseudocands[freepos]->pseudocandindex = freepos;
	         freepos = branchcand->npriopseudocands - 1;
	      }
	      branchcand->npriopseudocands--;
	   }
	   if( freepos != branchcand->npseudocands - 1 )
	   {
	      branchcand->pseudocands[freepos] = branchcand->pseudocands[branchcand->npseudocands - 1];
	      branchcand->pseudocands[freepos]->pseudocandindex = freepos;
	   }
	   branchcand->npseudocands--;
	
	   assert(0 <= branchcand->npriopseudocands && branchcand->npriopseudocands <= branchcand->npseudocands);
	   assert(0 <= branchcand->npriopseudobins && branchcand->npriopseudobins <= branchcand->npriopseudocands);
	   assert(0 <= branchcand->npriopseudoints && branchcand->npriopseudoints <= branchcand->npriopseudocands);
	
	   /* if all maximal priority candidates were removed, resort the array s.t. the new maximal priority candidates
	    * are at the front
	    */
	   if( branchcand->npriopseudocands == 0 )
	      branchcandSortPseudoCands(branchcand);
	}
	
	/** removes variable from branching candidate list */
	SCIP_RETCODE SCIPbranchcandRemoveVar(
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_VAR*             var                 /**< variable that changed its bounds */
	   )
	{
	   assert(var != NULL);
	
	   /* make sure, variable is not member of the pseudo branching candidate list */
	   if( var->pseudocandindex >= 0 )
	   {
	      branchcandRemovePseudoCand(branchcand, var);
	   }
	
	   return SCIP_OKAY;
	}
	
	/** updates branching candidate list for a given variable */
	SCIP_RETCODE SCIPbranchcandUpdateVar(
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_VAR*             var                 /**< variable that changed its bounds */
	   )
	{
	   assert(branchcand != NULL);
	   assert(var != NULL);
	
	   if( (SCIPvarGetStatus(var) == SCIP_VARSTATUS_LOOSE || SCIPvarGetStatus(var) == SCIP_VARSTATUS_COLUMN)
	      && SCIPvarGetType(var) != SCIP_VARTYPE_CONTINUOUS
	      && SCIPsetIsLT(set, SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var)) )
	   {
	      /* variable is neither continuous nor fixed and has non-empty domain: make sure it is member of the pseudo branching candidate list */
	      if( var->pseudocandindex == -1 )
	      {
	         SCIP_CALL( ensurePseudocandsSize(branchcand, set, branchcand->npseudocands+1) );
	
	         branchcand->npseudocands++;
	         branchcandInsertPseudoCand(branchcand, var, branchcand->npseudocands-1);
	      }
	   }
	   else
	   {
	      assert(SCIPvarGetStatus(var) == SCIP_VARSTATUS_ORIGINAL
	         || SCIPvarGetStatus(var) == SCIP_VARSTATUS_FIXED
	         || SCIPvarGetStatus(var) == SCIP_VARSTATUS_AGGREGATED
	         || SCIPvarGetStatus(var) == SCIP_VARSTATUS_MULTAGGR
	         || SCIPvarGetStatus(var) == SCIP_VARSTATUS_NEGATED
	         || SCIPvarGetType(var) == SCIP_VARTYPE_CONTINUOUS
	         || SCIPsetIsGE(set, SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var)));
	
	      /* variable is continuous or fixed or has empty domain: make sure it is not member of the pseudo branching candidate list */
	      SCIP_CALL( SCIPbranchcandRemoveVar(branchcand, var) );
	   }
	
	   return SCIP_OKAY;
	}
	
	/** updates branching priority of the given variable and update the pseudo candidate array if needed */
	SCIP_RETCODE SCIPbranchcandUpdateVarBranchPriority(
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_VAR*             var,                /**< variable that changed its bounds */
	   int                   branchpriority      /**< branch priority of the variable */
	   )
	{
	   int oldbranchpriority;
	   int pseudomaxpriority;
	
	   assert(branchcand != NULL);
	
	   oldbranchpriority = SCIPvarGetBranchPriority(var);
	
	   if( oldbranchpriority == branchpriority )
	      return SCIP_OKAY;
	
	   pseudomaxpriority = branchcand->pseudomaxpriority;
	
	   /* if the variable currently belongs to the priority set or the new branching priority is larger than the current one,
	    * remove it from the pseudo branch candidate array */
	   if( oldbranchpriority == pseudomaxpriority || branchpriority > pseudomaxpriority )
	   {
	      SCIP_CALL( SCIPbranchcandRemoveVar(branchcand, var) );
	      assert(var->pseudocandindex == -1);
	   }
	
	   /* change the branching priority of the variable */
	   SCIP_CALL( SCIPvarChgBranchPriority(var, branchpriority) );
	
	   /* if the variable is not part of the pseudo branching candidate array, check if it is a pseudo branching candidate
	    * and add it if so */
	   SCIP_CALL( SCIPbranchcandUpdateVar(branchcand, set, var) );
	
	   return SCIP_OKAY;
	}
	
	
	
	/*
	 * branching rule methods
	 */
	
	/** compares two branching rules w. r. to their priority */
	SCIP_DECL_SORTPTRCOMP(SCIPbranchruleComp)
	{  /*lint --e{715}*/
	   return ((SCIP_BRANCHRULE*)elem2)->priority - ((SCIP_BRANCHRULE*)elem1)->priority;
	}
	
	/** comparison method for sorting branching rules w.r.t. to their name */
	SCIP_DECL_SORTPTRCOMP(SCIPbranchruleCompName)
	{
	   return strcmp(SCIPbranchruleGetName((SCIP_BRANCHRULE*)elem1), SCIPbranchruleGetName((SCIP_BRANCHRULE*)elem2));
	}
	
	/** method to call, when the priority of a branching rule was changed */
	static
	SCIP_DECL_PARAMCHGD(paramChgdBranchrulePriority)
	{  /*lint --e{715}*/
	   SCIP_PARAMDATA* paramdata;
	
	   paramdata = SCIPparamGetData(param);
	   assert(paramdata != NULL);
	
	   /* use SCIPsetBranchrulePriority() to mark the branchrules unsorted */
	   SCIP_CALL( SCIPsetBranchrulePriority(scip, (SCIP_BRANCHRULE*)paramdata, SCIPparamGetInt(param)) ); /*lint !e740*/
	
	   return SCIP_OKAY;
	}
	
	/** copies the given branchrule to a new scip */
	SCIP_RETCODE SCIPbranchruleCopyInclude(
	   SCIP_BRANCHRULE*      branchrule,         /**< branchrule */
	   SCIP_SET*             set                 /**< SCIP_SET of SCIP to copy to */
	   )
	{
	   assert(branchrule != NULL);
	   assert(set != NULL);
	   assert(set->scip != NULL);
	
	   if( branchrule->branchcopy != NULL )
	   {
	      SCIPsetDebugMsg(set, "including branching rule %s in subscip %p\n", SCIPbranchruleGetName(branchrule), (void*)set->scip);
	      SCIP_CALL( branchrule->branchcopy(set->scip, branchrule) );
	   }
	
	   return SCIP_OKAY;
	}
	
	/** internal method for creating a branching rule */
	static
	SCIP_RETCODE doBranchruleCreate(
	   SCIP_BRANCHRULE**     branchrule,         /**< pointer to store branching rule */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_MESSAGEHDLR*     messagehdlr,        /**< message handler */
	   BMS_BLKMEM*           blkmem,             /**< block memory for parameter settings */
	   const char*           name,               /**< name of branching rule */
	   const char*           desc,               /**< description of branching rule */
	   int                   priority,           /**< priority of the branching rule */
	   int                   maxdepth,           /**< maximal depth level, up to which this branching rule should be used (or -1) */
	   SCIP_Real             maxbounddist,       /**< maximal relative distance from current node's dual bound to primal bound
	                                              *   compared to best node's dual bound for applying branching rule
	                                              *   (0.0: only on current best node, 1.0: on all nodes) */
	   SCIP_DECL_BRANCHCOPY  ((*branchcopy)),    /**< copy method of branching rule */
	   SCIP_DECL_BRANCHFREE  ((*branchfree)),    /**< destructor of branching rule */
	   SCIP_DECL_BRANCHINIT  ((*branchinit)),    /**< initialize branching rule */
	   SCIP_DECL_BRANCHEXIT  ((*branchexit)),    /**< deinitialize branching rule */
	   SCIP_DECL_BRANCHINITSOL((*branchinitsol)),/**< solving process initialization method of branching rule */
	   SCIP_DECL_BRANCHEXITSOL((*branchexitsol)),/**< solving process deinitialization method of branching rule */
	   SCIP_DECL_BRANCHEXECLP((*branchexeclp)),  /**< branching execution method for fractional LP solutions */
	   SCIP_DECL_BRANCHEXECEXT((*branchexecext)),/**< branching execution method for external solutions */
	   SCIP_DECL_BRANCHEXECPS((*branchexecps)),  /**< branching execution method for not completely fixed pseudo solutions */
	   SCIP_BRANCHRULEDATA*  branchruledata      /**< branching rule data */
	   )
	{
	   char paramname[SCIP_MAXSTRLEN];
	   char paramdesc[SCIP_MAXSTRLEN];
	
	   assert(branchrule != NULL);
	   assert(name != NULL);
	   assert(desc != NULL);
	
	   SCIP_ALLOC( BMSallocMemory(branchrule) );
	   BMSclearMemory(*branchrule);
	
	   SCIP_ALLOC( BMSduplicateMemoryArray(&(*branchrule)->name, name, strlen(name)+1) );
	   SCIP_ALLOC( BMSduplicateMemoryArray(&(*branchrule)->desc, desc, strlen(desc)+1) );
	   (*branchrule)->priority = priority;
	   (*branchrule)->maxdepth = maxdepth;
	   (*branchrule)->maxbounddist = maxbounddist;
	   (*branchrule)->branchcopy = branchcopy;
	   (*branchrule)->branchfree = branchfree;
	   (*branchrule)->branchinit = branchinit;
	   (*branchrule)->branchexit = branchexit;
	   (*branchrule)->branchinitsol = branchinitsol;
	   (*branchrule)->branchexitsol = branchexitsol;
	   (*branchrule)->branchexeclp = branchexeclp;
	   (*branchrule)->branchexecext = branchexecext;
	   (*branchrule)->branchexecps = branchexecps;
	   (*branchrule)->branchruledata = branchruledata;
	   SCIP_CALL( SCIPclockCreate(&(*branchrule)->setuptime, SCIP_CLOCKTYPE_DEFAULT) );
	   SCIP_CALL( SCIPclockCreate(&(*branchrule)->branchclock, SCIP_CLOCKTYPE_DEFAULT) );
	   (*branchrule)->nlpcalls = 0;
	   (*branchrule)->nexterncalls = 0;
	   (*branchrule)->npseudocalls = 0;
	   (*branchrule)->ncutoffs = 0;
	   (*branchrule)->ncutsfound = 0;
	   (*branchrule)->nconssfound = 0;
	   (*branchrule)->ndomredsfound = 0;
	   (*branchrule)->nchildren = 0;
	   (*branchrule)->initialized = FALSE;
	
	   /* add parameters */
	   (void) SCIPsnprintf(paramname, SCIP_MAXSTRLEN, "branching/%s/priority", name);
	   (void) SCIPsnprintf(paramdesc, SCIP_MAXSTRLEN, "priority of branching rule <%s>", name);
	   SCIP_CALL( SCIPsetAddIntParam(set, messagehdlr, blkmem, paramname, paramdesc,
	         &(*branchrule)->priority, FALSE, priority, INT_MIN/4, INT_MAX/4,
	         paramChgdBranchrulePriority, (SCIP_PARAMDATA*)(*branchrule)) ); /*lint !e740*/
	   (void) SCIPsnprintf(paramname, SCIP_MAXSTRLEN, "branching/%s/maxdepth", name);
	   (void) SCIPsnprintf(paramdesc, SCIP_MAXSTRLEN, "maximal depth level, up to which branching rule <%s> should be used (-1 for no limit)", name);
	   SCIP_CALL( SCIPsetAddIntParam(set, messagehdlr, blkmem, paramname, paramdesc,
	         &(*branchrule)->maxdepth, FALSE, maxdepth, -1, SCIP_MAXTREEDEPTH,
	         NULL, NULL) ); /*lint !e740*/
	   (void) SCIPsnprintf(paramname, SCIP_MAXSTRLEN, "branching/%s/maxbounddist", name);
	   (void) SCIPsnprintf(paramdesc, SCIP_MAXSTRLEN, "maximal relative distance from current node's dual bound to primal bound compared to best node's dual bound for applying branching rule (0.0: only on current best node, 1.0: on all nodes)");
	   SCIP_CALL( SCIPsetAddRealParam(set, messagehdlr, blkmem, paramname, paramdesc,
	         &(*branchrule)->maxbounddist, FALSE, maxbounddist, 0.0, 1.0,
	         NULL, NULL) ); /*lint !e740*/
	
	   return SCIP_OKAY;
	}
	
	/** creates a branching rule */
	SCIP_RETCODE SCIPbranchruleCreate(
	   SCIP_BRANCHRULE**     branchrule,         /**< pointer to store branching rule */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_MESSAGEHDLR*     messagehdlr,        /**< message handler */
	   BMS_BLKMEM*           blkmem,             /**< block memory for parameter settings */
	   const char*           name,               /**< name of branching rule */
	   const char*           desc,               /**< description of branching rule */
	   int                   priority,           /**< priority of the branching rule */
	   int                   maxdepth,           /**< maximal depth level, up to which this branching rule should be used (or -1) */
	   SCIP_Real             maxbounddist,       /**< maximal relative distance from current node's dual bound to primal bound
	                                              *   compared to best node's dual bound for applying branching rule
	                                              *   (0.0: only on current best node, 1.0: on all nodes) */
	   SCIP_DECL_BRANCHCOPY  ((*branchcopy)),    /**< copy method of branching rule */
	   SCIP_DECL_BRANCHFREE  ((*branchfree)),    /**< destructor of branching rule */
	   SCIP_DECL_BRANCHINIT  ((*branchinit)),    /**< initialize branching rule */
	   SCIP_DECL_BRANCHEXIT  ((*branchexit)),    /**< deinitialize branching rule */
	   SCIP_DECL_BRANCHINITSOL((*branchinitsol)),/**< solving process initialization method of branching rule */
	   SCIP_DECL_BRANCHEXITSOL((*branchexitsol)),/**< solving process deinitialization method of branching rule */
	   SCIP_DECL_BRANCHEXECLP((*branchexeclp)),  /**< branching execution method for fractional LP solutions */
	   SCIP_DECL_BRANCHEXECEXT((*branchexecext)),/**< branching execution method for external solutions */
	   SCIP_DECL_BRANCHEXECPS((*branchexecps)),  /**< branching execution method for not completely fixed pseudo solutions */
	   SCIP_BRANCHRULEDATA*  branchruledata      /**< branching rule data */
	   )
	{
	   assert(branchrule != NULL);
	   assert(name != NULL);
	   assert(desc != NULL);
	
	   SCIP_CALL_FINALLY( doBranchruleCreate(branchrule, set, messagehdlr, blkmem, name, desc, priority, maxdepth,
	      maxbounddist, branchcopy, branchfree, branchinit, branchexit, branchinitsol, branchexitsol, branchexeclp,
	      branchexecext, branchexecps, branchruledata), (void) SCIPbranchruleFree(branchrule, set) );
	
	   return SCIP_OKAY;
	}
	
	/** frees memory of branching rule */
	SCIP_RETCODE SCIPbranchruleFree(
	   SCIP_BRANCHRULE**     branchrule,         /**< pointer to branching rule data structure */
	   SCIP_SET*             set                 /**< global SCIP settings */
	   )
	{
	   assert(branchrule != NULL);
	   if( *branchrule == NULL )
	      return SCIP_OKAY;
	   assert(!(*branchrule)->initialized);
	   assert(set != NULL);
	
	   /* call destructor of branching rule */
	   if( (*branchrule)->branchfree != NULL )
	   {
	      SCIP_CALL( (*branchrule)->branchfree(set->scip, *branchrule) );
	   }
	
	   SCIPclockFree(&(*branchrule)->branchclock);
	   SCIPclockFree(&(*branchrule)->setuptime);
	   BMSfreeMemoryArrayNull(&(*branchrule)->name);
	   BMSfreeMemoryArrayNull(&(*branchrule)->desc);
	   BMSfreeMemory(branchrule);
	
	   return SCIP_OKAY;
	}
	
	/** initializes branching rule */
	SCIP_RETCODE SCIPbranchruleInit(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_SET*             set                 /**< global SCIP settings */
	   )
	{
	   assert(branchrule != NULL);
	   assert(set != NULL);
	
	   if( branchrule->initialized )
	   {
	      SCIPerrorMessage("branching rule <%s> already initialized\n", branchrule->name);
	      return SCIP_INVALIDCALL;
	   }
	
	   if( set->misc_resetstat )
	   {
	      SCIPclockReset(branchrule->setuptime);
	      SCIPclockReset(branchrule->branchclock);
	      branchrule->nlpcalls = 0;
	      branchrule->nexterncalls = 0;
	      branchrule->npseudocalls = 0;
	      branchrule->ncutoffs = 0;
	      branchrule->ncutsfound = 0;
	      branchrule->nconssfound = 0;
	      branchrule->ndomredsfound = 0;
	      branchrule->nchildren = 0;
	   }
	
	   if( branchrule->branchinit != NULL )
	   {
	      /* start timing */
	      SCIPclockStart(branchrule->setuptime, set);
	
	      SCIP_CALL( branchrule->branchinit(set->scip, branchrule) );
	
	      /* stop timing */
	      SCIPclockStop(branchrule->setuptime, set);
	   }
	   branchrule->initialized = TRUE;
	
	   return SCIP_OKAY;
	}
	
	/** deinitializes branching rule */
	SCIP_RETCODE SCIPbranchruleExit(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_SET*             set                 /**< global SCIP settings */
	   )
	{
	   assert(branchrule != NULL);
	   assert(set != NULL);
	
	   if( !branchrule->initialized )
	   {
	      SCIPerrorMessage("branching rule <%s> not initialized\n", branchrule->name);
	      return SCIP_INVALIDCALL;
	   }
	
	   if( branchrule->branchexit != NULL )
	   {
	      /* start timing */
	      SCIPclockStart(branchrule->setuptime, set);
	
	      SCIP_CALL( branchrule->branchexit(set->scip, branchrule) );
	
	      /* stop timing */
	      SCIPclockStop(branchrule->setuptime, set);
	   }
	   branchrule->initialized = FALSE;
	
	   return SCIP_OKAY;
	}
	
	/** informs branching rule that the branch and bound process is being started */
	SCIP_RETCODE SCIPbranchruleInitsol(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_SET*             set                 /**< global SCIP settings */
	   )
	{
	   assert(branchrule != NULL);
	   assert(set != NULL);
	
	   /* call solving process initialization method of branching rule */
	   if( branchrule->branchinitsol != NULL )
	   {
	      /* start timing */
	      SCIPclockStart(branchrule->setuptime, set);
	
	      SCIP_CALL( branchrule->branchinitsol(set->scip, branchrule) );
	
	      /* stop timing */
	      SCIPclockStop(branchrule->setuptime, set);
	   }
	
	   return SCIP_OKAY;
	}
	
	/** informs branching rule that the branch and bound process data is being freed */
	SCIP_RETCODE SCIPbranchruleExitsol(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_SET*             set                 /**< global SCIP settings */
	   )
	{
	   assert(branchrule != NULL);
	   assert(set != NULL);
	
	   /* call solving process deinitialization method of branching rule */
	   if( branchrule->branchexitsol != NULL )
	   {
	      /* start timing */
	      SCIPclockStart(branchrule->setuptime, set);
	
	      SCIP_CALL( branchrule->branchexitsol(set->scip, branchrule) );
	
	      /* stop timing */
	      SCIPclockStop(branchrule->setuptime, set);
	   }
	
	   return SCIP_OKAY;
	}
	
	/** executes branching rule for fractional LP solution */
	SCIP_RETCODE SCIPbranchruleExecLPSol(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_STAT*            stat,               /**< problem statistics */
	   SCIP_TREE*            tree,               /**< branch and bound tree */
	   SCIP_SEPASTORE*       sepastore,          /**< separation storage */
	   SCIP_Real             cutoffbound,        /**< global upper cutoff bound */
	   SCIP_Bool             allowaddcons,       /**< should adding constraints be allowed to avoid a branching? */
	   SCIP_RESULT*          result              /**< pointer to store the result of the callback method */
	   )
	{
	   assert(branchrule != NULL);
	   assert(set != NULL);
	   assert(tree != NULL);
	   assert(tree->focusnode != NULL);
	   assert(tree->nchildren == 0);
	   assert(result != NULL);
	
	   *result = SCIP_DIDNOTRUN;
	   if( branchrule->branchexeclp != NULL
	      && (branchrule->maxdepth == -1 || branchrule->maxdepth >= SCIPtreeGetCurrentDepth(tree)) )
	   {
	      SCIP_Real loclowerbound;
	      SCIP_Real glblowerbound;
	      SCIP_Bool runbranchrule;
	
	      loclowerbound = SCIPnodeGetLowerbound(tree->focusnode);
	      glblowerbound = SCIPtreeGetLowerbound(tree, set);
	
	      /* we distinguish between finite and infinite global lower bounds to avoid comparisons between different values > SCIPinfinity() */
	      if( SCIPsetIsInfinity(set, -glblowerbound) )
	         runbranchrule = SCIPsetIsInfinity(set, -loclowerbound) || SCIPsetIsGE(set, branchrule->maxbounddist, 1.0);
	      else
	      {
	         assert(!SCIPsetIsInfinity(set, -loclowerbound));
	         runbranchrule = SCIPsetIsLE(set, loclowerbound - glblowerbound, branchrule->maxbounddist * (cutoffbound - glblowerbound));
	      }
	
	      if( runbranchrule )
	      {
	         SCIP_Longint oldndomchgs;
	         SCIP_Longint oldnprobdomchgs;
	         SCIP_Longint oldnactiveconss;
	         int oldncuts;
	
	         SCIPsetDebugMsg(set, "executing LP branching rule <%s>\n", branchrule->name);
	
	         oldndomchgs = stat->nboundchgs + stat->nholechgs;
	         oldnprobdomchgs = stat->nprobboundchgs + stat->nprobholechgs;
	         oldncuts = SCIPsepastoreGetNCuts(sepastore);
	         oldnactiveconss = stat->nactiveconssadded;
	
	         /* start timing */
	         SCIPclockStart(branchrule->branchclock, set);
	
	         /* call external method */
	         SCIP_CALL( branchrule->branchexeclp(set->scip, branchrule, allowaddcons, result) );
	
	         /* stop timing */
	         SCIPclockStop(branchrule->branchclock, set);
	
	         /* evaluate result */
	         if( *result != SCIP_CUTOFF
	            && *result != SCIP_CONSADDED
	            && *result != SCIP_REDUCEDDOM
	            && *result != SCIP_SEPARATED
	            && *result != SCIP_BRANCHED
	            && *result != SCIP_DIDNOTFIND
	            && *result != SCIP_DIDNOTRUN )
	         {
	            SCIPerrorMessage("branching rule <%s> returned invalid result code <%d> from LP solution branching\n",
	               branchrule->name, *result);
	            return SCIP_INVALIDRESULT;
	         }
	         if( *result == SCIP_CONSADDED && !allowaddcons )
	         {
	            SCIPerrorMessage("branching rule <%s> added a constraint in LP solution branching without permission\n",
	               branchrule->name);
	            return SCIP_INVALIDRESULT;
	         }
	
	         /* update statistics */
	         if( *result != SCIP_DIDNOTRUN )
	            branchrule->nlpcalls++;
	         if( *result == SCIP_CUTOFF )
	            branchrule->ncutoffs++;
	         if( *result != SCIP_BRANCHED )
	         {
	            assert(tree->nchildren == 0);
	
	            /* update domain reductions; therefore remove the domain
	             * reduction counts which were generated in probing mode */
	            branchrule->ndomredsfound += stat->nboundchgs + stat->nholechgs - oldndomchgs;
	            branchrule->ndomredsfound -= (stat->nprobboundchgs + stat->nprobholechgs - oldnprobdomchgs);
	
	            branchrule->ncutsfound += SCIPsepastoreGetNCuts(sepastore) - oldncuts; /*lint !e776*/
	            branchrule->nconssfound += stat->nactiveconssadded - oldnactiveconss; /*lint !e776*/
	         }
	         else
	            branchrule->nchildren += tree->nchildren;
	      }
	   }
	
	   return SCIP_OKAY;
	}
	
	/** executes branching rule for external branching candidates */
	SCIP_RETCODE SCIPbranchruleExecExternSol(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_STAT*            stat,               /**< problem statistics */
	   SCIP_TREE*            tree,               /**< branch and bound tree */
	   SCIP_SEPASTORE*       sepastore,          /**< separation storage */
	   SCIP_Real             cutoffbound,        /**< global upper cutoff bound */
	   SCIP_Bool             allowaddcons,       /**< should adding constraints be allowed to avoid a branching? */
	   SCIP_RESULT*          result              /**< pointer to store the result of the callback method */
	   )
	{
	   assert(branchrule != NULL);
	   assert(set != NULL);
	   assert(tree != NULL);
	   assert(tree->focusnode != NULL);
	   assert(tree->nchildren == 0);
	   assert(result != NULL);
	
	   *result = SCIP_DIDNOTRUN;
	   if( branchrule->branchexecext != NULL
	      && (branchrule->maxdepth == -1 || branchrule->maxdepth >= SCIPtreeGetCurrentDepth(tree)) )
	   {
	      SCIP_Real loclowerbound;
	      SCIP_Real glblowerbound;
	      SCIP_Bool runbranchrule;
	
	      loclowerbound = SCIPnodeGetLowerbound(tree->focusnode);
	      glblowerbound = SCIPtreeGetLowerbound(tree, set);
	      assert(!SCIPsetIsInfinity(set, loclowerbound));
	
	      /* we distinguish between finite and infinite global lower bounds to avoid comparisons between different values > SCIPinfinity() */
	      if( SCIPsetIsInfinity(set, -glblowerbound) )
	         runbranchrule = SCIPsetIsInfinity(set, -loclowerbound) || SCIPsetIsGE(set, branchrule->maxbounddist, 1.0);
	      else
	      {
	         assert(!SCIPsetIsInfinity(set, -loclowerbound));
	         runbranchrule = SCIPsetIsLE(set, loclowerbound - glblowerbound, branchrule->maxbounddist * (cutoffbound - glblowerbound));
	      }
	
	      if( runbranchrule )
	      {
	         SCIP_Longint oldndomchgs;
	         SCIP_Longint oldnprobdomchgs;
	         int oldncuts;
	         int oldnactiveconss;
	
	         SCIPsetDebugMsg(set, "executing external solution branching rule <%s>\n", branchrule->name);
	
	         oldndomchgs = stat->nboundchgs + stat->nholechgs;
	         oldnprobdomchgs = stat->nprobboundchgs + stat->nprobholechgs;
	         oldncuts = SCIPsepastoreGetNCuts(sepastore);
	         oldnactiveconss = stat->nactiveconss;
	
	         /* start timing */
	         SCIPclockStart(branchrule->branchclock, set);
	
	         /* call external method */
	         SCIP_CALL( branchrule->branchexecext(set->scip, branchrule, allowaddcons, result) );
	
	         /* stop timing */
	         SCIPclockStop(branchrule->branchclock, set);
	
	         /* evaluate result */
	         if( *result != SCIP_CUTOFF
	            && *result != SCIP_CONSADDED
	            && *result != SCIP_REDUCEDDOM
	            && *result != SCIP_SEPARATED
	            && *result != SCIP_BRANCHED
	            && *result != SCIP_DIDNOTFIND
	            && *result != SCIP_DIDNOTRUN )
	         {
	            SCIPerrorMessage("branching rule <%s> returned invalid result code <%d> from external solution branching\n",
	               branchrule->name, *result);
	            return SCIP_INVALIDRESULT;
	         }
	         if( *result == SCIP_CONSADDED && !allowaddcons )
	         {
	            SCIPerrorMessage("branching rule <%s> added a constraint in external solution branching without permission\n",
	               branchrule->name);
	            return SCIP_INVALIDRESULT;
	         }
	
	         /* update statistics */
	         if( *result != SCIP_DIDNOTRUN )
	            branchrule->nexterncalls++;
	         if( *result == SCIP_CUTOFF )
	            branchrule->ncutoffs++;
	         if( *result != SCIP_BRANCHED )
	         {
	            assert(tree->nchildren == 0);
	
	            /* update domain reductions; therefore remove the domain
	             * reduction counts which were generated in probing mode */
	            branchrule->ndomredsfound += stat->nboundchgs + stat->nholechgs - oldndomchgs;
	            branchrule->ndomredsfound -= (stat->nprobboundchgs + stat->nprobholechgs - oldnprobdomchgs);
	
	            branchrule->ncutsfound += SCIPsepastoreGetNCuts(sepastore) - oldncuts; /*lint !e776*/
	            branchrule->nconssfound += stat->nactiveconss - oldnactiveconss; /*lint !e776*/
	         }
	         else
	            branchrule->nchildren += tree->nchildren;
	      }
	   }
	   return SCIP_OKAY;
	}
	
	/** executes branching rule for not completely fixed pseudo solution */
	SCIP_RETCODE SCIPbranchruleExecPseudoSol(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_STAT*            stat,               /**< problem statistics */
	   SCIP_TREE*            tree,               /**< branch and bound tree */
	   SCIP_Real             cutoffbound,        /**< global upper cutoff bound */
	   SCIP_Bool             allowaddcons,       /**< should adding constraints be allowed to avoid a branching? */
	   SCIP_RESULT*          result              /**< pointer to store the result of the callback method */
	   )
	{
	   assert(branchrule != NULL);
	   assert(set != NULL);
	   assert(tree != NULL);
	   assert(tree->nchildren == 0);
	   assert(result != NULL);
	
	   *result = SCIP_DIDNOTRUN;
	   if( branchrule->branchexecps != NULL
	      && (branchrule->maxdepth == -1 || branchrule->maxdepth >= SCIPtreeGetCurrentDepth(tree)) )
	   {
	      SCIP_Real loclowerbound;
	      SCIP_Real glblowerbound;
	      SCIP_Bool runbranchrule;
	
	      loclowerbound = SCIPnodeGetLowerbound(tree->focusnode);
	      glblowerbound = SCIPtreeGetLowerbound(tree, set);
	
	      /* we distinguish between finite and infinite global lower bounds to avoid comparisons between different values > SCIPinfinity() */
	      if( SCIPsetIsInfinity(set, -glblowerbound) )
	         runbranchrule = SCIPsetIsInfinity(set, -loclowerbound) || SCIPsetIsGE(set, branchrule->maxbounddist, 1.0);
	      else
	      {
	         assert(!SCIPsetIsInfinity(set, -loclowerbound));
	         runbranchrule = SCIPsetIsLE(set, loclowerbound - glblowerbound, branchrule->maxbounddist * (cutoffbound - glblowerbound));
	      }
	
	      if( runbranchrule )
	      {
	         SCIP_Longint oldndomchgs;
	         SCIP_Longint oldnprobdomchgs;
	         SCIP_Longint oldnactiveconss;
	
	         SCIPsetDebugMsg(set, "executing pseudo branching rule <%s>\n", branchrule->name);
	
	         oldndomchgs = stat->nboundchgs + stat->nholechgs;
	         oldnprobdomchgs = stat->nprobboundchgs + stat->nprobholechgs;
	         oldnactiveconss = stat->nactiveconss;
	
	         /* start timing */
	         SCIPclockStart(branchrule->branchclock, set);
	
	         /* call external method */
	         SCIP_CALL( branchrule->branchexecps(set->scip, branchrule, allowaddcons, result) );
	
	         /* stop timing */
	         SCIPclockStop(branchrule->branchclock, set);
	
	         /* evaluate result */
	         if( *result != SCIP_CUTOFF
	            && *result != SCIP_CONSADDED
	            && *result != SCIP_REDUCEDDOM
	            && *result != SCIP_BRANCHED
	            && *result != SCIP_DIDNOTFIND
	            && *result != SCIP_DIDNOTRUN )
	         {
	            SCIPerrorMessage("branching rule <%s> returned invalid result code <%d> from pseudo solution branching\n",
	               branchrule->name, *result);
	            return SCIP_INVALIDRESULT;
	         }
	         if( *result == SCIP_CONSADDED && !allowaddcons )
	         {
	            SCIPerrorMessage("branching rule <%s> added a constraint in pseudo solution branching without permission\n",
	               branchrule->name);
	            return SCIP_INVALIDRESULT;
	         }
	
	         /* update statistics */
	         if( *result != SCIP_DIDNOTRUN )
	            branchrule->npseudocalls++;
	         if( *result == SCIP_CUTOFF )
	            branchrule->ncutoffs++;
	         if( *result != SCIP_BRANCHED )
	         {
	            assert(tree->nchildren == 0);
	
	            /* update domain reductions; therefore remove the domain
	             * reduction counts which were generated in probing mode */
	            branchrule->ndomredsfound += stat->nboundchgs + stat->nholechgs - oldndomchgs;
	            branchrule->ndomredsfound -= (stat->nprobboundchgs + stat->nprobholechgs - oldnprobdomchgs);
	
	            branchrule->nconssfound += stat->nactiveconss - oldnactiveconss;
	         }
	         else
	            branchrule->nchildren += tree->nchildren;
	      }
	   }
	
	   return SCIP_OKAY;
	}
	
	/** gets user data of branching rule */
	SCIP_BRANCHRULEDATA* SCIPbranchruleGetData(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	

	   return branchrule->branchruledata;
	}
	
	/** sets user data of branching rule; user has to free old data in advance! */
	void SCIPbranchruleSetData(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_BRANCHRULEDATA*  branchruledata      /**< new branching rule user data */
	   )
	{
	   assert(branchrule != NULL);
	
	   branchrule->branchruledata = branchruledata;
	}
	
	/** sets copy method of branching rule */
	void SCIPbranchruleSetCopy(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_DECL_BRANCHCOPY  ((*branchcopy))     /**< copy method of branching rule or NULL if you don't want to copy your plugin into sub-SCIPs */
	   )
	{
	   assert(branchrule != NULL);
	
	   branchrule->branchcopy = branchcopy;
	}
	
	/** sets destructor method of branching rule */
	void SCIPbranchruleSetFree(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_DECL_BRANCHFREE  ((*branchfree))     /**< destructor of branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   branchrule->branchfree = branchfree;
	}
	
	/** sets initialization method of branching rule */
	void SCIPbranchruleSetInit(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_DECL_BRANCHINIT  ((*branchinit))     /**< initialize branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   branchrule->branchinit = branchinit;
	}
	
	/** sets deinitialization method of branching rule */
	void SCIPbranchruleSetExit(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_DECL_BRANCHEXIT  ((*branchexit))     /**< deinitialize branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   branchrule->branchexit = branchexit;
	}
	
	/** sets solving process initialization method of branching rule */
	void SCIPbranchruleSetInitsol(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_DECL_BRANCHINITSOL((*branchinitsol)) /**< solving process initialization method of branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   branchrule->branchinitsol = branchinitsol;
	}
	
	/** sets solving process deinitialization method of branching rule */
	void SCIPbranchruleSetExitsol(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_DECL_BRANCHEXITSOL((*branchexitsol)) /**< solving process deinitialization method of branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   branchrule->branchexitsol = branchexitsol;
	}
	
	
	
	/** sets branching execution method for fractional LP solutions */
	void SCIPbranchruleSetExecLp(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_DECL_BRANCHEXECLP((*branchexeclp))   /**< branching execution method for fractional LP solutions */
	   )
	{
	   assert(branchrule != NULL);
	
	   branchrule->branchexeclp = branchexeclp;
	}
	
	/** sets branching execution method for external candidates  */
	void SCIPbranchruleSetExecExt(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_DECL_BRANCHEXECEXT((*branchexecext)) /**< branching execution method for external candidates */
	   )
	{
	   assert(branchrule != NULL);
	
	   branchrule->branchexecext = branchexecext;
	}
	
	/** sets branching execution method for not completely fixed pseudo solutions */
	void SCIPbranchruleSetExecPs(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_DECL_BRANCHEXECPS((*branchexecps))   /**< branching execution method for not completely fixed pseudo solutions */
	   )
	{
	   assert(branchrule != NULL);
	
	   branchrule->branchexecps = branchexecps;
	}
	
	/** gets name of branching rule */
	const char* SCIPbranchruleGetName(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   return branchrule->name;
	}
	
	/** gets description of branching rule */
	const char* SCIPbranchruleGetDesc(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   return branchrule->desc;
	}
	
	/** gets priority of branching rule */
	int SCIPbranchruleGetPriority(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   return branchrule->priority;
	}
	
	/** sets priority of branching rule */
	void SCIPbranchruleSetPriority(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   int                   priority            /**< new priority of the branching rule */
	   )
	{
	   assert(branchrule != NULL);
	   assert(set != NULL);
	
	   branchrule->priority = priority;
	   set->branchrulessorted = FALSE;
	}
	
	/** gets maximal depth level, up to which this branching rule should be used (-1 for no limit) */
	int SCIPbranchruleGetMaxdepth(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   return branchrule->maxdepth;
	}
	
	/** sets maximal depth level, up to which this branching rule should be used (-1 for no limit) */
	void SCIPbranchruleSetMaxdepth(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   int                   maxdepth            /**< new maxdepth of the branching rule */
	   )
	{
	   assert(branchrule != NULL);
	   assert(maxdepth >= -1);
	
	   branchrule->maxdepth = maxdepth;
	}
	
	/** gets maximal relative distance from current node's dual bound to primal bound for applying branching rule */
	SCIP_Real SCIPbranchruleGetMaxbounddist(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   return branchrule->maxbounddist;
	}
	
	/** sets maximal relative distance from current node's dual bound to primal bound for applying branching rule */
	void SCIPbranchruleSetMaxbounddist(
	   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
	   SCIP_Real             maxbounddist        /**< new maxbounddist of the branching rule */
	   )
	{
	   assert(branchrule != NULL);
	   assert(maxbounddist >= -1);
	
	   branchrule->maxbounddist = maxbounddist;
	}
	
	/** enables or disables all clocks of \p branchrule, depending on the value of the flag */
	void SCIPbranchruleEnableOrDisableClocks(
	   SCIP_BRANCHRULE*      branchrule,         /**< the branching rule for which all clocks should be enabled or disabled */
	   SCIP_Bool             enable              /**< should the clocks of the branching rule be enabled? */
	   )
	{
	   assert(branchrule != NULL);
	
	   SCIPclockEnableOrDisable(branchrule->setuptime, enable);
	   SCIPclockEnableOrDisable(branchrule->branchclock, enable);
	}
	
	/** gets time in seconds used in this branching rule for setting up for next stages */
	SCIP_Real SCIPbranchruleGetSetupTime(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   return SCIPclockGetTime(branchrule->setuptime);
	}
	
	/** gets time in seconds used in this branching rule */
	SCIP_Real SCIPbranchruleGetTime(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   return SCIPclockGetTime(branchrule->branchclock);
	}
	
	/** gets the total number of times, the branching rule was called on an LP solution */
	SCIP_Longint SCIPbranchruleGetNLPCalls(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   return branchrule->nlpcalls;
	}
	
	/** gets the total number of times, the branching rule was called on an external solution */
	SCIP_Longint SCIPbranchruleGetNExternCalls(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   return branchrule->nexterncalls;
	}
	
	/** gets the total number of times, the branching rule was called on a pseudo solution */
	SCIP_Longint SCIPbranchruleGetNPseudoCalls(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   return branchrule->npseudocalls;
	}
	
	/** gets the total number of times, the branching rule detected a cutoff */
	SCIP_Longint SCIPbranchruleGetNCutoffs(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   return branchrule->ncutoffs;
	}
	
	/** gets the total number of cuts, the branching rule separated */
	SCIP_Longint SCIPbranchruleGetNCutsFound(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   return branchrule->ncutsfound;
	}
	
	/** gets the total number of constraints, the branching rule added to the respective local nodes (not counting constraints
	 *  that were added to the child nodes as branching decisions)
	 */
	SCIP_Longint SCIPbranchruleGetNConssFound(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   return branchrule->nconssfound;
	}
	
	/** gets the total number of domain reductions, the branching rule found */
	SCIP_Longint SCIPbranchruleGetNDomredsFound(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   return branchrule->ndomredsfound;
	}
	
	/** gets the total number of children, the branching rule created */
	SCIP_Longint SCIPbranchruleGetNChildren(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   return branchrule->nchildren;
	}
	
	/** is branching rule initialized? */
	SCIP_Bool SCIPbranchruleIsInitialized(
	   SCIP_BRANCHRULE*      branchrule          /**< branching rule */
	   )
	{
	   assert(branchrule != NULL);
	
	   return branchrule->initialized;
	}
	
	
	
	
	/*
	 * branching methods
	 */
	
	/** calculates the branching score out of the gain predictions for a binary branching */
	SCIP_Real SCIPbranchGetScore(
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_VAR*             var,                /**< variable, of which the branching factor should be applied, or NULL */
	   SCIP_Real             downgain,           /**< prediction of objective gain for rounding downwards */
	   SCIP_Real             upgain              /**< prediction of objective gain for rounding upwards */
	   )
	{
	   SCIP_Real score;
	   SCIP_Real eps;
	
	   assert(set != NULL);
	
	   /* adjust scores near zero to always yield product score greater than 0 */
	   eps = SCIPsetSumepsilon(set);
	   if( set->branch_sumadjustscore )
	   {
	      /* adjust scores by adding eps to keep near zero score differences between variables */
	      downgain = downgain + eps;
	      upgain = upgain + eps;
	   }
	   else
	   {
	      /* disregard near zero score differences between variables and consider the branching factor for them */
	      downgain = MAX(downgain, eps);
	      upgain = MAX(upgain, eps);
	   }
	
	   switch( set->branch_scorefunc )
	   {
	   case 's':  /* linear sum score function */
	      /* weigh the two child nodes with branchscorefac and 1-branchscorefac */
	      if( downgain > upgain )
	         score = set->branch_scorefac * downgain + (1.0-set->branch_scorefac) * upgain;
	      else
	         score = set->branch_scorefac * upgain + (1.0-set->branch_scorefac) * downgain;
	      break;
	
	   case 'p':  /* product score function */
	      score = downgain * upgain;
	      break;
	   case 'q': /* quotient score function */
	      if( downgain > upgain )
	         score = upgain * upgain / downgain;
	      else
	         score = downgain * downgain / upgain;
	      break;
	   default:
	      SCIPerrorMessage("invalid branching score function <%c>\n", set->branch_scorefunc);
	      SCIPABORT();
	      score = 0.0;
	   }
	
	   /* apply the branch factor of the variable */
	   if( var != NULL )
	      score *= SCIPvarGetBranchFactor(var);
	
	   return score;
	}
	
	/** calculates the branching score out of the gain predictions for a branching with arbitrary many children */
	SCIP_Real SCIPbranchGetScoreMultiple(
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_VAR*             var,                /**< variable, of which the branching factor should be applied, or NULL */
	   int                   nchildren,          /**< number of children that the branching will create */
	   SCIP_Real*            gains               /**< prediction of objective gain for each child */
	   )
	{
	   SCIP_Real min1;
	   SCIP_Real min2;
	   int c;
	
	   assert(nchildren == 0 || gains != NULL);
	
	   /* search for the two minimal gains in the child list and use these to calculate the branching score */
	   min1 = SCIPsetInfinity(set);
	   min2 = SCIPsetInfinity(set);
	   for( c = 0; c < nchildren; ++c )
	   {
	      if( gains[c] < min1 )
	      {
	         min2 = min1;
	         min1 = gains[c];
	      }
	      else if( gains[c] < min2 )
	         min2 = gains[c];
	   }
	
	   return SCIPbranchGetScore(set, var, min1, min2);
	}
	
	/** computes a branching point for a (not necessarily discrete) variable
	 * a suggested branching point is first projected onto the box
	 * if no point is suggested, then the value in the current LP or pseudo solution is used
	 * if this value is at infinity, then 0.0 projected onto the bounds and then moved inside the interval is used 
	 * for a discrete variable, it is ensured that the returned value is fractional
	 * for a continuous variable, the parameter branching/clamp defines how far a branching point need to be from the bounds of a variable
	 * the latter is only applied if no point has been suggested, or the suggested point is not inside the variable's interval
	 */
	SCIP_Real SCIPbranchGetBranchingPoint(
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_TREE*            tree,               /**< branch and bound tree */
	   SCIP_VAR*             var,                /**< variable, of which the branching point should be computed */
	   SCIP_Real             suggestion          /**< suggestion for branching point, or SCIP_INVALID if no suggestion */
	   )
	{
	   SCIP_Real branchpoint;
	   SCIP_Real lb;
	   SCIP_Real ub;
	
	   assert(set != NULL);
	   assert(var != NULL);
	
	   lb = SCIPvarGetLbLocal(var);
	   ub = SCIPvarGetUbLocal(var);
	
	   /* for a fixed variable, we cannot branch further */
	   assert(!SCIPsetIsEQ(set, lb, ub));
	
	   if( !SCIPsetIsInfinity(set, REALABS(suggestion)) )
	   {
	      /* use user suggested branching point */
	
	      /* first, project it onto the current domain */
	      branchpoint = MAX(lb, MIN(suggestion, ub));
	
	      if( SCIPvarGetType(var) != SCIP_VARTYPE_CONTINUOUS )
	      {
	         /* if it is a discrete variable, then round it down and up and accept this choice */
	         if( SCIPsetIsEQ(set, branchpoint, ub) )
	         {
	            /* in the right branch, variable is fixed to its current upper bound */
	            return SCIPsetFloor(set, branchpoint) - 0.5;
	         }
	         else
	         {
	            /* in the  left branch, variable is fixed to its current lower bound */
	            return SCIPsetFloor(set, branchpoint) + 0.5;
	         }
	      }
	      else if( (SCIPsetIsInfinity(set, -lb) || SCIPsetIsRelGT(set, branchpoint, lb)) &&
	                (SCIPsetIsInfinity(set,  ub) || SCIPsetIsRelLT(set, branchpoint, ub)) )
	      {
	         /* if it is continuous and inside the box, then accept it */ 
	         return branchpoint;
	      }
	      /* if it is continuous and suggestion is on of the bounds, continue below */
	   }
	   else
	   {
	      /* if no point is suggested, try the LP or pseudo solution */
	      branchpoint = SCIPvarGetSol(var, SCIPtreeHasCurrentNodeLP(tree));
	
	      if( REALABS(branchpoint) > 1e+12 )
	      {
	         /* if the value in the LP or pseudosolution is large (here 1e+12), use 0.0 (will be projected onto bounds below) */
	         branchpoint = 0.0;
	      }
	      else if( SCIPtreeHasCurrentNodeLP(tree) && set->branch_midpull > 0.0 && !SCIPsetIsInfinity(set, -lb) && !SCIPsetIsInfinity(set, ub) )
	      {
	         /* if the value is from the LP and midpull is activated, then push towards middle of domain */
	         SCIP_Real midpull = set->branch_midpull;
	         SCIP_Real glb;
	         SCIP_Real gub;
	         SCIP_Real reldomainwidth;
	
	         /* shrink midpull if width of local domain, relative to global domain, is small
	          * that is, if there has been already one or several branchings on this variable, then give more emphasis on LP solution
	          *
	          * do this only if the relative domain width is below the minreldomainwidth value
	          */
	         glb = SCIPvarGetLbGlobal(var);
	         gub = SCIPvarGetUbGlobal(var);
	         assert(glb < gub);
	
	         if( !SCIPsetIsInfinity(set, -glb) && !SCIPsetIsInfinity(set, gub) )
	            reldomainwidth = (ub - lb) / (gub - glb);
	         else
	            reldomainwidth = SCIPsetEpsilon(set);
	
	         if( reldomainwidth < set->branch_midpullreldomtrig )
	            midpull *= reldomainwidth;
	
	         branchpoint = midpull * (lb+ub) / 2.0 + (1.0 - midpull) * branchpoint;
	      }
	
	      /* make sure branchpoint is on interval, below we make sure that it is within bounds for continuous vars */
	      branchpoint = MAX(lb, MIN(branchpoint, ub));
	   }
	
	   /* if value is at +/- infty, then choose some value a bit off from bounds or 0.0 */
	   if( SCIPsetIsInfinity(set, branchpoint) )
	   {
	      /* if value is at +infty, then the upper bound should be at infinity */
	      assert(SCIPsetIsInfinity(set, ub));
	
	      /* choose 0.0 or something above lower bound if lower bound > 0 */
	      if( SCIPsetIsPositive(set, lb) )
	         branchpoint = lb + 1000.0;
	      else
	         branchpoint = 0.0;
	   }
	   else if( SCIPsetIsInfinity(set, -branchpoint) )
	   { 
	      /* if value is at -infty, then the lower bound should be at -infinity */
	      assert(SCIPsetIsInfinity(set, -lb));
	
	      /* choose 0.0 or something below upper bound if upper bound < 0 */
	      if( SCIPsetIsNegative(set, ub) )
	         branchpoint = ub - 1000.0;
	      else
	         branchpoint = 0.0;
	   }
	
	   assert(SCIPsetIsInfinity(set,  ub) || SCIPsetIsLE(set, branchpoint, ub));
	   assert(SCIPsetIsInfinity(set, -lb) || SCIPsetIsGE(set, branchpoint, lb));
	
	   if( SCIPvarGetType(var) >= SCIP_VARTYPE_IMPLINT )
	   {
	      if( !SCIPsetIsInfinity(set, -lb) || !SCIPsetIsInfinity(set, ub) )
	      {
	         /* if one bound is missing, we are temporarily guessing the other one, so we can apply the clamp below */
	         if( SCIPsetIsInfinity(set, ub) )
	         {
	            ub = lb + MIN(MAX(0.5 * REALABS(lb), 1000), 0.9 * (SCIPsetInfinity(set) - lb)); /*lint !e666*/
	         }
	         else if( SCIPsetIsInfinity(set, -lb) )
	         {
	            lb = ub - MIN(MAX(0.5 * REALABS(ub), 1000), 0.9 * (SCIPsetInfinity(set) + ub)); /*lint !e666*/
	         }
	
	         /* if branching point is too close to the bounds, move more into the middle of the interval */
	         if( SCIPrelDiff(ub, lb) <= 2.02 * SCIPsetEpsilon(set) )
	         {
	            /* for very tiny intervals we set it exactly into the middle */
	            branchpoint = (lb+ub)/2.0;
	         }
	         else
	         {
	            /* otherwise we project it away from the bounds */
	            SCIP_Real minbrpoint;
	            SCIP_Real maxbrpoint;
	            SCIP_Real scale;
	            SCIP_Real lbabs;
	            SCIP_Real ubabs;
	
	            lbabs = REALABS(lb);
	            ubabs = REALABS(ub);
	
	            scale = MAX3(lbabs, ubabs, 1.0);
	
	            /* the minimal branching point should be
	             * - set->clamp away from the lower bound - relative to the local domain size
	             * - SCIPsetEpsilon(set)*scale above the lower bound - in absolute value
	             */
	            minbrpoint = (1.0 - set->branch_clamp) * lb + set->branch_clamp * ub;
	            minbrpoint = MAX(lb + 1.01*SCIPsetEpsilon(set)*scale, minbrpoint);  /*lint !e666*/
	
	            /* the maximal branching point should be
	             * - set->clamp away from the upper bound - relative to the local domain size
	             * - SCIPsetEpsilon(set)*scale below the upper bound - in absolute value
	             */
	            maxbrpoint = set->branch_clamp * lb + (1.0 - set->branch_clamp) * ub;
	            maxbrpoint = MIN(ub - 1.01*SCIPsetEpsilon(set)*scale, maxbrpoint);  /*lint !e666*/
	
	            /* project branchpoint into [minbrpoint, maxbrpoint] */
	            branchpoint = MAX(minbrpoint, MIN(branchpoint, maxbrpoint));
	
	            /* if selected branching point is close to 0.0 and bounds are away from 0.0, it often makes sense to branch exactly on 0.0 */
	            if( SCIPsetIsFeasZero(set, branchpoint) && SCIPsetIsFeasNegative(set, lb) && SCIPsetIsFeasPositive(set, ub) )
	               branchpoint = 0.0;
	
	            assert(SCIPsetIsRelLT(set, SCIPvarGetLbLocal(var), branchpoint));
	            assert(SCIPsetIsRelLT(set, branchpoint, SCIPvarGetUbLocal(var)));
	         }
	      }
	
	      /* ensure fractional branching point for implicit integer variables */
	      if( SCIPvarGetType(var) == SCIP_VARTYPE_IMPLINT && SCIPsetIsIntegral(set, branchpoint) )
	      {
	         /* if branchpoint is integral but not on bounds, then it should be one of the value {lb+1, ..., ub-1} */
	         assert(SCIPsetIsGE(set, SCIPsetRound(set, branchpoint), lb + 1.0));
	         assert(SCIPsetIsLE(set, SCIPsetRound(set, branchpoint), ub - 1.0));
	         /* if branchpoint is integral, create one branch with x <= x'-1 and one with x >= x'
	          * @todo could in the same way be x <= x' and x >= x'+1; is there some easy way to know which is better?
	          */
	         return branchpoint - 0.5;
	      }
	
	      return branchpoint;
	   }
	   else
	   {
	      /* discrete variables */
	      if( branchpoint <= lb + 0.5 )
	      {
	         /* if branchpoint is on lower bound, create one branch with x = lb and one with x >= lb+1 */
	         return lb + 0.5;
	      }
	      else if( branchpoint >= ub - 0.5 )
	      {
	         /* if branchpoint is on upper bound, create one branch with x = ub and one with x <= ub-1 */
	         return ub - 0.5;
	      }
	      else if( SCIPsetIsIntegral(set, branchpoint) )
	      {
	         /* if branchpoint is integral but not on bounds, then it should be one of the value {lb+1, ..., ub-1} */
	         assert(SCIPsetIsGE(set, SCIPsetRound(set, branchpoint), lb + 1.0));
	         assert(SCIPsetIsLE(set, SCIPsetRound(set, branchpoint), ub - 1.0));
	         /* if branchpoint is integral, create one branch with x <= x'-1 and one with x >= x'
	          * @todo could in the same way be x <= x' and x >= x'+1; is there some easy way to know which is better? */
	         return branchpoint - 0.5;
	      }
	      else
	      {
	         /* branchpoint is somewhere between bounds and fractional, so just round down and up */
	         return branchpoint;
	      }
	   }
	}
	
	/** calls branching rules to branch on an LP solution; if no fractional variables exist, the result is SCIP_DIDNOTRUN;
	 *  if the branch priority of an unfixed variable is larger than the maximal branch priority of the fractional
	 *  variables, pseudo solution branching is applied on the unfixed variables with maximal branch priority
	 */
	SCIP_RETCODE SCIPbranchExecLP(
	   BMS_BLKMEM*           blkmem,             /**< block memory for parameter settings */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_STAT*            stat,               /**< problem statistics */
	   SCIP_PROB*            transprob,          /**< transformed problem after presolve */
	   SCIP_PROB*            origprob,           /**< original problem */
	   SCIP_TREE*            tree,               /**< branch and bound tree */
	   SCIP_REOPT*           reopt,              /**< reoptimization data structure */
	   SCIP_LP*              lp,                 /**< current LP data */
	   SCIP_SEPASTORE*       sepastore,          /**< separation storage */
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
	   SCIP_Real             cutoffbound,        /**< global upper cutoff bound */
	   SCIP_Bool             allowaddcons,       /**< should adding constraints be allowed to avoid a branching? */
	   SCIP_RESULT*          result              /**< pointer to store the result of the branching (s. branch.h) */
	   )
	{
	   int i;
	   int nalllpcands;  /* sum of binary, integer, and implicit branching candidates */
	
	   assert(branchcand != NULL);
	   assert(result != NULL);
	
	   *result = SCIP_DIDNOTRUN;
	
	   /* calculate branching candidates */
	   SCIP_CALL( branchcandCalcLPCands(branchcand, set, stat, lp) );
	   assert(0 <= branchcand->npriolpcands && branchcand->npriolpcands <= branchcand->nlpcands);
	   assert((branchcand->npriolpcands == 0) == (branchcand->nlpcands == 0));
	
	   SCIPsetDebugMsg(set, "branching on LP solution with %d (+%d) fractional (+implicit fractional) variables (%d of maximal priority)\n",
	      branchcand->nlpcands, branchcand->nimpllpfracs, branchcand->npriolpcands);
	
	   nalllpcands = branchcand->nlpcands + branchcand->nimpllpfracs;
	   /* do nothing, if no fractional variables exist */
	   if( nalllpcands == 0 )
	      return SCIP_OKAY;
	
	   /* if there is a non-fixed variable with higher priority than the maximal priority of the fractional candidates,
	    * use pseudo solution branching instead
	    */
	   if( branchcand->pseudomaxpriority > branchcand->lpmaxpriority )
	   {
	      SCIP_CALL( SCIPbranchExecPseudo(blkmem, set, stat, transprob, origprob, tree, reopt, lp, branchcand, eventqueue, cutoffbound,
	            allowaddcons, result) );
	      assert(*result != SCIP_DIDNOTRUN && *result != SCIP_DIDNOTFIND);
	      return SCIP_OKAY;
	   }
	
	   /* sort the branching rules by priority */
	   SCIPsetSortBranchrules(set);
	
	   /* try all branching rules until one succeeded to branch */
	   for( i = 0; i < set->nbranchrules && (*result == SCIP_DIDNOTRUN || *result == SCIP_DIDNOTFIND); ++i )
	   {
	      SCIP_CALL( SCIPbranchruleExecLPSol(set->branchrules[i], set, stat, tree, sepastore, cutoffbound, allowaddcons, result) );
	   }
	
	   if( *result == SCIP_DIDNOTRUN || *result == SCIP_DIDNOTFIND )
	   {
	      SCIP_VAR* var;
	      SCIP_Real factor;
	      SCIP_Real bestfactor;
	      int priority;
	      int bestpriority;
	      int bestcand;
	
	      /* no branching method succeeded in choosing a branching: just branch on the first fractional variable with maximal
	       * priority, and out of these on the one with maximal branch factor
	       */
	      bestcand = -1;
	      bestpriority = INT_MIN;
	      bestfactor = SCIP_REAL_MIN;
	      for( i = 0; i < nalllpcands; ++i )
	      {
	         priority = SCIPvarGetBranchPriority(branchcand->lpcands[i]);
	         factor = SCIPvarGetBranchFactor(branchcand->lpcands[i]);
	         if( priority > bestpriority || (priority == bestpriority && factor > bestfactor) )
	         {
	            bestcand = i;
	            bestpriority = priority;
	            bestfactor = factor;
	         }
	      }
	      assert(0 <= bestcand && bestcand < nalllpcands);
	
	      var = branchcand->lpcands[bestcand];
	      assert(SCIPvarGetType(var) != SCIP_VARTYPE_CONTINUOUS);
	      assert(branchcand->nlpcands == 0 || SCIPvarGetType(var) != SCIP_VARTYPE_IMPLINT);
	
	      assert(!SCIPsetIsEQ(set, SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var)));
	
	      SCIP_CALL( SCIPtreeBranchVar(tree, reopt, blkmem, set, stat, transprob, origprob, lp, branchcand, eventqueue, var, SCIP_INVALID,
	            NULL, NULL, NULL) );
	
	      *result = SCIP_BRANCHED;
	   }
	
	   return SCIP_OKAY;
	}
	
	/** calls branching rules to branch on an external solution; if no external branching candidates exist, the result is SCIP_DIDNOTRUN */
	SCIP_RETCODE SCIPbranchExecExtern(
	   BMS_BLKMEM*           blkmem,             /**< block memory for parameter settings */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_STAT*            stat,               /**< problem statistics */
	   SCIP_PROB*            transprob,          /**< transformed problem after presolve */
	   SCIP_PROB*            origprob,           /**< original problem */
	   SCIP_TREE*            tree,               /**< branch and bound tree */
	   SCIP_REOPT*           reopt,              /**< reoptimization data structure */
	   SCIP_LP*              lp,                 /**< current LP data */
	   SCIP_SEPASTORE*       sepastore,          /**< separation storage */
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
	   SCIP_Real             cutoffbound,        /**< global upper cutoff bound */
	   SCIP_Bool             allowaddcons,       /**< should adding constraints be allowed to avoid a branching? */
	   SCIP_RESULT*          result              /**< pointer to store the result of the branching (s. branch.h) */
	   )
	{
	   int i;
	
	   assert(branchcand != NULL);
	   assert(result != NULL);
	   assert(0 <= branchcand->nprioexterncands && branchcand->nprioexterncands <= branchcand->nexterncands);
	   assert((branchcand->nprioexterncands == 0) == (branchcand->nexterncands == 0));
	
	   *result = SCIP_DIDNOTRUN;
	
	   SCIPsetDebugMsg(set, "branching on external solution with %d branching candidates (%d of maximal priority)\n",
	      branchcand->nexterncands, branchcand->nprioexterncands);
	
	   /* do nothing, if no external candidates exist */
	   if( branchcand->nexterncands == 0 )
	      return SCIP_OKAY;
	
	   /* if there is a non-fixed variable with higher priority than the maximal priority of the external candidates,
	    * use pseudo solution branching instead
	    */
	   if( branchcand->pseudomaxpriority > branchcand->externmaxpriority )
	   {
	      /* @todo: adjust this, that also LP branching might be called, if lpmaxpriority != externmaxpriority.
	       * Therefor, it has to be clear which of both has the higher priority
	       */
	      SCIP_CALL( SCIPbranchExecPseudo(blkmem, set, stat, transprob, origprob, tree, reopt, lp, branchcand, eventqueue, cutoffbound,
	            allowaddcons, result) );
	      assert(*result != SCIP_DIDNOTRUN && *result != SCIP_DIDNOTFIND);
	      return SCIP_OKAY;
	   }
	
	   /* sort the branching rules by priority */
	   SCIPsetSortBranchrules(set);
	
	   /* try all branching rules until one succeeded to branch */
	   for( i = 0; i < set->nbranchrules && (*result == SCIP_DIDNOTRUN || *result == SCIP_DIDNOTFIND); ++i )
	   {
	      SCIP_CALL( SCIPbranchruleExecExternSol(set->branchrules[i], set, stat, tree, sepastore, cutoffbound, allowaddcons, result) );
	   }
	
	   if( *result == SCIP_DIDNOTRUN || *result == SCIP_DIDNOTFIND )
	   {
	      SCIP_VAR* var;
	      SCIP_Real val;
	      SCIP_Real bestfactor;
	      SCIP_Real bestdomain;
	      int bestpriority;
	      int bestcand;
	
	      /* if all branching rules did nothing, then they should also not have cleared all branching candidates */
	      assert(branchcand->nexterncands > 0);
	
	      /* no branching method succeeded in choosing a branching: just branch on the first branching candidates with maximal
	       * priority, and out of these on the one with maximal branch factor, and out of these on the one with largest domain
	       */
	      bestcand = -1;
	      bestpriority = INT_MIN;
	      bestfactor = SCIP_REAL_MIN;
	      bestdomain = 0.0;
	      for( i = 0; i < branchcand->nexterncands; ++i )
	      {
	         SCIP_VAR* cand;
	         SCIP_Real domain;
	         SCIP_Real factor;
	         int priority;
	
	         cand = branchcand->externcands[i];
	         priority = SCIPvarGetBranchPriority(cand);
	         factor = SCIPvarGetBranchFactor(cand);
	
	         /* the domain size is infinite, iff one of the bounds is infinite */
	         if( SCIPsetIsInfinity(set, -SCIPvarGetLbLocal(cand)) || SCIPsetIsInfinity(set, SCIPvarGetUbLocal(cand)) )
	            domain = SCIPsetInfinity(set);
	         else
	            domain = SCIPvarGetUbLocal(cand) - SCIPvarGetLbLocal(cand);
	
	         /* choose variable with higher priority, higher factor, larger domain (in that order) */
	         if( priority > bestpriority || (priority == bestpriority && factor > bestfactor) || (priority == bestpriority && factor == bestfactor && domain > bestdomain) ) /*lint !e777*/
	         {
	            bestcand = i;
	            bestpriority = priority;
	            bestfactor = factor;
	            bestdomain = domain;
	         }
	      }
	      assert(0 <= bestcand && bestcand < branchcand->nexterncands);
	
	      var = branchcand->externcands[bestcand];
	      val = SCIPbranchGetBranchingPoint(set, tree, var, branchcand->externcandssol[bestcand]);
	      assert(!SCIPsetIsEQ(set, SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var)));
	      assert(SCIPrelDiff(SCIPvarGetUbLocal(var), SCIPvarGetLbLocal(var)) <= 2.02 * SCIPsetEpsilon(set)
	         || SCIPsetIsLT(set, SCIPvarGetLbLocal(var), val));
	      assert(SCIPrelDiff(SCIPvarGetUbLocal(var), SCIPvarGetLbLocal(var)) <= 2.02 * SCIPsetEpsilon(set)
	         || SCIPsetIsLT(set, val, SCIPvarGetUbLocal(var)));
	
	      SCIPsetDebugMsg(set, "no branching method succeeded; fallback selected to branch on variable <%s> with bounds [%g, %g] on value %g\n",
	         SCIPvarGetName(var), SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var), val);
	
	      SCIP_CALL( SCIPtreeBranchVar(tree, reopt, blkmem, set, stat, transprob, origprob, lp, branchcand, eventqueue, var, val,
	            NULL, NULL, NULL) );
	
	      if( tree->nchildren >= 1 )
	         *result = SCIP_BRANCHED;
	      /* if the bounds are too close, it may happen that we cannot branch but rather fix the variable */
	      else
	      {
	         assert(SCIPsetIsEQ(set, SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var)));
	         *result = SCIP_REDUCEDDOM;
	      }
	   }
	
	   return SCIP_OKAY;
	}
	
	/** calls branching rules to branch on a pseudo solution; if no unfixed variables exist, the result is SCIP_DIDNOTRUN */
	SCIP_RETCODE SCIPbranchExecPseudo(
	   BMS_BLKMEM*           blkmem,             /**< block memory for parameter settings */
	   SCIP_SET*             set,                /**< global SCIP settings */
	   SCIP_STAT*            stat,               /**< problem statistics */
	   SCIP_PROB*            transprob,          /**< transformed problem after presolve */
	   SCIP_PROB*            origprob,           /**< original problem */
	   SCIP_TREE*            tree,               /**< branch and bound tree */
	   SCIP_REOPT*           reopt,              /**< reoptimization data structure */
	   SCIP_LP*              lp,                 /**< current LP data */
	   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
	   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
	   SCIP_Real             cutoffbound,        /**< global upper cutoff bound */
	   SCIP_Bool             allowaddcons,       /**< should adding constraints be allowed to avoid a branching? */
	   SCIP_RESULT*          result              /**< pointer to store the result of the branching (s. branch.h) */
	   )
	{
	   int i;
	
	   assert(branchcand != NULL);
	   assert(result != NULL);
	
	   SCIPsetDebugMsg(set, "branching on pseudo solution with %d unfixed variables\n", branchcand->npseudocands);
	
	   *result = SCIP_DIDNOTRUN;
	
	   /* do nothing, if no unfixed variables exist */
	   if( branchcand->npseudocands == 0 )
	      return SCIP_OKAY;
	
	   /* sort the branching rules by priority */
	   SCIPsetSortBranchrules(set);
	
	   /* try all branching rules until one succeeded to branch */
	   for( i = 0; i < set->nbranchrules && (*result == SCIP_DIDNOTRUN || *result == SCIP_DIDNOTFIND); ++i )
	   {
	      SCIP_CALL( SCIPbranchruleExecPseudoSol(set->branchrules[i], set, stat, tree, cutoffbound, allowaddcons, result) );
	   }
	
	   if( *result == SCIP_DIDNOTRUN || *result == SCIP_DIDNOTFIND )
	   {
	      SCIP_VAR* var;
	      SCIP_Real factor;
	      SCIP_Real bestfactor;
	      int priority;
	      int bestpriority;
	      int bestcand;
	
	      /* no branching method succeeded in choosing a branching: just branch on the first unfixed variable with maximal
	       * priority, and out of these on the one with maximal branch factor
	       */
	      bestcand = -1;
	      bestpriority = INT_MIN;
	      bestfactor = SCIP_REAL_MIN;
	      for( i = 0; i < branchcand->npseudocands; ++i )
	      {
	         priority = SCIPvarGetBranchPriority(branchcand->pseudocands[i]);
	         factor = SCIPvarGetBranchFactor(branchcand->pseudocands[i]);
	         if( priority > bestpriority || (priority == bestpriority && factor > bestfactor) )
	         {
	            bestcand = i;
	            bestpriority = priority;
	            bestfactor = factor;
	         }
	      }
	      assert(0 <= bestcand && bestcand < branchcand->npseudocands);
	
	      var = branchcand->pseudocands[bestcand];
	      assert(SCIPvarGetType(var) != SCIP_VARTYPE_CONTINUOUS);
	      assert(!SCIPsetIsEQ(set, SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var)));
	
	      SCIP_CALL( SCIPtreeBranchVar(tree, reopt, blkmem, set, stat, transprob, origprob, lp, branchcand, eventqueue, var, SCIP_INVALID,
	            NULL, NULL, NULL) );
	
	      *result = SCIP_BRANCHED;
	   }
	
	   return SCIP_OKAY;
	}