# HG changeset patch
# User marci
# Date 1108653253 0
# Node ID 4b0468de3a31df3bb344ce57f53348f67888ceb6
# Parent  1765ff9fefa1d1f4b15db090943f3a5a222caf57
if you have a nuclear power plant and wanna compute small magic squares, then let's do it

diff -r 1765ff9fefa1 -r 4b0468de3a31 src/work/marci/lp/lp_solver_base.h
--- a/src/work/marci/lp/lp_solver_base.h	Wed Feb 16 21:40:16 2005 +0000
+++ b/src/work/marci/lp/lp_solver_base.h	Thu Feb 17 15:14:13 2005 +0000
@@ -619,6 +619,8 @@
     virtual void _setColCont(int i) = 0;
     /// \e
     virtual void _setColInt(int i) = 0;
+    /// \e
+    virtual _Value _getMIPPrimal(int i) = 0;
   public:
     /// \e
     void setColCont(Col col) {
@@ -628,6 +630,10 @@
     void setColInt(Col col) {
       _setColInt(col_iter_map[col]);
     }
+    /// \e
+    _Value getMIPPrimal(Col col) {
+      return _getMIPPrimal(col_iter_map[col]);
+    }
     //@}
   };
   
@@ -1096,9 +1102,11 @@
     void setMIP() { lpx_set_class(lp, LPX_MIP); }
   protected:
     /// \e
-    void _setColCont(int i) {lpx_set_col_kind(lp, i, LPX_CV); }
+    void _setColCont(int i) { lpx_set_col_kind(lp, i, LPX_CV); }
     /// \e
-    void _setColInt(int i) {lpx_set_col_kind(lp, i, LPX_IV); }
+    void _setColInt(int i) { lpx_set_col_kind(lp, i, LPX_IV); }
+    /// \e
+    double _getMIPPrimal(int i) { return lpx_mip_col_val(lp, i); }
   };
   
   /// @}
diff -r 1765ff9fefa1 -r 4b0468de3a31 src/work/marci/lp/magic_square.cc
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/work/marci/lp/magic_square.cc	Thu Feb 17 15:14:13 2005 +0000
@@ -0,0 +1,88 @@
+// -*- c++ -*-
+#include <iostream>
+#include <fstream>
+
+#include <lemon/time_measure.h>
+#include <lp_solver_base.h>
+
+using std::cout;
+using std::endl;
+using namespace lemon;
+
+/*
+  for n=3,4 , the program is very fast
+  for n=5, with glpk, the run takes hours
+ */
+
+int main(int, char **) {
+  const int n=4;
+  const double row_sum=(1.0+n*n)*n/2;
+  Timer ts;
+  ts.reset();
+  typedef LPGLPK LPSolver;
+  typedef LPSolver::Col Col;
+  LPSolver lp;
+  typedef std::map<std::pair<int, int>, Col> Coords;
+  Coords x;
+  // we create a new variable for each entry 
+  // of the magic square
+  for (int i=1; i<=n; ++i) {
+    for (int j=1; j<=n; ++j) { 
+      Col col=lp.addCol();
+      x[std::make_pair(i,j)]=col;
+      lp.setColLowerBound(col, 1.0);
+      lp.setColUpperBound(col, double(n*n));
+    }
+  }
+  LPSolver::Expression expr3, expr4;
+  for (int i=1; i<=n; ++i) {
+    LPSolver::Expression expr1, expr2;
+    for (int j=1; j<=n; ++j) {
+      expr1+=x[std::make_pair(i, j)];
+      expr2+=x[std::make_pair(j, i)];
+    }
+    // sum of rows and columns
+    lp.addRow(expr1==row_sum);
+    lp.addRow(expr2==row_sum);
+    expr3+=x[std::make_pair(i, i)];
+    expr4+=x[std::make_pair(i, (n+1)-i)];
+  }
+  // sum of the diagonal entries
+  lp.addRow(expr3==row_sum);
+  lp.addRow(expr4==row_sum);
+  lp.solveSimplex();
+  cout << "elapsed time: " << ts << endl;
+  for (int i=1; i<=n; ++i) {
+    for (int j=1; j<=n; ++j) { 
+      cout << "x("<<i<<","<<j<<")="<<lp.getPrimal(x[std::make_pair(i,j)]) 
+	   << endl;
+    }
+  }
+  // we make new binary variables for each pair of 
+  // entries of the square to achieve that 
+  // the values of different entries are different
+  lp.setMIP();
+  for (Coords::const_iterator it=x.begin(); it!=x.end(); ++it) {
+    Coords::const_iterator jt=it; ++jt;
+    for(; jt!=x.end(); ++jt) {
+      Col col1=(*it).second;
+      Col col2=(*jt).second;
+      Col col=lp.addCol();
+      lp.setColLowerBound(col, 0.0);
+      lp.setColUpperBound(col, 1.0);
+      lp.addRow(double(-n*n+1.0)<=1.0*col2-1.0*col1-double(n*n)*col<=-1.0);
+      lp.setColInt(col);
+    }
+  }
+  cout << "elapsed time: " << ts << endl;
+  lp.solveSimplex();
+  // let's solve the integer problem
+  lp.solveBandB();
+  cout << "elapsed time: " << ts << endl;
+  for (int i=1; i<=n; ++i) {
+    for (int j=1; j<=n; ++j) { 
+      cout << "x("<<i<<","<<j<<")="<<lp.getMIPPrimal(x[std::make_pair(i,j)]) 
+	   << endl;
+    }
+  }
+}
diff -r 1765ff9fefa1 -r 4b0468de3a31 src/work/marci/lp/makefile
--- a/src/work/marci/lp/makefile	Wed Feb 16 21:40:16 2005 +0000
+++ b/src/work/marci/lp/makefile	Thu Feb 17 15:14:13 2005 +0000
@@ -5,7 +5,7 @@
 CXXFLAGS = -g -O2 -W -Wall $(INCLUDEDIRS) -ansi -pedantic
 LDFLAGS  =  -lglpk#-lcplex -lm -lpthread -lilocplex -L/usr/local/cplex/cplex75/lib/i86_linux2_glibc2.2_gcc3.0/static_mt# -L$(GLPKROOT)/lib
 
-BINARIES = max_flow_expression expression_test max_flow_by_lp# sample sample2 sample11 sample15
+BINARIES = magic_square max_flow_expression expression_test max_flow_by_lp# sample sample2 sample11 sample15
 
 #include ../makefile