# Math 567 Spring 2025
# AMPL session for the Google problem


ampl: option solver gurobi;
ampl: option gurobi_options 'tech:timing=1';
ampl: reset; model Google.mod.txt; solve;
Gurobi 10.0.0: tech:timing=1
NL model read time = 0.000216s
NL model conversion time = 0.000601s
Setup time = 0.002711s
Solution time = 0.021432s
Output time = 0.001389s
Gurobi 10.0.0: optimal solution; objective 0
225 simplex iterations
1 branching nodes
ampl: 
ampl: for {i in 1..9, j in 0..9}{ if x[i,j]==1 then printf " %d %d\n",i,j; };
 1 7 # W
 2 5 # D
 3 8 # O
 4 9 # T
 5 1 # G
 6 0 # L
 7 6 # E
 8 4 # C
 9 3 # M

ampl:

## Model using set of letters 

ampl: reset; model setGoogle.mod.txt; solve;
Gurobi 10.0.0: tech:timing=1
NL model read time = 0.000283s
NL model conversion time = 0.000689s
Setup time = 0.003573s
Solution time = 0.024540s
Output time = 0.001121s
Gurobi 10.0.0: optimal solution; objective 0
225 simplex iterations
1 branching nodes
ampl: 
ampl: for {i in L, j in 0..9}{ if x[i,j]==1 then printf " %s %d\n",i,j; };
 W 7
 D 5
 O 8
 T 9
 G 1
 L 0
 E 6
 C 4
 M 3
ampl: