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### matrix2.py

#!/usr/bin/env python3.7

# Copyright 2020, Gurobi Optimization, LLC

# This example uses the Python matrix API to formulate the n-queens
# problem; it maximizes the number queens placed on an n x n
# chessboard without threatening each other.
#
# This example demonstrates NumPy slicing.

import numpy as np
import scipy.sparse as sp
import gurobipy as gp
from gurobipy import GRB

# Size of the n x n chess board
n = 8

try:
# Create a new model
m = gp.Model("matrix2")

# Create a 2-D array of binary variables
# x[i,j]=1 means that a queen is placed at square (i,j)
x = m.addMVar((n, n), vtype=GRB.BINARY, name="x")

# Set objective - maximize number of queens
m.setObjective(x.sum(), GRB.MAXIMIZE)

# Add row and column constraints
for i in range(n):

# At most one queen per row
m.addConstr(x[i, :].sum() <= 1, name="row"+str(i))

# At most one queen per column
m.addConstr(x[:, i].sum() <= 1, name="col"+str(i))

# Add diagonal constraints
for i in range(1, 2*n):

# At most one queen per diagonal
diagn = (range(max(0, i-n), min(n, i)), range(min(n, i)-1, max(0, i-n)-1, -1))
m.addConstr(x[diagn].sum() <= 1, name="diag"+str(i))

# At most one queen per anti-diagonal
adiagn = (range(max(0, i-n), min(n, i)), range(max(0, n-i), min(n, 2*n-i)))

# Optimize model
m.optimize()

print(x.X)
print('Queens placed: %g' % m.objVal)

except gp.GurobiError as e:
print('Error code ' + str(e.errno) + ": " + str(e))

except AttributeError:
print('Encountered an attribute error')


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