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matrix2.py
#!/usr/bin/env python3.11 # Copyright 2024, Gurobi Optimization, LLC # This example uses the matrix friendly 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 slicing on MVar objects. import numpy as np import gurobipy as gp from gurobipy import GRB n = 8 m = gp.Model("nqueens") # n-by-n binary variables; x[i, j] decides whether a queen is placed at # position (i, j) x = m.addMVar((n, n), vtype=GRB.BINARY, name="x") # Maximize the number of placed queens m.setObjective(x.sum(), GRB.MAXIMIZE) # At most one queen per row; this adds n linear constraints m.addConstr(x.sum(axis=1) <= 1, name="row") # At most one queen per column; this adds n linear constraints m.addConstr(x.sum(axis=0) <= 1, name="col") for i in range(-n + 1, n): # At most one queen on diagonal i m.addConstr(x.diagonal(i).sum() <= 1, name=f"diag{i:d}") # At most one queen on anti-diagonal i m.addConstr(x[:, ::-1].diagonal(i).sum() <= 1, name=f"adiag{i:d}") # Solve the problem m.optimize() print(x.X) print(f"Queens placed: {m.ObjVal:.0f}")