#!/usr/bin/env python3# Copyright 2025, 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.importnumpyasnpimportgurobipyasgpfromgurobipyimportGRBn=8m=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 queensm.setObjective(x.sum(),GRB.MAXIMIZE)# At most one queen per row; this adds n linear constraintsm.addConstr(x.sum(axis=1)<=1,name="row")# At most one queen per column; this adds n linear constraintsm.addConstr(x.sum(axis=0)<=1,name="col")foriinrange(-n+1,n):# At most one queen on diagonal im.addConstr(x.diagonal(i).sum()<=1,name=f"diag{i:d}")# At most one queen on anti-diagonal im.addConstr(x[:,::-1].diagonal(i).sum()<=1,name=f"adiag{i:d}")# Solve the problemm.optimize()print(x.X)print(f"Queens placed:{m.ObjVal:.0f}")