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#!/usr/bin/python
# -*- coding: utf-8 -*-
def solveIt(n):
# Modify this code to run your puzzle solving algorithm
# to be consistent with other example code, we will
# represent the decision variables as an array (not a matrix)
# there is no need to do this in your solver
# define the domains of all the variables (1..n*n)
domains = [range(1,n*n+1)]*(n*n)
# start a trivial depth first search for a solution
sol = tryall([],domains)
# prepare the solution in the specified output format
# if no solution is found, put 0s
outputData = str(n) + '\n'
if sol == None:
print 'no solution found.'
for i in range(0,n):
outputData += ' '.join(map(str, [0]*n))+'\n'
else:
for i in range(0,n):
outputData += ' '.join(map(str, sol[i*n:(i+1)*n]))+'\n'
return outputData
# this is a depth first search of all assignments
def tryall(assignment, domains):
# base-case: if the domains list is empty, all values are assigned
# check if it is a solution, return None if it is not
if len(domains) == 0:
if checkIt(assignment):
return assignment
else:
return None
# recursive-case: try each value in the next domain
# if we find a solution return it. otherwise, try the next value
else:
for v in domains[0]:
if not v in assignment:
sol = tryall(assignment[:]+[v],domains[1:])
if sol != None:
return sol
# checks if an assignment is feasible
# because sol is an array (not a matrix), checks are more cryptic
import math
def checkIt(sol):
n = int(math.sqrt(len(sol)))
m = n*(n*n+1)/2
#for i in range(0,n):
# print sol[i*n:(i+1)*n]
items = set(sol)
if len(items) != len(sol):
#print len(items),len(sol)
return False
for i in range(0,n):
#print 'row',i,sol[i*n:(i+1)*n]
if sum(sol[i*n:(i+1)*n]) != m:
return False
#print 'column',i,sol[i:len(sol):n]
if sum(sol[i:len(sol):n]) != m:
return False
if i < n-1:
if sol[i*n+i] > sol[(i+1)*n+(i+1)]:
return False
#print 'diag 1',i,[sol[i*n+i] for i in range(0,n)]
if sum([sol[i*n+i] for i in range(0,n)]) != m:
return False
#print 'diag 2',i,[sol[i*n+(n-i-1)] for i in range(0,n)]
if sum([sol[i*n+(n-i-1)] for i in range(0,n)]) != m:
return False
return True
import sys
if __name__ == "__main__":
if len(sys.argv) > 1:
try:
n = int(sys.argv[1].strip())
except:
print sys.argv[1].strip(), 'is not an integer'
print 'Solving Size:', n
print(solveIt(n))
else:
print('This test requires an instance size. Please select the size of problem to solve. (i.e. python magicSquareSolver.py 3)')
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