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  1. from collections import defaultdict, deque
  2. from copy import copy, deepcopy
  3.  
  4. def magicSum(n):
  5. 	return int((n*n * (n*n + 1)) / 6)
  6.  
  7. def validate(sumDict, n):
  8. 	for k, v in sumDict.items():
  9. 		if v > magicSum(n):
  10. 			return False
  11. 	return True
  12.  
  13. def check(sumDict, n):
  14. 	for k, v in sumDict.items():
  15. 		if v != magicSum(n):
  16. 			return False
  17. 	return True
  18.  
  19. def isValid(m, n):
  20. 	rowSum = defaultdict(int)
  21. 	colSum = defaultdict(int)
  22. 	diagSum = defaultdict(int)
  23.  
  24. 	isLeft = False
  25.  
  26. 	for i in range(n):
  27. 		for j in range(n):
  28. 			if m[i][j] == 0: isLeft = True
  29. 			rowSum[i] += m[i][j]
  30. 			colSum[j] += m[i][j]
  31. 			if i == j: diagSum[0] += m[i][j]
  32. 			if i + j == n - 1: diagSum[n - 1] += m[i][j]
  33.  
  34. 	if isLeft:
  35. 		return (validate(rowSum, n) and validate(colSum, n) and validate(diagSum, n))		
  36. 	return (check(rowSum, n) and check(colSum, n) and check(diagSum, n))		
  37.  
  38. def next(cur, m, n):
  39. 	possible = []
  40. 	for i in range(n): 
  41. 		for j in range(n):
  42. 			if m[i][j] == 0:
  43. 				nextM = deepcopy(m)
  44. 				nextM[i][j] = cur
  45. 				if isValid(nextM, n):
  46. 					possible.append(nextM)
  47. 	return possible
  48.  
  49. def printM(m):
  50. 	for i in range(len(m)):
  51. 			print(m[i])
  52. 	print("\n\n")
  53.  
  54. def gen(n):
  55. 	startM = [[0 for x in range(n)] for y in range(n)]
  56. 	magic = []
  57. 	Q = deque([(1, startM)])
  58. 	while len(Q):
  59. 		state = Q.popleft()
  60. 		cur = state[0]
  61. 		m = state[1]
  62. 		if cur == n * n + 1:
  63. 			magic.append(m)
  64. 			printM(m)
  65. 			continue
  66. 		for w in next(cur, m, n):
  67. 			Q.append((cur + 1, w))
  68. 	return magic
  69.  
  70. magic = gen(3)
Time limit exceeded #stdin #stdout 5s 76480KB
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https://ideone.com/0aewnJ
language:
Python 3 (python  3.12)
created:
7 years ago
visibility:
public

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