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###Code We've solved "if a gird is magic square" problem with five methods, which I've just slightly modify those and included timeit benchmarking. If you would like to review the codes, or add other methods or anything else or provide any change/improvement recommendations please do so, and I'd really appreciate that.

These variables can be assigned differently for testing:

###Code We've solved "if a grid is magic square" problem with five methods, which I've just slightly modified those and included timeit benchmarking. If you would like to review the code, or add other methods or anything else or provide any change/improvement recommendations please do so, and I'd really appreciate that.

These variables can be assigned differently for testing:

###Test

These variables can be assigned differently for testing:

NUMBER_OF_RUNS = 64
CPROFILING_ON = False
BENCHMARK_ON = True

###A Sample Output

🍏🍎🍏🍎🍏🍎🍏🍎🍏🍎
Multifunctions Benchmark:  5.588784874
🍏 Multifunctions: "[[4, 3, 8], [9, 5, 1], [2, 7, 6]]" is a magic square.
Multifunctions Benchmark:  5.549960512000001
🍏 Multifunctions: "[[8, 1, 6], [3, 5, 7], [4, 9, 2]]" is a magic square.
Multifunctions Benchmark:  5.783070463
🍏 Multifunctions: "[[1, 14, 4, 15], [8, 11, 5, 10], [13, 2, 16, 3], [12, 7, 9, 6]]" is a magic square.
Multifunctions Benchmark:  6.041834480999999
🍏 Multifunctions: "[[9, 3, 22, 16, 15], [2, 21, 20, 14, 8], [25, 19, 13, 7, 1], [18, 12, 6, 5, 24], [11, 10, 4, 23, 17]]" is a magic square.
Multifunctions Benchmark:  6.304372493999999
🍎 Multifunctions: "[[16, 14, 7, 30, 23], [24, 17, 10, 8, 31], [32, 25, 18, 11, 4], [5, 28, 26, 19, 12], [13, 6, 29, 22, 20]]" is not a magic square.
Multifunctions Benchmark:  6.737646978000001
🍏 Multifunctions: "[[1, 35, 4, 33, 32, 6], [25, 11, 9, 28, 8, 30], [24, 14, 18, 16, 17, 22], [13, 23, 19, 21, 20, 15], [12, 26, 27, 10, 29, 7], [36, 2, 34, 3, 5, 31]]" is a magic square.
Multifunctions Benchmark:  6.330970278999999
🍎 Multifunctions: "[[35, 26, 17, 1, 62, 53, 44], [46, 37, 21, 12, 3, 64, 55], [57, 41, 32, 23, 14, 5, 66], [61, 52, 43, 34, 25, 16, 7], [2, 63, 54, 45, 36, 27, 11], [13, 4, 65, 56, 47, 31, 22], [24, 15, 6, 67, 51, 42, 33]]" is not a magic square.
Multifunctions Benchmark:  6.320764873000002
🍏 Multifunctions: "[[60, 53, 44, 37, 4, 13, 20, 29], [3, 14, 19, 30, 59, 54, 43, 38], [58, 55, 42, 39, 2, 15, 18, 31], [1, 16, 17, 32, 57, 56, 41, 40], [61, 52, 45, 36, 5, 12, 21, 28], [6, 11, 22, 27, 62, 51, 46, 35], [63, 50, 47, 34, 7, 10, 23, 26], [8, 9, 24, 25, 64, 49, 48, 33]]" is a magic square.
Multifunctions Benchmark:  6.070653400000005
🍏 Multifunctions: "[[22, 47, 16, 41, 10, 35, 4], [5, 23, 48, 17, 42, 11, 29], [30, 6, 24, 49, 18, 36, 12], [13, 31, 7, 25, 43, 19, 37], [38, 14, 32, 1, 26, 44, 20], [21, 39, 8, 33, 2, 27, 45], [46, 15, 40, 9, 34, 3, 28]]" is a magic square.
Multifunctions Benchmark:  5.944438742000003
🍏 Multifunctions: "[[8, 58, 59, 5, 4, 62, 63, 1], [49, 15, 14, 52, 53, 11, 10, 56], [41, 23, 22, 44, 45, 19, 18, 48], [32, 34, 35, 29, 28, 38, 39, 25], [40, 26, 27, 37, 36, 30, 31, 33], [17, 47, 46, 20, 21, 43, 42, 24], [9, 55, 54, 12, 13, 51, 50, 16], [64, 2, 3, 61, 60, 6, 7, 57]]" is a magic square.
Multifunctions Benchmark:  5.747417926999994
🍏 Multifunctions: "[[37, 78, 29, 70, 21, 62, 13, 54, 5], [6, 38, 79, 30, 71, 22, 63, 14, 46], [47, 7, 39, 80, 31, 72, 23, 55, 15], [16, 48, 8, 40, 81, 32, 64, 24, 56], [57, 17, 49, 9, 41, 73, 33, 65, 25], [26, 58, 18, 50, 1, 42, 74, 34, 66], [67, 27, 59, 10, 51, 2, 43, 75, 35], [36, 68, 19, 60, 11, 52, 3, 44, 76], [77, 28, 69, 20, 61, 12, 53, 4, 45]]" is a magic square.
🍏🍎🍏🍎🍏🍎🍏🍎🍏🍎
Linguine Benchmark:  5.696244382999993
🍏 Linguine: "[[4, 3, 8], [9, 5, 1], [2, 7, 6]]" is a magic square.
Linguine Benchmark:  5.674139272000005
🍏 Linguine: "[[8, 1, 6], [3, 5, 7], [4, 9, 2]]" is a magic square.
Linguine Benchmark:  5.92109452599999
🍏 Linguine: "[[1, 14, 4, 15], [8, 11, 5, 10], [13, 2, 16, 3], [12, 7, 9, 6]]" is a magic square.
Linguine Benchmark:  5.958363641999995
🍏 Linguine: "[[9, 3, 22, 16, 15], [2, 21, 20, 14, 8], [25, 19, 13, 7, 1], [18, 12, 6, 5, 24], [11, 10, 4, 23, 17]]" is a magic square.
Linguine Benchmark:  5.686515516
🍎 Linguine: "[[16, 14, 7, 30, 23], [24, 17, 10, 8, 31], [32, 25, 18, 11, 4], [5, 28, 26, 19, 12], [13, 6, 29, 22, 20]]" is not a magic square.
Linguine Benchmark:  5.728992446999996
🍏 Linguine: "[[1, 35, 4, 33, 32, 6], [25, 11, 9, 28, 8, 30], [24, 14, 18, 16, 17, 22], [13, 23, 19, 21, 20, 15], [12, 26, 27, 10, 29, 7], [36, 2, 34, 3, 5, 31]]" is a magic square.
Linguine Benchmark:  5.650582772000007
🍎 Linguine: "[[35, 26, 17, 1, 62, 53, 44], [46, 37, 21, 12, 3, 64, 55], [57, 41, 32, 23, 14, 5, 66], [61, 52, 43, 34, 25, 16, 7], [2, 63, 54, 45, 36, 27, 11], [13, 4, 65, 56, 47, 31, 22], [24, 15, 6, 67, 51, 42, 33]]" is not a magic square.
Linguine Benchmark:  5.616721932000004
🍏 Linguine: "[[60, 53, 44, 37, 4, 13, 20, 29], [3, 14, 19, 30, 59, 54, 43, 38], [58, 55, 42, 39, 2, 15, 18, 31], [1, 16, 17, 32, 57, 56, 41, 40], [61, 52, 45, 36, 5, 12, 21, 28], [6, 11, 22, 27, 62, 51, 46, 35], [63, 50, 47, 34, 7, 10, 23, 26], [8, 9, 24, 25, 64, 49, 48, 33]]" is a magic square.
Linguine Benchmark:  5.492888303000001
🍏 Linguine: "[[22, 47, 16, 41, 10, 35, 4], [5, 23, 48, 17, 42, 11, 29], [30, 6, 24, 49, 18, 36, 12], [13, 31, 7, 25, 43, 19, 37], [38, 14, 32, 1, 26, 44, 20], [21, 39, 8, 33, 2, 27, 45], [46, 15, 40, 9, 34, 3, 28]]" is a magic square.
Linguine Benchmark:  5.574545161999993
🍏 Linguine: "[[8, 58, 59, 5, 4, 62, 63, 1], [49, 15, 14, 52, 53, 11, 10, 56], [41, 23, 22, 44, 45, 19, 18, 48], [32, 34, 35, 29, 28, 38, 39, 25], [40, 26, 27, 37, 36, 30, 31, 33], [17, 47, 46, 20, 21, 43, 42, 24], [9, 55, 54, 12, 13, 51, 50, 16], [64, 2, 3, 61, 60, 6, 7, 57]]" is a magic square.
Linguine Benchmark:  5.479747597999989
🍏 Linguine: "[[37, 78, 29, 70, 21, 62, 13, 54, 5], [6, 38, 79, 30, 71, 22, 63, 14, 46], [47, 7, 39, 80, 31, 72, 23, 55, 15], [16, 48, 8, 40, 81, 32, 64, 24, 56], [57, 17, 49, 9, 41, 73, 33, 65, 25], [26, 58, 18, 50, 1, 42, 74, 34, 66], [67, 27, 59, 10, 51, 2, 43, 75, 35], [36, 68, 19, 60, 11, 52, 3, 44, 76], [77, 28, 69, 20, 61, 12, 53, 4, 45]]" is a magic square.
🍏🍎🍏🍎🍏🍎🍏🍎🍏🍎
Vermicelli Benchmark:  5.610320167999987
🍏 Vermicelli: "[[4, 3, 8], [9, 5, 1], [2, 7, 6]]" is a magic square.
Vermicelli Benchmark:  5.473386472000016
🍏 Vermicelli: "[[8, 1, 6], [3, 5, 7], [4, 9, 2]]" is a magic square.
Vermicelli Benchmark:  5.50186076
🍏 Vermicelli: "[[1, 14, 4, 15], [8, 11, 5, 10], [13, 2, 16, 3], [12, 7, 9, 6]]" is a magic square.
Vermicelli Benchmark:  5.465219862999987
🍏 Vermicelli: "[[9, 3, 22, 16, 15], [2, 21, 20, 14, 8], [25, 19, 13, 7, 1], [18, 12, 6, 5, 24], [11, 10, 4, 23, 17]]" is a magic square.
Vermicelli Benchmark:  5.538681058999998
🍎 Vermicelli: "[[16, 14, 7, 30, 23], [24, 17, 10, 8, 31], [32, 25, 18, 11, 4], [5, 28, 26, 19, 12], [13, 6, 29, 22, 20]]" is not a magic square.
Vermicelli Benchmark:  5.466972800000008
🍏 Vermicelli: "[[1, 35, 4, 33, 32, 6], [25, 11, 9, 28, 8, 30], [24, 14, 18, 16, 17, 22], [13, 23, 19, 21, 20, 15], [12, 26, 27, 10, 29, 7], [36, 2, 34, 3, 5, 31]]" is a magic square.
Vermicelli Benchmark:  5.542082810000011
🍎 Vermicelli: "[[35, 26, 17, 1, 62, 53, 44], [46, 37, 21, 12, 3, 64, 55], [57, 41, 32, 23, 14, 5, 66], [61, 52, 43, 34, 25, 16, 7], [2, 63, 54, 45, 36, 27, 11], [13, 4, 65, 56, 47, 31, 22], [24, 15, 6, 67, 51, 42, 33]]" is not a magic square.
Vermicelli Benchmark:  5.477112298999998
🍏 Vermicelli: "[[60, 53, 44, 37, 4, 13, 20, 29], [3, 14, 19, 30, 59, 54, 43, 38], [58, 55, 42, 39, 2, 15, 18, 31], [1, 16, 17, 32, 57, 56, 41, 40], [61, 52, 45, 36, 5, 12, 21, 28], [6, 11, 22, 27, 62, 51, 46, 35], [63, 50, 47, 34, 7, 10, 23, 26], [8, 9, 24, 25, 64, 49, 48, 33]]" is a magic square.
Vermicelli Benchmark:  5.534445683000001
🍏 Vermicelli: "[[22, 47, 16, 41, 10, 35, 4], [5, 23, 48, 17, 42, 11, 29], [30, 6, 24, 49, 18, 36, 12], [13, 31, 7, 25, 43, 19, 37], [38, 14, 32, 1, 26, 44, 20], [21, 39, 8, 33, 2, 27, 45], [46, 15, 40, 9, 34, 3, 28]]" is a magic square.
Vermicelli Benchmark:  5.473650165999999
🍏 Vermicelli: "[[8, 58, 59, 5, 4, 62, 63, 1], [49, 15, 14, 52, 53, 11, 10, 56], [41, 23, 22, 44, 45, 19, 18, 48], [32, 34, 35, 29, 28, 38, 39, 25], [40, 26, 27, 37, 36, 30, 31, 33], [17, 47, 46, 20, 21, 43, 42, 24], [9, 55, 54, 12, 13, 51, 50, 16], [64, 2, 3, 61, 60, 6, 7, 57]]" is a magic square.
Vermicelli Benchmark:  5.516359977000008
🍏 Vermicelli: "[[37, 78, 29, 70, 21, 62, 13, 54, 5], [6, 38, 79, 30, 71, 22, 63, 14, 46], [47, 7, 39, 80, 31, 72, 23, 55, 15], [16, 48, 8, 40, 81, 32, 64, 24, 56], [57, 17, 49, 9, 41, 73, 33, 65, 25], [26, 58, 18, 50, 1, 42, 74, 34, 66], [67, 27, 59, 10, 51, 2, 43, 75, 35], [36, 68, 19, 60, 11, 52, 3, 44, 76], [77, 28, 69, 20, 61, 12, 53, 4, 45]]" is a magic square.
🍏🍎🍏🍎🍏🍎🍏🍎🍏🍎
Single Method Benchmark:  5.792159653999988
🍏 Single Method: "[[4, 3, 8], [9, 5, 1], [2, 7, 6]]" is a magic square.
Single Method Benchmark:  5.452938262999993
🍏 Single Method: "[[8, 1, 6], [3, 5, 7], [4, 9, 2]]" is a magic square.
Single Method Benchmark:  5.8117709149999826
🍏 Single Method: "[[1, 14, 4, 15], [8, 11, 5, 10], [13, 2, 16, 3], [12, 7, 9, 6]]" is a magic square.
Single Method Benchmark:  5.46323830099999
🍏 Single Method: "[[9, 3, 22, 16, 15], [2, 21, 20, 14, 8], [25, 19, 13, 7, 1], [18, 12, 6, 5, 24], [11, 10, 4, 23, 17]]" is a magic square.
Single Method Benchmark:  5.8472462789999895
🍎 Single Method: "[[16, 14, 7, 30, 23], [24, 17, 10, 8, 31], [32, 25, 18, 11, 4], [5, 28, 26, 19, 12], [13, 6, 29, 22, 20]]" is not a magic square.
Single Method Benchmark:  5.433652160999998
🍏 Single Method: "[[1, 35, 4, 33, 32, 6], [25, 11, 9, 28, 8, 30], [24, 14, 18, 16, 17, 22], [13, 23, 19, 21, 20, 15], [12, 26, 27, 10, 29, 7], [36, 2, 34, 3, 5, 31]]" is a magic square.
Single Method Benchmark:  5.805129637999983
🍎 Single Method: "[[35, 26, 17, 1, 62, 53, 44], [46, 37, 21, 12, 3, 64, 55], [57, 41, 32, 23, 14, 5, 66], [61, 52, 43, 34, 25, 16, 7], [2, 63, 54, 45, 36, 27, 11], [13, 4, 65, 56, 47, 31, 22], [24, 15, 6, 67, 51, 42, 33]]" is not a magic square.
Single Method Benchmark:  5.48093770700001
🍏 Single Method: "[[60, 53, 44, 37, 4, 13, 20, 29], [3, 14, 19, 30, 59, 54, 43, 38], [58, 55, 42, 39, 2, 15, 18, 31], [1, 16, 17, 32, 57, 56, 41, 40], [61, 52, 45, 36, 5, 12, 21, 28], [6, 11, 22, 27, 62, 51, 46, 35], [63, 50, 47, 34, 7, 10, 23, 26], [8, 9, 24, 25, 64, 49, 48, 33]]" is a magic square.
Single Method Benchmark:  5.818483440999984
🍏 Single Method: "[[22, 47, 16, 41, 10, 35, 4], [5, 23, 48, 17, 42, 11, 29], [30, 6, 24, 49, 18, 36, 12], [13, 31, 7, 25, 43, 19, 37], [38, 14, 32, 1, 26, 44, 20], [21, 39, 8, 33, 2, 27, 45], [46, 15, 40, 9, 34, 3, 28]]" is a magic square.
Single Method Benchmark:  5.494786433999991
🍏 Single Method: "[[8, 58, 59, 5, 4, 62, 63, 1], [49, 15, 14, 52, 53, 11, 10, 56], [41, 23, 22, 44, 45, 19, 18, 48], [32, 34, 35, 29, 28, 38, 39, 25], [40, 26, 27, 37, 36, 30, 31, 33], [17, 47, 46, 20, 21, 43, 42, 24], [9, 55, 54, 12, 13, 51, 50, 16], [64, 2, 3, 61, 60, 6, 7, 57]]" is a magic square.
Single Method Benchmark:  5.769875240999994
🍏 Single Method: "[[37, 78, 29, 70, 21, 62, 13, 54, 5], [6, 38, 79, 30, 71, 22, 63, 14, 46], [47, 7, 39, 80, 31, 72, 23, 55, 15], [16, 48, 8, 40, 81, 32, 64, 24, 56], [57, 17, 49, 9, 41, 73, 33, 65, 25], [26, 58, 18, 50, 1, 42, 74, 34, 66], [67, 27, 59, 10, 51, 2, 43, 75, 35], [36, 68, 19, 60, 11, 52, 3, 44, 76], [77, 28, 69, 20, 61, 12, 53, 4, 45]]" is a magic square.
🍏🍎🍏🍎🍏🍎🍏🍎🍏🍎
Numpy Benchmark:  5.541609400999988
🍏 Numpy: "[[4, 3, 8], [9, 5, 1], [2, 7, 6]]" is a magic square.
Numpy Benchmark:  5.829946971000027
🍏 Numpy: "[[8, 1, 6], [3, 5, 7], [4, 9, 2]]" is a magic square.
Numpy Benchmark:  5.444178211999997
🍏 Numpy: "[[1, 14, 4, 15], [8, 11, 5, 10], [13, 2, 16, 3], [12, 7, 9, 6]]" is a magic square.
Numpy Benchmark:  5.820747697000002
🍏 Numpy: "[[9, 3, 22, 16, 15], [2, 21, 20, 14, 8], [25, 19, 13, 7, 1], [18, 12, 6, 5, 24], [11, 10, 4, 23, 17]]" is a magic square.
Numpy Benchmark:  5.5407621650000465
🍎 Numpy: "[[16, 14, 7, 30, 23], [24, 17, 10, 8, 31], [32, 25, 18, 11, 4], [5, 28, 26, 19, 12], [13, 6, 29, 22, 20]]" is not a magic square.
Numpy Benchmark:  5.764756991000013
🍏 Numpy: "[[1, 35, 4, 33, 32, 6], [25, 11, 9, 28, 8, 30], [24, 14, 18, 16, 17, 22], [13, 23, 19, 21, 20, 15], [12, 26, 27, 10, 29, 7], [36, 2, 34, 3, 5, 31]]" is a magic square.
Numpy Benchmark:  5.588026968999998
🍎 Numpy: "[[35, 26, 17, 1, 62, 53, 44], [46, 37, 21, 12, 3, 64, 55], [57, 41, 32, 23, 14, 5, 66], [61, 52, 43, 34, 25, 16, 7], [2, 63, 54, 45, 36, 27, 11], [13, 4, 65, 56, 47, 31, 22], [24, 15, 6, 67, 51, 42, 33]]" is not a magic square.
Numpy Benchmark:  5.712816462999967
🍏 Numpy: "[[60, 53, 44, 37, 4, 13, 20, 29], [3, 14, 19, 30, 59, 54, 43, 38], [58, 55, 42, 39, 2, 15, 18, 31], [1, 16, 17, 32, 57, 56, 41, 40], [61, 52, 45, 36, 5, 12, 21, 28], [6, 11, 22, 27, 62, 51, 46, 35], [63, 50, 47, 34, 7, 10, 23, 26], [8, 9, 24, 25, 64, 49, 48, 33]]" is a magic square.
Numpy Benchmark:  5.540658426999983
🍏 Numpy: "[[22, 47, 16, 41, 10, 35, 4], [5, 23, 48, 17, 42, 11, 29], [30, 6, 24, 49, 18, 36, 12], [13, 31, 7, 25, 43, 19, 37], [38, 14, 32, 1, 26, 44, 20], [21, 39, 8, 33, 2, 27, 45], [46, 15, 40, 9, 34, 3, 28]]" is a magic square.
Numpy Benchmark:  5.761296496999989
🍏 Numpy: "[[8, 58, 59, 5, 4, 62, 63, 1], [49, 15, 14, 52, 53, 11, 10, 56], [41, 23, 22, 44, 45, 19, 18, 48], [32, 34, 35, 29, 28, 38, 39, 25], [40, 26, 27, 37, 36, 30, 31, 33], [17, 47, 46, 20, 21, 43, 42, 24], [9, 55, 54, 12, 13, 51, 50, 16], [64, 2, 3, 61, 60, 6, 7, 57]]" is a magic square.
Numpy Benchmark:  5.583522877999997
🍏 Numpy: "[[37, 78, 29, 70, 21, 62, 13, 54, 5], [6, 38, 79, 30, 71, 22, 63, 14, 46], [47, 7, 39, 80, 31, 72, 23, 55, 15], [16, 48, 8, 40, 81, 32, 64, 24, 56], [57, 17, 49, 9, 41, 73, 33, 65, 25], [26, 58, 18, 50, 1, 42, 74, 34, 66], [67, 27, 59, 10, 51, 2, 43, 75, 35], [36, 68, 19, 60, 11, 52, 3, 44, 76], [77, 28, 69, 20, 61, 12, 53, 4, 45]]" is a magic square.

import numpy as np
from typing import List, Iterable, Callable
from functools import partial

Grid = List[List[int]]  # Might as well create an alias for this


def has_correct_dimensions(grid: Grid) -> bool:
    """Returns whether or not the grid is a non-jagged square."""
    return all(len(row) == len(grid) for row in grid)


def is_normal_square(grid: Grid) -> bool:
    """Returns whether or not the function contains unique numbers from 1 to n**2."""
    max_n = len(grid[0]) ** 2
    # Does the set of numbers in the flattened grid contain the same numbers as a range set from 1 to n**2?
    return set(e for row in grid for e in row) == set(range(1, max_n + 1))


def check_each(iterable: Iterable[Iterable[int]], magic_sum: int) -> bool:
    """Returns whether or not every sub-iterable collection sums to the magic sum"""
    return all(sum(elem) == magic_sum for elem in iterable)


def diagonal_of(grid: Grid, y_indexer: Callable[[int], int]) -> Iterable[int]:
    """Generates a line of elements from the grid. y = y_indexer(x)."""
    return (grid[y_indexer(x)][x] for x in range(len(grid)))


def magic_constant(grid: Grid) -> int:
    """Returns the magic sum integer value"""
    return len(grid) * (len(grid) ** 2 + 1) / 2


def is_magic_square_multifunctions(grid: Grid) -> bool:
    """Returns whether or not the supplied grid is a proper normal magic square."""

    magic_sum = magic_constant(grid)

    check = partial(check_each, magic_sum=magic_sum)

    return is_normal_square(grid) and \
        has_correct_dimensions(grid) and \
        check(grid) and \
        check(zip(*grid)) and \
        check([diagonal_of(grid, lambda x: x),
               diagonal_of(grid, lambda x: len(grid) - x - 1)])


def is_magic_square_linguini(grid: Grid) -> bool:
    length = len(grid)
    if length == 0:
        return False

    magic_sum = magic_constant(grid)

    sum_three, sum_four = int(), int()
    for index_row in range(length):
        sum_one, sum_two = int(), int()
        unique_elements = dict()
        for index_col in range(length):
            if grid[index_row][index_col] in unique_elements:
                return False
            unique_elements[grid[index_row][index_col]] = True

            sum_one += grid[index_row][index_col]
            sum_two += grid[index_col][index_row]
            if index_row == index_col:
                sum_three += grid[index_col][index_row]
            if (index_row + index_col) == length - 1:
                sum_four += grid[index_row][index_col]
        if sum_one != magic_sum or sum_two != magic_sum:
            return False

    if sum_three != magic_sum or sum_four != magic_sum:
        return False
    return True


def is_magic_square_vermicelli(grid: List[List[int]]) -> bool:
    """Returns a boolean if an input grid is magic square"""
    grid_length = len(grid)
    magic_sum = magic_constant(grid)
    diag_positive, diag_negative = [], []
    diag_count_positive, diag_count_negative = 0, grid_length - 1
    col_grid = np.zeros(shape=(grid_length, grid_length))
    unique_elements = set()
    for index_row, lists in enumerate(grid):
        diag_negative.append(lists[diag_count_negative])
        diag_count_negative -= 1

        if len(grid[index_row]) != grid_length:
            return False

        if sum(lists) != magic_sum:
            return False

        for index_col in range(grid_length):
            unique_elements.add(lists[index_col])
            col_grid[index_col][index_row] = lists[index_col]
            if index_col == grid_length and index_row == grid_length - 1 and len(unique_elements) != grid_length ** 2 - 1:
                return False

        if index_row == grid_length - 1:
            sum_col, temp_col = sum(col_grid), np.array(
                [magic_sum] * grid_length)
            if str(temp_col) != str(sum_col):
                return False

        if diag_count_positive == index_row:
            diag_positive.append(lists[index_row])
            diag_count_positive += 1

        if diag_count_positive == grid_length and sum(diag_positive) != magic_sum:
            return False

        if index_row == grid_length - 1 and sum(diag_negative) != magic_sum:
            return False

    return True


def is_magic_square_single_method(grid: List[List[int]]) -> bool:
    """Returns a boolean if an input grid is magic square"""

    grid_length = len(grid)
    grid_area = grid_length ** 2
    magic_sum = magic_constant(grid)

    # check the length of all rows
    if any(len(row) != grid_length for row in grid):
        return False

    # check it has all the numbers in sequence
    if set(x for row in grid for x in row) != set(range(1, grid_area + 1)):
        return False

    # check all the rows add up to the magic_number
    if any(sum(row) != magic_sum for row in grid):
        return False

    # check all the columns add up to the magic_number
    if any(sum(row[col] for row in grid) != magic_sum for col in range(grid_length)):
        return False

    # check each diagonal adds up to the magic_number
    if (sum(grid[i][i] for i in range(grid_length)) != magic_sum
            or sum(grid[i][grid_length - i - 1] for i in range(grid_length)) != magic_sum):
        return False

    return True


def is_magic_square_numpy(grid: List[List[int]]) -> bool:
    """Returns a boolean if an input grid is magic square"""

    grid_length = len(grid)
    magic_sum = magic_constant(grid)

    # check the length of all rows
    if any(len(row) != grid_length for row in grid):
        return False

    npgrid = np.array(grid)

    # check it has all ints from 1 to grid_length**2 (inclusive)
    if len(np.setdiff1d(npgrid, np.arange(1, grid_length ** 2 + 1))):
        return False

    # check all the rows add up to the magic_number
    if any(np.not_equal(npgrid.sum(axis=0), magic_sum)):
        return False

    # check all the columns add up to the magic_number
    if any(np.not_equal(npgrid.sum(axis=1), magic_sum)):
        return False

    # check both diagonals add up to the magic_number
    if (npgrid.diagonal().sum() != magic_sum
            or np.fliplr(npgrid).diagonal().sum() != magic_sum):
        return False

    return True


if __name__ == '__main__':
    # ---------------------------- TEST ---------------------------
    import timeit
    import cProfile

    DIVIDER_DASH_LINE = '-' * 50
    GREEN_APPLE = '\U0001F34F'
    RED_APPLE = '\U0001F34E'

    magic_squares = (
        [[4, 3, 8],
         [9, 5, 1],
         [2, 7, 6]],

        [[8, 1, 6],
         [3, 5, 7],
         [4, 9, 2]],


        [[1, 14, 4, 15],
         [8, 11, 5, 10],
         [13, 2, 16, 3],
         [12, 7, 9, 6]],


        [[9, 3, 22, 16, 15],
         [2, 21, 20, 14, 8],
         [25, 19, 13, 7, 1],
         [18, 12, 6, 5, 24],
         [11, 10, 4, 23, 17]],

        [[16, 14, 7, 30, 23],
         [24, 17, 10, 8, 31],
         [32, 25, 18, 11, 4],
         [5, 28, 26, 19, 12],
         [13, 6, 29, 22, 20]],


        [[1, 35, 4, 33, 32, 6],
         [25, 11, 9, 28, 8, 30],
         [24, 14, 18, 16, 17, 22],
         [13, 23, 19, 21, 20, 15],
         [12, 26, 27, 10, 29, 7],
         [36, 2, 34, 3, 5, 31]],


        [[35, 26, 17, 1, 62, 53, 44],
         [46, 37, 21, 12, 3, 64, 55],
         [57, 41, 32, 23, 14, 5, 66],
         [61, 52, 43, 34, 25, 16, 7],
         [2, 63, 54, 45, 36, 27, 11],
         [13, 4, 65, 56, 47, 31, 22],
         [24, 15, 6, 67, 51, 42, 33]],


        [[60, 53, 44, 37, 4, 13, 20, 29],
         [3, 14, 19, 30, 59, 54, 43, 38],
         [58, 55, 42, 39, 2, 15, 18, 31],
         [1, 16, 17, 32, 57, 56, 41, 40],
         [61, 52, 45, 36, 5, 12, 21, 28],
         [6, 11, 22, 27, 62, 51, 46, 35],
         [63, 50, 47, 34, 7, 10, 23, 26],
         [8, 9, 24, 25, 64, 49, 48, 33]],


        [[22, 47, 16, 41, 10, 35, 4],
         [5, 23, 48, 17, 42, 11, 29],
            [30, 6, 24, 49, 18, 36, 12],
            [13, 31, 7, 25, 43, 19, 37],
            [38, 14, 32, 1, 26, 44, 20],
            [21, 39, 8, 33, 2, 27, 45],
            [46, 15, 40, 9, 34, 3, 28]],

        [[8, 58, 59, 5, 4, 62, 63, 1],
         [49, 15, 14, 52, 53, 11, 10, 56],
            [41, 23, 22, 44, 45, 19, 18, 48],
            [32, 34, 35, 29, 28, 38, 39, 25],
            [40, 26, 27, 37, 36, 30, 31, 33],
            [17, 47, 46, 20, 21, 43, 42, 24],
            [9, 55, 54, 12, 13, 51, 50, 16],
            [64, 2, 3, 61, 60, 6, 7, 57]],

        [[37, 78, 29, 70, 21, 62, 13, 54, 5],
         [6, 38, 79, 30, 71, 22, 63, 14, 46],
            [47, 7, 39, 80, 31, 72, 23, 55, 15],
            [16, 48, 8, 40, 81, 32, 64, 24, 56],
            [57, 17, 49, 9, 41, 73, 33, 65, 25],
            [26, 58, 18, 50, 1, 42, 74, 34, 66],
            [67, 27, 59, 10, 51, 2, 43, 75, 35],
            [36, 68, 19, 60, 11, 52, 3, 44, 76],
            [77, 28, 69, 20, 61, 12, 53, 4, 45]],

    )

    test_methods = (
        ("Multifunctions", is_magic_square_multifunctions),
        ("Linquini", is_magic_square_linguini),
        ("Vermicelli", is_magic_square_vermicelli),
        ("Single Method", is_magic_square_single_method),
        ("Numpy", is_magic_square_numpy),
    )

    # --------------------------------- PROFILING AND BANCHMARK SETTINGS --------------------------------------
    NUMBER_OF_RUNS = 64
    CPROFILING_ON = False
    BENCHMARK_ON = True

    for description, method in test_methods:
        print((GREEN_APPLE + RED_APPLE) * 5)

        for magic_square in magic_squares:
            if CPROFILING_ON is True:
                print(f'{description} cProfiling: ', cProfile.run("method(magic_square)"))
            if BENCHMARK_ON is True:
                print(f'{description} Benchmark: ', timeit.Timer(
                    f'for i in range({NUMBER_OF_RUNS}): {method(magic_square)}', 'gc.enable()').timeit())

            if method(magic_square) is True:
                print(f'{GREEN_APPLE} {description}: "{magic_square}" is a magic square.')
            else:
                print(f'{RED_APPLE} {description}: "{magic_square}" is not a magic square.')

import numpy as np
from typing import List, Iterable, Callable
from functools import partial

Grid = List[List[int]]  # Might as well create an alias for this


def has_correct_dimensions(grid: Grid) -> bool:
    """Returns whether or not the grid is a non-jagged square."""
    return all(len(row) == len(grid) for row in grid)


def is_normal_square(grid: Grid) -> bool:
    """Returns whether or not the function contains unique numbers from 1 to n**2."""
    max_n = len(grid[0]) ** 2
    # Does the set of numbers in the flattened grid contain the same numbers as a range set from 1 to n**2?
    return set(e for row in grid for e in row) == set(range(1, max_n + 1))


def check_each(iterable: Iterable[Iterable[int]], magic_sum: int) -> bool:
    """Returns whether or not every sub-iterable collection sums to the magic sum"""
    return all(sum(elem) == magic_sum for elem in iterable)


def diagonal_of(grid: Grid, y_indexer: Callable[[int], int]) -> Iterable[int]:
    """Generates a line of elements from the grid. y = y_indexer(x)."""
    return (grid[y_indexer(x)][x] for x in range(len(grid)))


def magic_constant(grid: Grid) -> int:
    """Returns the magic sum integer value"""
    return len(grid) * (len(grid) ** 2 + 1) / 2


def is_magic_square_multifunctions(grid: Grid) -> bool:
    """Returns whether or not the supplied grid is a proper normal magic square."""

    magic_sum = magic_constant(grid)

    check = partial(check_each, magic_sum=magic_sum)

    return is_normal_square(grid) and \
        has_correct_dimensions(grid) and \
        check(grid) and \
        check(zip(*grid)) and \
        check([diagonal_of(grid, lambda x: x),
               diagonal_of(grid, lambda x: len(grid) - x - 1)])


def is_magic_square_linguini(grid: Grid) -> bool:
    length = len(grid)
    if length == 0:
        return False

    magic_sum = magic_constant(grid)

    sum_three, sum_four = int(), int()
    for index_row in range(length):
        sum_one, sum_two = int(), int()
        unique_elements = dict()
        for index_col in range(length):
            if grid[index_row][index_col] in unique_elements:
                return False
            unique_elements[grid[index_row][index_col]] = True

            sum_one += grid[index_row][index_col]
            sum_two += grid[index_col][index_row]
            if index_row == index_col:
                sum_three += grid[index_col][index_row]
            if (index_row + index_col) == length - 1:
                sum_four += grid[index_row][index_col]
        if sum_one != magic_sum or sum_two != magic_sum:
            return False

    if sum_three != magic_sum or sum_four != magic_sum:
        return False
    return True


def is_magic_square_vermicelli(grid: List[List[int]]) -> bool:
    """Returns a boolean if an input grid is magic square"""
    grid_length = len(grid)
    magic_sum = magic_constant(grid)
    diag_positive, diag_negative = [], []
    diag_count_positive, diag_count_negative = 0, grid_length - 1
    col_grid = np.zeros(shape=(grid_length, grid_length))
    unique_elements = set()
    for index_row, lists in enumerate(grid):
        diag_negative.append(lists[diag_count_negative])
        diag_count_negative -= 1

        if len(grid[index_row]) != grid_length:
            return False

        if sum(lists) != magic_sum:
            return False

        for index_col in range(grid_length):
            unique_elements.add(lists[index_col])
            col_grid[index_col][index_row] = lists[index_col]
            if index_col == grid_length and index_row == grid_length - 1 and len(unique_elements) != grid_length ** 2 - 1:
                return False

        if index_row == grid_length - 1:
            sum_col, temp_col = sum(col_grid), np.array(
                [magic_sum] * grid_length)
            if str(temp_col) != str(sum_col):
                return False

        if diag_count_positive == index_row:
            diag_positive.append(lists[index_row])
            diag_count_positive += 1

        if diag_count_positive == grid_length and sum(diag_positive) != magic_sum:
            return False

        if index_row == grid_length - 1 and sum(diag_negative) != magic_sum:
            return False

    return True


def is_magic_square_single_method(grid: List[List[int]]) -> bool:
    """Returns a boolean if an input grid is magic square"""

    grid_length = len(grid)
    grid_area = grid_length ** 2
    magic_sum = magic_constant(grid)

    # check the length of all rows
    if any(len(row) != grid_length for row in grid):
        return False

    # check it has all the numbers in sequence
    if set(x for row in grid for x in row) != set(range(1, grid_area + 1)):
        return False

    # check all the rows add up to the magic_number
    if any(sum(row) != magic_sum for row in grid):
        return False

    # check all the columns add up to the magic_number
    if any(sum(row[col] for row in grid) != magic_sum for col in range(grid_length)):
        return False

    # check each diagonal adds up to the magic_number
    if (sum(grid[i][i] for i in range(grid_length)) != magic_sum
            or sum(grid[i][grid_length - i - 1] for i in range(grid_length)) != magic_sum):
        return False

    return True


def is_magic_square_numpy(grid: List[List[int]]) -> bool:
    """Returns a boolean if an input grid is magic square"""

    grid_length = len(grid)
    magic_sum = magic_constant(grid)

    # check the length of all rows
    if any(len(row) != grid_length for row in grid):
        return False

    npgrid = np.array(grid)

    # check it has all ints from 1 to grid_length**2 (inclusive)
    if len(np.setdiff1d(npgrid, np.arange(1, grid_length ** 2 + 1))):
        return False

    # check all the rows add up to the magic_number
    if any(np.not_equal(npgrid.sum(axis=0), magic_sum)):
        return False

    # check all the columns add up to the magic_number
    if any(np.not_equal(npgrid.sum(axis=1), magic_sum)):
        return False

    # check both diagonals add up to the magic_number
    if (npgrid.diagonal().sum() != magic_sum
            or np.fliplr(npgrid).diagonal().sum() != magic_sum):
        return False

    return True


if __name__ == '__main__':
    # ---------------------------- TEST ---------------------------
    import timeit
    import cProfile

    DIVIDER_DASH_LINE = '-' * 50
    GREEN_APPLE = '\U0001F34F'
    RED_APPLE = '\U0001F34E'

    magic_squares = (
        [[4, 3, 8],
         [9, 5, 1],
         [2, 7, 6]],

        [[8, 1, 6],
         [3, 5, 7],
         [4, 9, 2]],


        [[1, 14, 4, 15],
         [8, 11, 5, 10],
         [13, 2, 16, 3],
         [12, 7, 9, 6]],


        [[9, 3, 22, 16, 15],
         [2, 21, 20, 14, 8],
         [25, 19, 13, 7, 1],
         [18, 12, 6, 5, 24],
         [11, 10, 4, 23, 17]],

        [[16, 14, 7, 30, 23],
         [24, 17, 10, 8, 31],
         [32, 25, 18, 11, 4],
         [5, 28, 26, 19, 12],
         [13, 6, 29, 22, 20]],


        [[1, 35, 4, 33, 32, 6],
         [25, 11, 9, 28, 8, 30],
         [24, 14, 18, 16, 17, 22],
         [13, 23, 19, 21, 20, 15],
         [12, 26, 27, 10, 29, 7],
         [36, 2, 34, 3, 5, 31]],


        [[35, 26, 17, 1, 62, 53, 44],
         [46, 37, 21, 12, 3, 64, 55],
         [57, 41, 32, 23, 14, 5, 66],
         [61, 52, 43, 34, 25, 16, 7],
         [2, 63, 54, 45, 36, 27, 11],
         [13, 4, 65, 56, 47, 31, 22],
         [24, 15, 6, 67, 51, 42, 33]],


        [[60, 53, 44, 37, 4, 13, 20, 29],
         [3, 14, 19, 30, 59, 54, 43, 38],
         [58, 55, 42, 39, 2, 15, 18, 31],
         [1, 16, 17, 32, 57, 56, 41, 40],
         [61, 52, 45, 36, 5, 12, 21, 28],
         [6, 11, 22, 27, 62, 51, 46, 35],
         [63, 50, 47, 34, 7, 10, 23, 26],
         [8, 9, 24, 25, 64, 49, 48, 33]],


        [[22, 47, 16, 41, 10, 35, 4],
         [5, 23, 48, 17, 42, 11, 29],
            [30, 6, 24, 49, 18, 36, 12],
            [13, 31, 7, 25, 43, 19, 37],
            [38, 14, 32, 1, 26, 44, 20],
            [21, 39, 8, 33, 2, 27, 45],
            [46, 15, 40, 9, 34, 3, 28]],

        [[8, 58, 59, 5, 4, 62, 63, 1],
         [49, 15, 14, 52, 53, 11, 10, 56],
            [41, 23, 22, 44, 45, 19, 18, 48],
            [32, 34, 35, 29, 28, 38, 39, 25],
            [40, 26, 27, 37, 36, 30, 31, 33],
            [17, 47, 46, 20, 21, 43, 42, 24],
            [9, 55, 54, 12, 13, 51, 50, 16],
            [64, 2, 3, 61, 60, 6, 7, 57]],

        [[37, 78, 29, 70, 21, 62, 13, 54, 5],
         [6, 38, 79, 30, 71, 22, 63, 14, 46],
            [47, 7, 39, 80, 31, 72, 23, 55, 15],
            [16, 48, 8, 40, 81, 32, 64, 24, 56],
            [57, 17, 49, 9, 41, 73, 33, 65, 25],
            [26, 58, 18, 50, 1, 42, 74, 34, 66],
            [67, 27, 59, 10, 51, 2, 43, 75, 35],
            [36, 68, 19, 60, 11, 52, 3, 44, 76],
            [77, 28, 69, 20, 61, 12, 53, 4, 45]],

    )

    test_methods = (
        ("Multifunctions", is_magic_square_multifunctions),
        ("Linguine", is_magic_square_linguini),
        ("Vermicelli", is_magic_square_vermicelli),
        ("Single Method", is_magic_square_single_method),
        ("Numpy", is_magic_square_numpy),
    )

    # --------------------------------- PROFILING AND BANCHMARK SETTINGS --------------------------------------
    NUMBER_OF_RUNS = 64
    CPROFILING_ON = False
    BENCHMARK_ON = True

    for description, method in test_methods:
        print((GREEN_APPLE + RED_APPLE) * 5)

        for magic_square in magic_squares:
            if CPROFILING_ON is True:
                print(f'{description} cProfiling: ', cProfile.run("method(magic_square)"))
            if BENCHMARK_ON is True:
                print(f'{description} Benchmark: ', timeit.Timer(
                    f'for i in range({NUMBER_OF_RUNS}): {method(magic_square)}', 'gc.enable()').timeit())

            if method(magic_square) is True:
                print(f'{GREEN_APPLE} {description}: "{magic_square}" is a magic square.')
            else:
                print(f'{RED_APPLE} {description}: "{magic_square}" is not a magic square.')