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12679151
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2012-10-01T18:47:37.917
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2012-10-02T06:17:41.020
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2012-10-02T06:17:41.020
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Euler problem 11 is really easy with Numpy: First, create your Numpy matrix: <pre><code>>>> import numpy as np >>> LoL=np.array([map(int,ss.split()) for ss in """\ ... 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 ... 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 ... 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 ... 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91 ... 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80 ... 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50 ... 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70 ... 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21 ... 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72 ... 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95 ... 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92 ... 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57 ... 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58 ... 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40 ... 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66 ... 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69 ... 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36 ... 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16 ... 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54 ... 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48\ ... """.splitlines()]) </code></pre> Now, you can treat each 225 of the 4x4 matrixes as its own easy piece: <pre><code>def maxOfSub4x4(a): l=[] for i in range(4): # each line of 4x4 square l.append(a[i]) l.append(a[:,i]) l.append(a.diagonal()) l.append(a[::-1].diagonal()) # opposite diagonal print l return max([reduce(int.__mul__,[int(i) for i in e]) for e in l]) </code></pre> Now the max of the particular square at LoL[0:4,0,4] can be seen: <pre><code> print maxOfSub4x4(LoL[0:4,0:4]) </code></pre> Prints the elements of the 4x4 sub array, including the two diagonals, and the max product of those array elements: <pre><code>[array([ 8, 2, 22, 97]), array([ 8, 49, 81, 52]), array([49, 49, 99, 40]), array([ 2, 49, 49, 70]), array([81, 49, 31, 73]), array([22, 99, 31, 95]), array([52, 70, 95, 23]), array([97, 40, 73, 23]), array([ 8, 49, 31, 23]), array([52, 49, 99, 97])] 24468444 </code></pre> Now, just iterate over all 225 4x4 sub arrays in the 20 x 20 full array -- done.
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