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Lars Yencken committed 1ddcbeb

Python 11.

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python/11-greatest-product.py

+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+#
+#  11-greatest-product.py
+#  euler
+#
+#  Created by Lars Yencken on 2012-06-14.
+#  Copyright 2012 Lars Yencken. All rights reserved.
+#
+
+"""
+What is the greatest product of four adjacent numbers in any direction (up,
+down, left, right, or diagonally) in the 2020 grid?
+"""
+
+from operator import mul
+import unittest
+
+import numpy as np 
+
+grid = np.array([
+ [8,  2, 22, 97, 38, 15,  0, 40,  0, 75,  4,  5,  7, 78, 52, 12, 50, 77, 91,  8],
+[49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48,  4, 56, 62,  0],
+[81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30,  3, 49, 13, 36, 65],
+[52, 70, 95, 23,  4, 60, 11, 42, 69, 24, 68, 56,  1, 32, 56, 71, 37,  2, 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,  3, 45,  2, 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,  2, 62, 12, 20, 95, 63, 94, 39, 63,  8, 40, 91, 66, 49, 94, 21],
+[24, 55, 58,  5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72],
+[21, 36, 23,  9, 75,  0, 76, 44, 20, 45, 35, 14,  0, 61, 33, 97, 34, 31, 33, 95],
+[78, 17, 53, 28, 22, 75, 31, 67, 15, 94,  3, 80,  4, 62, 16, 14,  9, 53, 56, 92],
+[16, 39,  5, 42, 96, 35, 31, 47, 55, 58, 88, 24,  0, 17, 54, 24, 36, 29, 85, 57],
+[86, 56,  0, 48, 35, 71, 89,  7,  5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58],
+[19, 80, 81, 68,  5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77,  4, 89, 55, 40],
+ [4, 52,  8, 83, 97, 35, 99, 16,  7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66],
+[88, 36, 68, 87, 57, 62, 20, 72,  3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69],
+ [4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18,  8, 46, 29, 32, 40, 62, 76, 36],
+[20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74,  4, 36, 16],
+[20, 73, 35, 29, 78, 31, 90,  1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57,  5, 54],
+ [1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52,  1, 89, 19, 67, 48],
+])
+
+
+def max_line(ls):
+    "Return the maximum of products of four consecutive items, or zero."
+    m = 0
+    for i in xrange(len(ls) - 3):
+        m = max(m, reduce(mul, ls[i:i+4]))
+    return m
+
+def greatest_product():
+    m = 0
+
+    # look for straight lines
+    for i in xrange(20):
+        m = max(m, max_line(grid[i, :]))
+        m = max(m, max_line(grid[:, i]))
+
+    # look for down-right diagonals
+    for i in xrange(20 - 3):
+        # build the diagonal
+        diag_upper = [grid[i + j, j] for j in xrange(20 - i)]
+        m = max(m, max_line(diag_upper))
+
+        diag_lower = [grid[j, i + j] for j in xrange(20 - i)]
+        m = max(m, max_line(diag_lower))
+
+    # look for up-right diagonals
+    for i in xrange(20 - 3):
+        # build the diagonal
+        diag_upper = [grid[i + j, 20 - j - 1] for j in xrange(20 - i)]
+        m = max(m, max_line(diag_upper))
+
+        diag_lower = [grid[j, 20 - (i + j) - 1] for j in xrange(20 - i)]
+        m = max(m, max_line(diag_lower))
+
+    return m
+
+class GreatestProductTest(unittest.TestCase):
+    def test_result(self):
+        self.assertEqual(greatest_product(), 70600674)
+
+if __name__ == '__main__':
+    unittest.TextTestRunner(verbosity=2).run(unittest.makeSuite(GreatestProductTest))