From 1ddcbeb2d1030165d48cc93d9c7b5d3d836d56f2 Mon Sep 17 00:00:00 2001 From: Lars Yencken Date: Thu, 14 Jun 2012 17:45:34 +1000 Subject: [PATCH] Python 11. --- python/11-greatest-product.py | 85 +++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 85 insertions(+) create mode 100644 python/11-greatest-product.py diff --git a/python/11-greatest-product.py b/python/11-greatest-product.py new file mode 100644 index 0000000..5eaff52 --- /dev/null +++ b/python/11-greatest-product.py @@ -0,0 +1,85 @@ +#!/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)) -- 2.7.4.1.g5468f9e