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euler / python / 11-greatest-product.py

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#!/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))