My solutions to the problems found at Project Euler.

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Problem 11


#! /usr/bin/python
# Problem: Find the greatest product of four adjacent numbers in
#          any direction in a 20x20 grid.
# Plan: Brute force, check every set of numbers in our grid and compare them.
# Note: I actually found the soultion before implenting down-right and down-left diagonal searches
#       but added them for completeness. :)

import re
import copy

def sortByProduct(number_list):
  product = 1
  for number in number_list:
    product *= number
    
  return product
  

if __name__ == "__main__":
  grid = """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"""
            
  grid = re.sub(r'\s', '', grid)
  grid = [int(grid[i:i+2]) for i in xrange(len(grid)) if i % 2 == 0]
  w,h = 20,20
  
  factor_sets = []
  for n in xrange(len(grid)):
    n = int(n)
    x = n % 20
    y = n / 20
        
    if x > 3: # Do reverse-horizantal search.
      factors = [grid[n], grid[n-1], grid[n-2], grid[n-3]]
      if not factors in factor_sets:
        factor_sets.append(factors)
    
    if x + 3 < w - 1: #Do foward-horizantal search.
      factors = [grid[n], grid[n+1], grid[n+2], grid[n+3]]
      if not factors in factor_sets:
        factor_sets.append(factors)
      
    if y > 3: # Do upward-vertical search.
      factors = [grid[n], grid[n-w], grid[n-w*2], grid[n-w*3]]
      if not factors in factor_sets:
        factor_sets.append(factors)
        
    if y + 3 < h - 1: #Do downward-vertical search
      factors = [grid[n], grid[n+w], grid[n+w*2], grid[n+w*3]]
      if not factors in factor_sets:
        factor_sets.append(factors)
        
    if x > 3 and y > 3: #Do up-left diagonal search.
      factors = [grid[n], grid[n-w-1], grid[n-w*2-2], grid[n-w*3-3]]
      if not factors in factor_sets:
        factor_sets.append(factors)
    
    if x + 3 < w - 1 and y > 3: #Do up-right diagonal search. 
      factors = [grid[n], grid[n-w+1], grid[n-w*2+2], grid[n-w*3+3]]
      if not factors in factor_sets:
        factor_sets.append(factors)
        
    if x > 3 and y + 3 < h - 1: # Do down-left diaganol search.
      factors = [grid[n], grid[n+w-1], grid[n+w*2-2], grid[n+w*3-3]]
      if not factors in factor_sets:
        factor_sets.append(factors)
        
    if x + 3 < w - 1 and y + 3 < h - 1: # Do down-right diaganol search.
      factors = [grid[n], grid[n+w+1], grid[n+w*2+2], grid[n+w*3+3]]
      if not factors in factor_sets:
        factor_sets.append(factors)
        
  factor_sets.sort(key=sortByProduct)
  
  print 'Set of numbers with the highest product: ' + str(factor_sets[-1:][0])
  print 'And it\'s product: ' + str(sortByProduct(factor_sets.pop()))
  

jb