princeofsudan

ProjectEuler#11 Largest product in a grid

Mar 3rd, 2013
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  1. #In the 20×20 grid below, four numbers along a diagonal line have been marked in red.
  2. #The product of these numbers is 26 × 63 × 78 × 14 = 1788696.
  3.  
  4. #What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) #in the 20×20 grid?
  5.  
  6. #Iterate through the rows, columns and diagonals to find four adjacent cells that produce a maximum product.
  7.  
  8. digitsList = [[8,2,22,97,38,15,0,40,0,75,4,5,7,78,52,12,50,77,91,8],
  9. [49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48,4,56,62,0],
  10. [81,49,31,73,55,79,14,29,93,71,40,67,53,88,30,3,49,13,36,65],
  11. [52,70,95,23,4,60,11,42,69,24,68,56,1,32,56,71,37,2,36,91],
  12. [22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80],
  13. [24,47,32,60,99,3,45,2,44,75,33,53,78,36,84,20,35,17,12,50],
  14. [32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70],
  15. [67,26,20,68,2,62,12,20,95,63,94,39,63,8,40,91,66,49,94,21],
  16. [24,55,58,5,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72],
  17. [21,36,23,9,75,0,76,44,20,45,35,14,0,61,33,97,34,31,33,95],
  18. [78,17,53,28,22,75,31,67,15,94,3,80,4,62,16,14,9,53,56,92],
  19. [16,39,5,42,96,35,31,47,55,58,88,24,0,17,54,24,36,29,85,57],
  20. [86,56,0,48,35,71,89,7,5,44,44,37,44,60,21,58,51,54,17,58],
  21. [19,80,81,68,5,94,47,69,28,73,92,13,86,52,17,77,4,89,55,40],
  22. [4,52,8,83,97,35,99,16,7,97,57,32,16,26,26,79,33,27,98,66],
  23. [88,36,68,87,57,62,20,72,3,46,33,67,46,55,12,32,63,93,53,69],
  24. [4,42,16,73,38,25,39,11,24,94,72,18,8,46,29,32,40,62,76,36],
  25. [20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74,4,36,16],
  26. [20,73,35,29,78,31,90,1,74,31,49,71,48,86,81,16,23,57,5,54],
  27. [1,70,54,71,83,51,54,69,16,92,33,48,61,43,52,1,89,19,67,48]]
  28.  
  29. maxp = 0
  30. rows, cols, token = 20, 20, 4
  31. for i in range(rows):
  32.   for j in range(cols-token+1):
  33.     phv = max(n[i][j] * n[i][j+1] * n[i][j+2] * n[i][j+3],
  34.               n[j][i] * n[j+1][i] * n[j+2][i] * n[j+3][i])
  35.     if i<rows-token:
  36.       pd = max(n[i][j] * n[i+1][j+1] * n[i+2][j+2] * n[i+3][j+3],
  37.                n[i][j+3] * n[i+1][j+2] * n[i+2][j+1] * n[i+3][j])
  38.     maxp = max(maxp, phv, pd)
  39.  
  40. print maxp
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