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euler_011.py
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euler_011.py
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"""In the 20x20 grid below, four numbers along a diagonal line have
been marked in red.
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
The product of these numbers is 26 x 63 x 78 x 14 = 1788696.
What is the greatest product of four adjacent numbers in the same
direction (up, down, left, right, or diagonally) in the 20x20 grid?
"""
from collections import defaultdict
GRID = [[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 group(index_list, n_adj, step):
groups = []
for idx in index_list:
group = [idx]
curr_lev = idx/20
for i in range(1, n_adj):
next_idx = idx+step*i
next_lev = next_idx/20
if i != len(group):
break
if next_idx < 0 or next_idx >= len(GRID)**2:
break
if abs(step) == 1 and next_lev != curr_lev:
break
if abs(20-abs(step)) == 1 and abs(next_lev-curr_lev)!=i:
break
if next_idx in index_list:
group.append(next_idx)
if len(group) == n_adj:
groups.append(group)
return groups
def check_adjacent(index_list, n_adj):
if len(index_list) < n_adj:
return
groups = group(index_list, n_adj, 1)
groups.extend(group(index_list, n_adj, -1))
groups.extend(group(index_list, n_adj, 19))
groups.extend(group(index_list, n_adj, -19))
groups.extend(group(index_list, n_adj, 20))
groups.extend(group(index_list, n_adj, -20))
groups.extend(group(index_list, n_adj, 21))
groups.extend(group(index_list, n_adj, -21))
possible_adjacents = [a_group for a_group in groups if len(a_group) == n_adj]
return possible_adjacents
def largest_product(n_adj=4):
grid_list = []
for row in GRID:
grid_list.extend(row)
position_dict = defaultdict(list)
# store the index positions for each value in the grid
for idx, value in enumerate(grid_list):
position_dict[value].append(idx)
max_index_list = []
for value in sorted(position_dict.keys(), reverse=True):
max_index_list.extend(position_dict[value])
adj_groups = check_adjacent(max_index_list, n_adj)
if adj_groups:
break
max_prod = 0
for adj_group in adj_groups:
prod = 1
for idx in adj_group:
prod*=grid_list[idx]
if prod > max_prod:
max_prod = prod
return max_prod, adj_groups