q11.py

##In the 20×20 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 × 63 × 78 × 14 = 1788696.

## What is the greatest product of four adjacent numbers in the same
## direction (up, down, left, right, or diagonally) in the 20×20 grid?


with open("prob11_data.txt", 'r') as f:
	data = [map(int, line.split()) for line in f]


maxnum = 0

# Find max of any sequence horizontally
for i in range(20):
	for j in range(20):
		if j <= 16:
			product = data[i][j]*data[i][j+1]*data[i][j+2]*data[i][j+3]
			if product > maxnum:
				maxnum = product
print maxnum

# Find max of any sequence vertically
i = j = 0
for i in range(20):
	for j in range (20):
		if j <= 16:
			product = data[j][i]*data[j+1][i]*data[j+2][i]*data[j+3][i]
			if product > maxnum:
				maxnum = product
				print "search vertical", j, i, maxnum

# Find max of any diagonal sequence from bottom left to top right
for i in range (3, 20):
	for j in range(17):
		print i, j
		product = data[i][j]*data[i-1][j+1]*data[i-2][j+2]*data[i-3][j+3]
		if product > maxnum:
			maxnum = product
print maxnum

# Find max of any diagonal sequence from top left to bottom right
for i in range (17):
	for j in range (16,-1,-1):
		product = data[i][j]*data[i+1][j+1]*data[i+2][j+2]*data[i+3][j+3]
		if product > maxnum:
			maxnum = product

print maxnum

f.close()