### Problem 11

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?

### Solution 1:

``````#I used formatter so that I can use 1 function for all up or right and diagonal

s = '''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'''

#This will return list of list formatted
#cod 0 in right or
#cod 1 down or
#cod 2 and cod 3 right diagonal and left diagonal
#Only this function is bulky and unorganized

def formatter(s, cod):
li = s.split("\n")
lis = []

for i in range(len(li)):
lis.insert(len(lis), list(map(int, li[i].split())))

lis1 = lis[:]
if cod:
lis2 = []
for i in range(len(lis)):
temp = []
for j in range(len(lis)):
temp += [lis[j][i]]
lis2.insert(len(lis2), temp)
lis = lis2
if cod == 2:
liss2 = []
lis1.reverse()
lis.reverse()
for i in range(len(lis)):
temp = []
temp2 = []
for j in range((i + 1)):
temp += [lis[j][i-j]]
temp2 += [lis1[j][i-j]]
liss2.insert(len(liss2), temp)
liss2.insert(len(liss2), temp2)
lis = liss2
elif cod == 3:
lis1.reverse()
for i in range(len(lis1)):
lis1[i].reverse()
liss2 = []
for i in range(len(lis)):
temp = []
temp2 = []
for j in range((i + 1)):
temp += [lis[j][i-j]]
temp2 += [lis1[j][i-j]]
liss2.insert(len(liss2), temp)
liss2.insert(len(liss2), temp2)
lis = liss2

#print("[+] Out of formatter func\n[+] Returning formatted list of len")
#print(lis)
return lis

def prod(li):
li = list(map(int, li))
return reduce(mul, li, 1)

li = formatter(s, i)
ma = 0
trace = 0
l1 = len(li)
for i in range(l1):
li2 = li[i]
l2 = len(li2)

#if li contains list
for j in range(l2 - k + 1):
if ma < prod(li2[j:j+k]):
ma = prod(li2[j:j+k])
trace = li2[j:j+k]

#print("[+] Out of max_adj() func\n[+] Returning max product of "
#+ str(k) + " adj\n[+]found at " + str(trace)
#+ "\n" + str(ma))
return ma

cod = [0,1,2,3]
ma = []
for i in cod: