Project Euler Problem 11: Largest product in a grid

Largest product in a grid

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?

C++(Faster):

#include <iostream>

using namespace std;

const int MAXN = 20;
const int TWO = 2;
const int FOUR = 4;

int grid[MAXN][MAXN];
int product2[MAXN][MAXN];

int main()
{
int maxproduct = 0, temp;

for(int i=0; i<MAXN; i++)
for(int j=0; j<MAXN; j++)
cin >> grid[i][j];

for(int i=0; i<MAXN-TWO; i++)
for(int j=0; j<MAXN-TWO; j++)
product2[i][j] = grid[i][j] * grid[i+1][j+1];
for(int i=0; i<MAXN-FOUR; i++)
for(int j=0; j<MAXN-FOUR; j++) {
temp = product2[i][j] * product2[i+2][j+2];
if(temp > maxproduct)
maxproduct = temp;
}

for(int i=0; i<MAXN-TWO; i++)
for(int j=0; j<MAXN-TWO; j++)
product2[i][j] = grid[i][j+3] * grid[i+1][j+2];
for(int i=0; i<MAXN-FOUR; i++)
for(int j=0; j<MAXN-FOUR; j++) {
temp = product2[i][j+3] * product2[i+2][j+1];
if(temp > maxproduct)
maxproduct = temp;
}

for(int i=0; i<MAXN; i++)
for(int j=0; j<MAXN-TWO; j++)
product2[i][j] = grid[i][j] * grid[i][j+1];
for(int i=0; i<MAXN; i++)
for(int j=0; j<MAXN-FOUR; j++) {
temp = product2[i][j] * product2[i][j+2];
if(temp > maxproduct)
maxproduct = temp;
}

for(int i=0; i<MAXN; i++)
for(int j=0; j<MAXN-TWO; j++)
product2[j][i] = grid[j][i] * grid[j][i+1];
for(int i=0; i<MAXN; i++)
for(int j=0; j<MAXN-FOUR; j++) {
temp = product2[j][i] * product2[j][i+2];
if(temp > maxproduct)
maxproduct = temp;
}

cout << maxproduct << endl;

return 0;
}

C++:

#include <iostream>

using namespace std;

const int MAXN = 20;
const int FOUR = 4;

int grid[MAXN][MAXN];

int main()
{
int maxproduct = 0, temp;

for(int i=0; i<MAXN; i++)
for(int j=0; j<MAXN; j++)
cin >> grid[i][j];

for(int i=0; i<MAXN-FOUR; i++)
for(int j=0; j<MAXN-FOUR; j++) {
temp = grid[i][j] * grid[i+1][j+1] * grid[i+2][j+2] * grid[i+3][j+3];
if(temp > maxproduct)
maxproduct = temp;

temp = grid[i][j+3] * grid[i+1][j+2] * grid[i+2][j+1] * grid[i+3][j];
if(temp > maxproduct)
maxproduct = temp;
}

for(int i=0; i<MAXN; i++)
for(int j=0; j<MAXN-FOUR; j++) {
temp = grid[i][j] * grid[i][j+1] * grid[i][j+2] * grid[i][j+3];
if(temp > maxproduct)
maxproduct = temp;

temp = grid[j][i] * grid[j][i+1] * grid[j][i+2] * grid[j][i+3];
if(temp > maxproduct)
maxproduct = temp;
}

cout << maxproduct << endl;

return 0;
}

Input data:

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