Problem 11
Statement
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 any direction (up, down, left, right, or diagonally) in the 20×20 grid?
Solution
The code, in C.
#include <stdio.h>
#define SIZE 20
long long int maxProd(int a[][SIZE]){
int i,j,k;
unsigned long n,m=0;
for(i=0;i<SIZE;i++)
for(j=0;j<SIZE;j++){
if(i<=SIZE-4){
n=1;
for(k=0;k<4;k++)
n*=a[i+k][j];
if(n>m)m=n;
}
if(j<=SIZE-4){
n=1;
for(k=0;k<4;k++)
n*=a[i][j+k];
if(n>m)m=n;
}
if(i<=SIZE-4 && j<=SIZE-4){
n=1;
for(k=0;k<4;k++)
n*=a[i+k][j+k];
if(n>m)m=n;
}
if(i>=3 && j<=SIZE-4){
n=1;
for(k=0;k<4;k++)
n*=a[i-k][j+k];
if(n>m)m=n;
}
}
return m;
}
int main(void){
int a[SIZE][SIZE]={ 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};
printf("%lld\n",maxProd(a));
return 0;
}
Answer
70600674
SPEAK / ADD YOUR COMMENT
Comments are moderated.
Posts