In the 20×20 grid below, four numbers along a diagonal line have been marked in red.
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?
Largest product in a grid : Problem 11 Source: Euler Project
I have saved the matrix in a file "11.txt"
C Code:
#include<stdio.h>
#include<malloc.h>
int main()
{
int **matrix,row,col,maxProduct=1;
int i,j;
int s1,s2,s3,s4,s5,s6,s7,s8;
FILE *fp;
matrix = (int **)malloc(20*sizeof(int*));
for(i=0;i<20;i++)
matrix[i]=(int *)malloc(20*sizeof(int));
fp = fopen("11.txt","r");
while(!feof(fp)) {
for(row=0;row<20;row++) {
for(col=0;col<20;col++) {
fscanf(fp,"%d",&matrix[row][col]);
}
}
}
for(i=0;i<20;i++) {
s1=s2=s3=s4=s5=s6=s7=s8=1;
for(j=0;j<20;j++) {
// left-sum
if(j-3 < 0)
s1 = 1;
else
s1 = matrix[i][j]*matrix[i][j-1]*matrix[i][j-2]*matrix[i][j-3];
if (maxProduct < s1)
maxProduct =s1;
// right-sum
if(j+3 >= 20)
s2 = 1;
else
s2 = matrix[i][j]*matrix[i][j+1]*matrix[i][j+2]*matrix[i][j+3];
if (maxProduct < s2)
maxProduct =s2;
// up-sum
if(i-3 <0)
s3 = 1;
else
s3 = matrix[i][j]*matrix[i-1][j]*matrix[i-2][j]*matrix[i-3][j];
if (maxProduct < s3)
maxProduct =s3;
// down-sum
if(i+3 >= 20)
s4 = 1;
else
s4 = matrix[i][j]*matrix[i+1][j]*matrix[i+2][j]*matrix[i+3][j];
if (maxProduct < s4)
maxProduct =s4;
// diag-up-left
if(j-3 < 0 || i - 3 < 0)
s5 = 1;
else
s5 = matrix[i][j]*matrix[i-1][j-1]*matrix[i-2][j-2]*matrix[i-3][j-3];
if (maxProduct < s5)
maxProduct =s5;
// diag-up-right
if(i-3 < 0 || j + 3 >= 20)
s6 = 1;
else
s6 = matrix[i][j]*matrix[i-1][j+1]*matrix[i-2][j+2]*matrix[i-3][j+3];
if (maxProduct < s6)
maxProduct =s6;
// diag-down-left
if(i+3 >= 20 || j-3 < 0)
s7 = 1;
else
s7 = matrix[i][j]*matrix[i+1][j-1]*matrix[i+2][j-2]*matrix[i+3][j-3];
if (maxProduct < s7)
maxProduct =s7;
// diag-down-right
if(i+3 >= 20 || j+3 >=20)
s8 = 1;
else
s8 = matrix[i][j]*matrix[i+1][j+1]*matrix[i+2][j+2]*matrix[i+3][j+3];
if (maxProduct < s8)
maxProduct =s8;
}
}
printf("\nLargest Product is %d",maxProduct);
fclose(fp);
return 0;
}
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
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
What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?
Largest product in a grid : Problem 11 Source: Euler Project
I have saved the matrix in a file "11.txt"
C Code:
#include<stdio.h>
#include<malloc.h>
int main()
{
int **matrix,row,col,maxProduct=1;
int i,j;
int s1,s2,s3,s4,s5,s6,s7,s8;
FILE *fp;
matrix = (int **)malloc(20*sizeof(int*));
for(i=0;i<20;i++)
matrix[i]=(int *)malloc(20*sizeof(int));
fp = fopen("11.txt","r");
while(!feof(fp)) {
for(row=0;row<20;row++) {
for(col=0;col<20;col++) {
fscanf(fp,"%d",&matrix[row][col]);
}
}
}
for(i=0;i<20;i++) {
s1=s2=s3=s4=s5=s6=s7=s8=1;
for(j=0;j<20;j++) {
// left-sum
if(j-3 < 0)
s1 = 1;
else
s1 = matrix[i][j]*matrix[i][j-1]*matrix[i][j-2]*matrix[i][j-3];
if (maxProduct < s1)
maxProduct =s1;
// right-sum
if(j+3 >= 20)
s2 = 1;
else
s2 = matrix[i][j]*matrix[i][j+1]*matrix[i][j+2]*matrix[i][j+3];
if (maxProduct < s2)
maxProduct =s2;
// up-sum
if(i-3 <0)
s3 = 1;
else
s3 = matrix[i][j]*matrix[i-1][j]*matrix[i-2][j]*matrix[i-3][j];
if (maxProduct < s3)
maxProduct =s3;
// down-sum
if(i+3 >= 20)
s4 = 1;
else
s4 = matrix[i][j]*matrix[i+1][j]*matrix[i+2][j]*matrix[i+3][j];
if (maxProduct < s4)
maxProduct =s4;
// diag-up-left
if(j-3 < 0 || i - 3 < 0)
s5 = 1;
else
s5 = matrix[i][j]*matrix[i-1][j-1]*matrix[i-2][j-2]*matrix[i-3][j-3];
if (maxProduct < s5)
maxProduct =s5;
// diag-up-right
if(i-3 < 0 || j + 3 >= 20)
s6 = 1;
else
s6 = matrix[i][j]*matrix[i-1][j+1]*matrix[i-2][j+2]*matrix[i-3][j+3];
if (maxProduct < s6)
maxProduct =s6;
// diag-down-left
if(i+3 >= 20 || j-3 < 0)
s7 = 1;
else
s7 = matrix[i][j]*matrix[i+1][j-1]*matrix[i+2][j-2]*matrix[i+3][j-3];
if (maxProduct < s7)
maxProduct =s7;
// diag-down-right
if(i+3 >= 20 || j+3 >=20)
s8 = 1;
else
s8 = matrix[i][j]*matrix[i+1][j+1]*matrix[i+2][j+2]*matrix[i+3][j+3];
if (maxProduct < s8)
maxProduct =s8;
}
}
printf("\nLargest Product is %d",maxProduct);
fclose(fp);
return 0;
}
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