—–

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

3

7 4

2 4 6

8 5 9 3

That is, 3 + 7 + 4 + 9 = 23.

Find the maximum total from top to bottom of the triangle below:

75

95 64

17 47 82

18 35 87 10

20 04 82 47 65

19 01 23 75 03 34

88 02 77 73 07 63 67

99 65 04 28 06 16 70 92

41 41 26 56 83 40 80 70 33

41 48 72 33 47 32 37 16 94 29

53 71 44 65 25 43 91 52 97 51 14

70 11 33 28 77 73 17 78 39 68 17 57

91 71 52 38 17 14 91 43 58 50 27 29 48

63 66 04 68 89 53 67 30 73 16 69 87 40 31

04 62 98 27 23 09 70 98 73 93 38 53 60 04 23

NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)

—–

**My Solution**

```
#include <stdio.h>
#include <math.h>
int main(){
int mat [15][15];
int n,i,j,sum,sumfinal,sumparcial,x,y,max;
for (i=0;i<15;i++)
for (j=0;j<15;j++)
if (j<=i){
scanf("%d",&x);
mat[i][j]=x;
}
else
mat[i][j]=0;
int best [15][15];
best[0][0]=mat[0][0];
for (i=1;i<15;i++){
best[i][0] = mat[i][0] + best[i-1][0];
best[i][i] = mat[i][i] + best[i-1][i-1];
for (j=1;j<i;j++){
best[i][j] = mat[i][j] + fmax(best[i-1][j-1],best[i-1][j]);
}
}
max = 0;
for (j=0;j<15;j++)
if (best[14][j] > max)
max = best[14][j];
printf("%dn",max);
return 0;
}
```