Dice sum ways

Challenge

Implement:

long long count_dice_sum(int dice, int faces, int target);

Return the number of ways dice dice, each showing 1..faces, can sum to target.

Input format

dice >= 0, faces >= 1, target.

Output format

Number of ways.

Constraints

Sums below dice or above dice*faces are impossible.

Starter code

#include <stddef.h>
/* Number of ways `dice` dice (each showing 1..faces) can sum to target. dice>=0, faces>=1. */
long long count_dice_sum(int dice,int faces,int target){ (void)dice;(void)faces;(void)target; return 0; }

Common mistakes

Naive recursion over faces^dice is too slow; bound the reachable sums.

Edge cases to handle

0 dice hit target 0 in exactly 1 way.

Background lessons

• Counting with recursion