You have d dice, and each die has f faces numbered 1, 2, ..., f.
Return the number of possible ways (out of fd total ways) modulo 10^9 + 7 to roll the dice so the sum of the face up numbers equals target.
Example 1:
Input: d = 1, f = 6, target = 3
Output: 1
Explanation:
You throw one die with 6 faces. There is only one way to get a sum of 3.
Example 2:
Input: d = 2, f = 6, target = 7
Output: 6
Explanation:
You throw two dice, each with 6 faces. There are 6 ways to get a sum of 7:
1+6, 2+5, 3+4, 4+3, 5+2, 6+1.
Example 3:
Input: d = 2, f = 5, target = 10
Output: 1
Explanation:
You throw two dice, each with 5 faces. There is only one way to get a sum of 10: 5+5.
Example 4:
Input: d = 1, f = 2, target = 3
Output: 0
Explanation:
You throw one die with 2 faces. There is no way to get a sum of 3.
Example 5:
Input: d = 30, f = 30, target = 500
Output: 222616187
Explanation:
The answer must be returned modulo 10^9 + 7.
Solution:
class Solution {
public int numRollsToTarget(int d, int f, int target) {
// dp[d][target] = sum(dp[d - 1][target - f])
// dp[1][1 - f] = 1
long[][] dp = new long[d + 1][target + 1];
int mod = (int) 1e9 + 7;
for (int j = 1; j <= Math.min(f, target); j ++) {
dp[1][j] = 1;
}
for (int i = 2; i <= d; i ++) {
for (int j = 1; j <= target; j ++) {
for (int k = 1; k <= f; k ++) {
if (j - k >= 0 && dp[i - 1][j - k] != 0) {
dp[i][j] = (dp[i][j] + dp[i - 1][j - k]) % mod;
}
}
}
}
return (int) dp[d][target];
}
}