1155. Number of Dice Rolls With Target Sum

Medium

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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.
class Solution {
    public int numRollsToTarget(int d, int f, int target) {
        int [][]dp = new int[d + 1][target + 1];
        int mod = 1000000007;
        dp[0][0] = 1;
        for(int i = 1;i <= d;i ++) {
            for(int j = 1;j <= f;j ++) {
                for(int k = j;k <= target;k ++) {
                    dp[i][k] = (dp[i][k] + dp[i - 1][k - j]) % mod;
                }
            }
        }
        return dp[d][target];
    }
}