LeetCode [1155] Number of Dice Rolls With Target Sum

 1155. Number of Dice Rolls With Target Sum

Medium

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.

 

Constraints:

• 1 <= d, f <= 30
• 1 <= target <= 1000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

class Solution { int MOD = (int)Math.pow(10, 9) + 7; public int numRollsToTarget(int d, int f, int target) { long[][] dp = new long[d+1][target+1]; dp[0][0] = 1; for(int i=1; i<=d; ++i){ for(int t=0; t<=target; ++t){ for(int k=1; k<=f; ++k){ if(k<=t){ dp[i][t] = (dp[i][t] + dp[i-1][t-k])%MOD; }else{ break; } } } } return (int)dp[d][target]; } }