1155. Number of Dice Rolls With Target Sum

Description

You have n dice and each die has k faces numbered from 1 to k.

Given three integers n, k, and target, return the number of possible ways (out of the kn total ways) to roll the dice so the sum of the face-up numbers equals target. Since the answer may be too large, return it modulo 109 + 7.

Example 1:

Input: n = 1, k = 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: n = 2, k = 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: n = 30, k = 30, target = 500
Output: 222616187
Explanation: The answer must be returned modulo 109 + 7.

Constraints:

• 1 <= n, k <= 30
• 1 <= target <= 1000

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Solutions

class Solution {
public:
    int numRollsToTarget(int n, int k, int target) {
        const int MOD = 1e9 + 7;
        vector<int> f(target + 1, 0);
        f[0] = 1;
        for (int i = 1; i <= n; i++) {// 枚举所有物品
            for (int j = target; j >= 0; j--) { // 枚举体积, 从大到小 
                f[j] = 0;
                for (int u = 1; u <= k & u <= j; u++) {
                    f[j] = (f[j] + f[j - u]) % MOD;
                }
            }
        }
        return f[target];
    }
};