1155. Number of Dice Rolls With Target Sum

Problem Link

Description

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You have n dice, and each dice 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

Solution

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Python3

class Solution:
    def numRollsToTarget(self, n: int, k: int, target: int) -> int:
        MOD = 10 ** 9 + 7
 
        @cache
        def go(index, curr):
            if index == n:
                return curr == target
            
            res = 0
 
            for v in range(1, k + 1):
                if curr + v > target: break
                
                res += go(index + 1, curr + v)
            
            return res % MOD
        
        return go(0, 0)