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

Solution

number-of-dice-rolls-with-target-sum.py

class Solution:
    def numRollsToTarget(self, n: int, k: int, target: int) -> int:
        M = 10 ** 9 + 7

        @cache
        def go(dices, total):
            if dices == 0:
                return int(total == target)

            count = 0

            for x in range(1, k + 1):
                if x + total > target: break

                count += go(dices - 1, x + total)
                count %= M

            return count 

        return go(n, 0)