Number of Dice Rolls With Target Sum — LeetCode 1155 Python Solution

The problem

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.

Example

Input

n = 1, k = 6, target = 3

Output

1

Explanation

You throw one die with 6 faces.

Python solution

class Solution:
    def numRollsToTarget(self, n: int, k: int, target: int) -> int:
        f = [[0] * (target + 1) for _ in range(n + 1)]
        f[0][0] = 1
        mod = 10**9 + 7
        for i in range(1, n + 1):
            for j in range(1, min(i * k, target) + 1):
                for h in range(1, min(j, k) + 1):
                    f[i][j] = (f[i][j] + f[i - 1][j - h]) % mod
        return f[n][target]

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 1155. Number of Dice Rolls With Target Sum is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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