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1155. Number of Dice Rolls With Target Sum

中文文档

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

Solutions

Python3

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]

Java

class Solution {
    public int numRollsToTarget(int n, int k, int target) {
        final int mod = (int) 1e9 + 7;
        int[][] f = new int[n + 1][target + 1];
        f[0][0] = 1;
        for (int i = 1; i <= n; ++i) {
            for (int j = 1; j <= Math.min(target, i * k); ++j) {
                for (int h = 1; h <= Math.min(j, k); ++h) {
                    f[i][j] = (f[i][j] + f[i - 1][j - h]) % mod;
                }
            }
        }
        return f[n][target];
    }
}

C++

class Solution {
public:
    int numRollsToTarget(int n, int k, int target) {
        const int mod = 1e9 + 7;
        int f[n + 1][target + 1];
        memset(f, 0, sizeof f);
        f[0][0] = 1;
        for (int i = 1; i <= n; ++i) {
            for (int j = 1; j <= min(target, i * k); ++j) {
                for (int h = 1; h <= min(j, k); ++h) {
                    f[i][j] = (f[i][j] + f[i - 1][j - h]) % mod;
                }
            }
        }
        return f[n][target];
    }
};

Go

func numRollsToTarget(n int, k int, target int) int {
	const mod int = 1e9 + 7
	f := make([][]int, n+1)
	for i := range f {
		f[i] = make([]int, target+1)
	}
	f[0][0] = 1
	for i := 1; i <= n; i++ {
		for j := 1; j <= min(target, i*k); j++ {
			for h := 1; h <= min(j, k); h++ {
				f[i][j] = (f[i][j] + f[i-1][j-h]) % mod
			}
		}
	}
	return f[n][target]
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

TypeScript

function numRollsToTarget(n: number, k: number, target: number): number {
    const f = Array(n + 1)
        .fill(0)
        .map(() => Array(target + 1).fill(0));
    f[0][0] = 1;
    const mod = 1e9 + 7;
    for (let i = 1; i <= n; ++i) {
        for (let j = 1; j <= Math.min(i * k, target); ++j) {
            for (let h = 1; h <= Math.min(j, k); ++h) {
                f[i][j] = (f[i][j] + f[i - 1][j - h]) % mod;
            }
        }
    }
    return f[n][target];
}

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