题解 | #数的划分#

import java.util.*;


public class Solution {
    /**
     * 代码中的类名、方法名、参数名已经指定，请勿修改，直接返回方法规定的值即可
     *
     * 
     * @param n int 被划分的数
     * @param k int 化成k份
     * @return int
     */
    public int divideNumber(int n, int k) {
        // write code here
        if (k > n) {
            return 0;
        }
        if (n == k || k == 1 || n == k + 1) {
            return 1;
        }
        int mod = 1000000007;
        int[][] dp = new int[n + 1][k + 1];
        dp[0][0] = 1;
        // 当前的数为 n，最多划分成 n 份(即 k <= n)
        for (int currentNumber = 1; currentNumber <= n; currentNumber++) {
            for (int currentSplit = 1; currentSplit <= k; currentSplit++) {
                if (currentSplit <= currentNumber) {
                    dp[currentNumber][currentSplit] = (dp[currentNumber - 1][currentSplit - 1] + dp[currentNumber - currentSplit][currentSplit]) % mod;
                }
            }
        }
        return dp[n][k];
    }
}