题解 | #放苹果#

import java.util.*;
public class Main{
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        //apple个数
        int appleNum = in.nextInt();
        //盘子个数
        int plateNum = in.nextInt();
        //计算分法
        System.out.print(devideWays(appleNum, plateNum));
    }
    //递归方法
//     public static int devideWays(int appleNum, int plateNum){
//         if(appleNum < 0 || plateNum <= 0){
//             return 0;
//         }
//         if(appleNum == 0 || appleNum == 1 || plateNum == 1){
//             return 1;
//         }
//         else{
//             return devideWays(appleNum, plateNum - 1) + devideWays(appleNum - plateNum, plateNum);
//         }
//     }
    
    //动态规划
    public static int devideWays(int appleNum, int plateNum){
        int len1 = appleNum;
        int len2 = plateNum;
        int[][] dp = new int[len1 + 1][len2 + 1];
        //一个盘子或没有盘子的时候
        for(int i = 0; i <= len1; i++){
            dp[i][1] = 1;
        }
        //一个苹果或者凌哥果
        for(int j = 0; j <= len2; j++){
            dp[0][j] = 1;
            dp[1][j] = 1;
        }
        for(int i = 2; i <= len1; i++){
            for(int j = 1; j <= len2; j++){
                dp[i][j] = dp[i][j - 1] + (i >= j ? dp[i - j][j] : 0);
            }
        }
        return dp[len1][len2];
   }
}