2022-03-30：有m个同样的苹果，认为苹果之间无差别，有n个同样的盘子，认为盘子之间也无差别

package main

import "fmt"

func main() {
  ret := ways3(5, 4)
  fmt.Println(ret)
}

var dp [][]int

func ways3(apples, plates int) int {
  if dp == nil {
    dp = make([][]int, 11)
    for i := 0; i < 11; i++ {
      dp[i] = make([]int, 11)
    }
    for i := 0; i <= 10; i++ {
      for j := 0; j <= 10; j++ {
        dp[i][j] = -1
      }
    }
  }
  return process3(apples, plates, dp)
}

func process3(apples, plates int, dp [][]int) int {
  if dp[apples][plates] != -1 {
    return dp[apples][plates]
  }
  ans := 0
  if apples == 0 {
    ans = 1
  } else if plates == 0 {
    ans = 0
  } else if plates > apples {
    ans = process3(apples, apples, dp)
  } else {
    ans = process3(apples, plates-1, dp) + process3(apples-plates, plates, dp)
  }
  dp[apples][plates] = ans
  return ans
}