#include <bits/stdc++.h>
using namespace std;
#define MAX_N 400
int dp[MAX_N][MAX_N];
int part_sum(int ,int );//输出种数
int part_print(int,int,int,int sec[],int);
int max_part;
int sec[MAX_N];
int main()
{
int n,m;
cin>>n>>m;
cout<<"1:递归"<<endl;
int sum = part_sum(n,m);
cout<<sum<<endl;
cout<<"2:DP"<<endl;
int ndp=n,mdp=m;
for(int i = 0;i<=100;i++){
for(int j = 0;j<=100;j++)
dp[i][j] = 0;
dp[i][1] = 1;
}
dp[0][0]=1,dp[0][1]=1,dp[1][0]=1,dp[1][1]=1;
for(int n = 2;n<=ndp;n++){
for(int m = 1;m<=n;m++){
if(n-m<=m){
dp[n][m] = dp[n][m-1] + dp[n-m][n-m];
}
else{
dp[n][m] = dp[n][m-1] + dp[n-m][m];
}
}
}
cout<<dp[ndp][mdp]<<endl;
cout<<"3.可输出表达式的递归:"<<endl;
max_part = m;
for(int i = 1;i<=m;i++){
cout<<"种数:"<<part_print(n,i,1,sec,0)<<endl;
}
return 0;
}
int part_sum(int n,int k)
{
if(k == 1) return 1;
else if(k > n) return part_sum(n,n);
else if(k == n) return (part_sum(n,k-1) +1 );//这一种是 n = n;
else if(k < n) return (part_sum(n,k-1) + part_sum(n-k,k) );
}
int part_print(int n,int m,int start,int sec[MAX_N],int index)
{
//n:整数,m:分成m份 start:从start开始分类 数组sec[]:存储分类的情况 index:数组下标,从0开始
if(m == 1){
sec[index] = n;
for(int i = 0;sec[i]!=0;i++){
cout<<sec[i]<<" ";
}
cout<<endl;
return 1;
}
int sum = 0;
for(int i = start;i<=n/m;i++){
sec[index] = i;
sum = sum + part_print(n-i,m-1,i,sec,index+1);
}
return sum;
}
【菜鸟er】经典题目_划分整数
最新推荐文章于 2022-02-12 22:48:29 发布