luogu 2389

对序列{a} ，选择m个连续段，求总和最大

O(n^3) 

 const int N=1e3;
 int a[N],s[N],n,m,f[N][N];
 
 int sum(int i,int j){
 	return s[j]-s[i-1];
 }
 void solve(){
 	int i,j,k;
 	for(i=1;i<=n;i++)
 	 for(j=1;j<=m;j++){
 	 	f[i][j]=f[i-1][j];
 	 	 for(k=0;k<i;k++){
 	 	 	 f[i][j]=max(f[i][j],f[k][j-1]+sum(k+1,i));
		   }
	  }
	cout<<f[n][m]; 
 }

 signed main(){
 	cin>>n>>m;
 	for(int i=1;i<=n;i++) 
	  cin>>a[i],s[i]=s[i-1]+a[i];
	solve(); 
 }

O(n^2)

#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std ;
 const int N=1e3;
 int a[N],n,m,f[N][N][2];
 
 void solve(){
 	int i,j,k;
 	for(i=1;i<=n;i++)
 	 for(j=1;j<=m;j++){
 	 	f[i][j][0]=max(f[i-1][j][0],f[i-1][j][1]);
 	 	f[i][j][1]=max(f[i-1][j][1]+a[i],f[i-1][j-1][0]+a[i]);
	  }
	cout<<max(f[n][m][0],f[n][m][1]); 
 }

 signed main(){
 	cin>>n>>m;
 	for(int i=1;i<=n;i++) 
	  cin>>a[i];
	solve(); 
 }