2023年牛客基础训练营4-D

题目链接：https://ac.nowcoder.com/acm/contest/46812/D

思路：01背包，当要从一段物品中选一件出来，可以像前缀和和后缀和一样，进行前缀dp和后缀dp。

代码：

#include<bits/stdc++.h>
using namespace std;
const int N = 5010;
long long dp[N],dpp[N];
long long pre[N][N],suf[N][N];
long long cnt[N];
int w[N],v[N];
int main(){
	int n,m;
	cin>>n>>m;
	cnt[0] = 1;
	for (int i=1;i<=n;i++) cin>>v[i]>>w[i];
	for (int i=1;i<=n;i++){
		for (int j=1;j<=m;j++){
			pre[i][j] = pre[i-1][j];
			if (j>=v[i]) pre[i][j] = max(pre[i][j],pre[i-1][j-v[i]]+w[i]);
		}
	}
	for (int i=n;i>=1;i--){
		for (int j=1;j<=m;j++){
			suf[i][j] = suf[i+1][j];
			if (j>=v[i]) suf[i][j] = max(suf[i][j],suf[i+1][j-v[i]]+w[i]);
		}
	}
    for (int k=1;k<=n;k++){
        long long val = 0,val2 = 0;
        for (int i=0;i<=m;i++){
            val = max(val,pre[k-1][i]+suf[k+1][m-i]);
            if (m-v[k]>=i) val2 = max(val2,pre[k-1][i]+w[k]+suf[k+1][m-v[k]-i]);
        }
        long long ans = max(0LL,val+1-val2);
        cout<<ans<<'\n';
    }
	return 0;
}