DP 2

单调区间
最大子序和

#include<algorithm>
#include<climits>
#include<deque>
#include<iostream>

using namespace std;

const int N=3e5+10;

typedef long long ll;

int n,m;
deque<int> q;
ll s[N];

int main(){
    cin>>n>>m;
    for(int i=1;i<=n;i++){
        cin>>s[i];
        s[i]+=s[i-1];
    }
    ll res=INT_MIN;
    q.push_back(0);
    for(int i=1;i<=n;i++){
        if(!q.empty()&&i-q.front()>m)
            q.pop_front();
        res=max(res,s[i]-s[q.front()]);
        while(!q.empty()&&s[q.back()]>=s[i])
            q.pop_back();
        q.push_back(i);    
        
    }
    cout<<res<<endl;
}

斜率优化 https://www.acwing.com/problem/content/description/302/

#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;
const int N=5010;
int t[N],c[N];
int f[N];
int n,s; 

int main(){
    cin>>n>>s;
    for(int i=1;i<=n;i++){
        cin>>t[i]>>c[i];
        t[i]+=t[i-1];
        c[i]+=c[i-1];
    }
    memset(f,0x3f,sizeof f);
    f[0]=0;
    for(int i=1;i<=n;i++)
        for(int j=0;j<i;j++)
            f[i]=min(f[i],f[j]+(c[i]-c[j])*t[i]+(c[n]-c[j])*s);
    cout<<f[n]<<endl;        
    
}