摆渡车(斜率优化dp)


注意不要把q[h+1]写成q[h-1];

#include<iostream>
using namespace std;
#define int long long
const int N=4*1e6+200;
int f[N];
int s[N];
int c[N];
int q[N];
double slope(int i,int j){
    return (double)(f[i]+s[i]-f[j]-s[j])/(c[i]==c[j]?1e-9:c[i]-c[j]);
}
signed main(){
    int n,m;
    cin>>n>>m;
    int last=0;
    for(int i=1;i<=n;i++){
        int t;
        cin>>t;
        c[t]++;
        s[t]+=t;
        last=max(last,t);
    }
    for(int i=1;i<last+m;i++)c[i]+=c[i-1],s[i]+=s[i-1];
    for(int i=0;i<m;i++)f[i]=c[i]*i-s[i];//若last<m
    int h=1,t=0;
    int ans=1e18;
    for(int i=1;i<last+m;i++){
        while(h<t&&slope(i-m,q[t])<=slope(q[t],q[t-1]))t--;
        q[++t]=i-m;
        while(h<t&&slope(q[h+1],q[h])<=i)h++;
        f[i]=f[q[h]]+(c[i]-c[q[h]])*i-(s[i]-s[q[h]]);
        if(i>=last)ans=min(ans,f[i]);
    }
    cout<<ans;
    return 0;
}
posted @ 2025-02-18 14:33  郭轩均  阅读(17)  评论(0)    收藏  举报