【hdu3507】Print Article 【斜率优化dp】

题意

  https://cn.vjudge.net/problem/HDU-3507

分析

  斜率优化的模板题

  

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>

using namespace std;
typedef long long LL;
const int maxn=500000+10;
int n,m;
int c[maxn],sum[maxn],f[maxn],q[maxn];
int head,tail;
int Y(int j){
    return f[j]+sum[j]*sum[j];
}
int X(int j){
    return sum[j];
}

double grand(int i,int j){
    return (Y(i)-Y(j))/(X(i)-X(j));
}

int main(){
    while(scanf("%d%d",&n,&m)!=EOF){
        for(int i=1;i<=n;i++){
            scanf("%d",&c[i]);
            sum[i]=sum[i-1]+c[i];
        }
        head=tail=0;
        q[tail++]=0;
        for(int i=1;i<=n;i++){
            while(head+1<tail&&((Y(q[head+1])-Y(q[head]))<=2*sum[i]*(X(q[head+1])-X(q[head]))))head++;
            f[i]=f[q[head]]+(sum[i]-sum[q[head]])*(sum[i]-sum[q[head]])+m;
//            printf("%d %d %d
",i,q[head],f[i]);
//            printf("%d %d
",head,tail);
            while(head+1<tail&&((Y(q[tail-1])-Y(q[tail-2]))*(X(i)-X(q[tail-1]))>=(X(q[tail-1])-X(q[tail-2]))*(Y(i)-Y(q[tail-1]))))tail--;
            q[tail++]=i;
        }

        printf("%d
",f[n]);
    }
return 0;
}