dp斜率优化小计

对于斜率dp优化，强烈推荐一篇博客http://www.cnblogs.com/Rlemon/p/3184899.html

感觉这篇博客把斜率dp讲的很全面了

hdu3507的题解：

/*
 * Problem:  
 * Author:  SHJWUDP
 * Created Time:  2015/4/21 星期二 23:44:54
 * File Name: 233.cpp
 * State: 
 * Memo: 
 */
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

typedef long long LL;

const int MaxA=5e5+7;

int N, M;
LL sum[MaxA];
int deque[MaxA];
LL f[MaxA];
LL func(int i, int j) {
    return (sum[i]-sum[j])*(sum[i]-sum[j])+M+f[j];
}
LL getY(int i, int j) {
    return (sum[j]*sum[j]+f[j])-(sum[i]*sum[i]+f[i]);
}
LL getX(int i, int j) {
    return sum[j]-sum[i];
}
void solve() {
    int front=0, tail=0;
    f[0]=0;
    deque[tail++]=0;
    for(int i=1; i<=N; i++) {
        while(front+1<tail && func(i, deque[front])>=func(i, deque[front+1])) front++;
        f[i]=func(i, deque[front]);
        while(tail-1>front &&
                getY(i, deque[tail-1])*getX(deque[tail-1], deque[tail-2])<=
                getY(deque[tail-1], deque[tail-2])*getX(i, deque[tail-1])) --tail;
        deque[tail++]=i;
    }
    printf("%lld
", f[N]);
}
int main() {
#ifndef ONLINE_JUDGE
    freopen("in", "r", stdin);
    //freopen("out", "w", stdout);
#endif
    while(~scanf("%d%d", &N, &M)) {
        sum[0]=0;
        for(int i=1; i<=N; i++) {
            int x;
            scanf("%d", &x);
            sum[i]=sum[i-1]+x;
        }
        solve();
    }
    return 0;
}