HDU3507-Print Article-斜率dp入门题

为了学CDQ分治，从斜率dp和凸包开始做吧。。

代码就是维护一个凸包。利用递增的性质丢掉不合适的点。

http://www.cnblogs.com/Rlemon/p/3184899.html

代码学的上面 很模板

#include <cstdio>
#include <algorithm>

using namespace std;
//typedef long long LL;

struct Point{
    int x,y;
    Point (int _x=0,int _y=0):x(_x),y(_y){}
    Point operator - (const Point &rhs) const
    {
        return Point(x-rhs.x,y-rhs.y);
    }
};
typedef Point Vector;
inline int Cross(const Vector &u,const Vector &v)
{
    return u.x*v.y - u.y*v.x;
}

const int maxn = 5e5+10;
int N,M;
int sum[maxn],save[maxn];
int dp[maxn];
struct dequeue{
    Point q[maxn];
    int head,tail;
    void init()
    {
        head = 1;tail = 0;
        //q[head].x = 0;q[head].y = 0;
    }
    void push(const Point &u)
    {
        while(head < tail && Cross(q[tail]-q[tail-1],u-q[tail])<=0) tail--;
        q[++tail] = u;
    }
    Point pop(const int &k)
    {
        while(head < tail && k*q[head].x+q[head].y >= k*q[head+1].x + q[head+1].y) head++;
        //printf("head:%d x:%d y:%d\n",head,q[head].x,q[head].y);
        return q[head];
    }
}H;

int main()
{
    //freopen("input.txt","r",stdin);
    while(~scanf("%d%d",&N,&M))
    {
        sum[0] = 0;
        for(int i=1;i<=N;i++)
        {
            scanf("%d",&save[i]);
            sum[i] = sum[i-1]+save[i];
        }
        H.init();
        H.push(Point(0,0));
        dp[0] = 0;
        for(int i=1;i<=N;i++)
        {
            int k = -2*sum[i];
            Point u = H.pop(k);
            //printf("i:%d k:%d u.x:%d u.y:%d\n",i,k,u.x,u.y);
            dp[i] = u.x*k + u.y + sum[i]*sum[i] + M;
            H.push(Point(sum[i],dp[i]+sum[i]*sum[i]));
            //printf("push:%d %d\n",sum[i],dp[i]+sum[i]*sum[i]);
        }
        printf("%d\n",dp[N]);
    }
}