hdu 4258 斜率DP

最新推荐文章于 2018-08-03 19:34:14 发布

转载最新推荐文章于 2018-08-03 19:34:14 发布 · 57 阅读

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原文链接：http://www.cnblogs.com/wangfang20/p/3358947.html

本文介绍了一种使用动态规划解决特定问题的方法，通过不断更新状态数组来优化求解过程。利用队列实现高效的状态转移，降低了算法的时间复杂度。

思路：dp[i]=dp[j]+(num[i]-num[j+1])^2;

#include<iostream>
#include<cstring>
#include<algorithm>
#include<cstdio>
#define Maxn 1000010
#define LL unsigned __int64
using namespace std;
LL dp[Maxn],num[Maxn];
int que[Maxn*3];
inline int ReadInt()
{
     char ch = getchar();
     int data = 0;
     while (ch < '0' || ch > '9')
         ch = getchar();
     do
     {
         data = data*10 + ch-'0';
         ch = getchar();
     } while (ch >= '0' && ch <= '9');
     return data;
 }
int main()
{
    int n,i,j;
    LL c;
    while(scanf("%d%I64u",&n,&c)!=EOF,n||c){
        memset(dp,0,sizeof(dp));
        for(i=1;i<=n;i++)
            num[i]=(LL)ReadInt();
        int head,rear;
        head=1;rear=0;
        que[++rear]=0;
        dp[1]=0;
        for(i=1;i<=n;i++){
            while(head<rear&&(dp[que[head+1]]+num[que[head+1]+1]*num[que[head+1]+1]-(dp[que[head]]+num[que[head]+1]*num[que[head]+1])<=2*num[i]*(num[que[head+1]+1]-num[que[head]+1])))
                head++;
            dp[i]=dp[que[head]]+(num[i]-num[que[head]+1])*(num[i]-num[que[head]+1])+c;
            while(head<rear&&(dp[i]+num[i+1]*num[i+1]-(dp[que[rear]]+num[que[rear]+1]*num[que[rear]+1]))*(num[que[rear]+1]-num[que[rear-1]+1])<=(dp[que[rear]]+num[que[rear]+1]*num[que[rear]+1]-(dp[que[rear-1]]+num[que[rear-1]+1]*num[que[rear-1]+1]))*(num[i+1]-num[que[rear]+1]))
                rear--;
            que[++rear]=i;
        }
        printf("%I64u\n",dp[n]);
    }
    return 0;
}

转载于:https://www.cnblogs.com/wangfang20/p/3358947.html