POJ 2796 Feel Good 单调队列

题目链接：http://poj.org/problem?id=2796

题目大意：给定一个数组，求一个权值最大的区间，区间权值的定义为 该区间的和 × 该区间最小值。

这题乍一看还以为是线段树的题，原来是单调队列。

首先两遍单调队列，分别求每个元素，左边最近的小于该元素的那个值的下标，右边最近的小于该元素的值的下标，复杂度 O(n) 。

这样对于每一个元素就能以 O(1) 的复杂度，知道它能扩展的最宽区间，该区间的和可通过 前缀数组 求得，

遍历每个元素，求 最大值 及 区间下标 。总体复杂度O(n)。

 

注：该题会爆int，卡cin。

 

代码：

#include 
#include 
#define N 100005 
#define ll long long
using namespace std;

struct node{
	ll v,p;
};

ll n;
ll a[N];
ll sum[N];
ll f[N],b[N];

void Subsequence_f()
{
	node q[N];
	ll i,j=0;
	q[0].v=-1;
	q[0].p=0;
	for(i=1;i<=n;i++)
	{
		while(q[j].v>=a[i]) j--;
		f[i]=q[j].p;
		q[++j].v=a[i];
		q[j].p=i;
	}
}

void Subsequence_b()
{
	node q[N];
	ll i,j=0;
	q[0].v=-1;
	q[0].p=n+1;
	for(i=n;i>=1;i--)
	{
		while(q[j].v>=a[i]) j--;
		b[i]=q[j].p;
		q[++j].v=a[i];
		q[j].p=i;
	}
	
}

int main()
{
	cin>>n;
	for(ll i=1;i<=n;i++)
	{
		scanf("%lld",&a[i]);
		sum[i]=sum[i-1]+a[i];
	}
	
	Subsequence_f();
	Subsequence_b();
	
	ll ans=-1,l,r,tmp;
	for(ll i=1;i<=n;i++)
	{
		tmp=a[i]*(sum[b[i]-1]-sum[f[i]]);
		if(tmp>ans)
		{
			ans=tmp;
			l=f[i]+1;
			r=b[i]-1;
		}
	}
	cout<

 

Feel Good

Time Limit: 3000MS		Memory Limit: 65536K
Total Submissions: 20682		Accepted: 5711
Case Time Limit: 1000MS		Special Judge

Description

Bill is developing a new mathematical theory for human emotions. His recent investigations are dedicated to studying how good or bad days influent people's memories about some period of life. 

A new idea Bill has recently developed assigns a non-negative integer value to each day of human life. 

Bill calls this value the emotional value of the day. The greater the emotional value is, the better the daywas. Bill suggests that the value of some period of human life is proportional to the sum of the emotional values of the days in the given period, multiplied by the smallest emotional value of the day in it. This schema reflects that good on average period can be greatly spoiled by one very bad day. 

Now Bill is planning to investigate his own life and find the period of his life that had the greatest value. Help him to do so.

Input

The first line of the input contains n - the number of days of Bill's life he is planning to investigate(1 <= n <= 100 000). The rest of the file contains n integer numbers a1, a2, ... an ranging from 0 to 106 - the emotional values of the days. Numbers are separated by spaces and/or line breaks.

Output

Print the greatest value of some period of Bill's life in the first line. And on the second line print two numbers l and r such that the period from l-th to r-th day of Bill's life(inclusive) has the greatest possible value. If there are multiple periods with the greatest possible value,then print any one of them.

Sample Input

6
3 1 6 4 5 2

Sample Output

60
3 5

Source

Northeastern Europe 2005