POJ 2128：Highways

Highways

Description

In a distant country Lineland there are N cities and they are all located along the highway. The highway is a straight line; it starts from the first city and runs through the second, third city and so on, ending in the N-th city. The i-th city is located at
the distance of X i miles from the first one.

The highway is wide and smooth, so it is a pleasure for all people to drive along it. But there is one problem --- all roads in Lineland, including the highway, are one-way. So people are only allowed to drive along the highway from the city with smaller number
to the city with greater number and they have to use country roads to get back, and that is not such a great pleasure indeed.

After the new president Mr. Pathwayson was elected in Lineland, he has decided that he would like to make it easier for people to get from one town to another. But he does not dare to change the traditions, and make the highway two-way. Therefore he has decided
to build new highways to connect the cities, so that it would be possible to get from any city to any other one by highways. Traditionally, the new highways must be one-way.

Of course, Mr. Pathwayson is a great president, and he wants people to remember him in years. After a thought he has decided that building just one highway would not be enough for that. Therefore he has decided that he must build two new highways. Each highway
would connect two different cities. Since people are anxious about their health, and cars running along the highway produce dangerous wastes, each new highway must not pass through any cities, except the cities it connects. Also building two new highways in
one city would disturb people too much, so all the cities that would be the ends of the new highways must be different.

You are the assistant of the minister of transportation of Lineland, so you are asked to choose the cities to be connected by the new highways. Since the cost of building a highway is proportional to its length, the total length of the highways must be minimal
possible. Write a program to solve this problem. You may assume that the distance between two cities along the new highway is equal to the distance between those cities along the main highway.

Input

The first line of the input contains N (2 <= N <= 50 000).

Next line contains N - 1 integer numbers: X2 , X3 , . . . , XN (1 <= X2 < X3 < . . . < XN <= 10⁹ ).

Output

If it is impossible to build the highways satisfying all requirements, print number 0 on the first line of the output.

In the other case on the first line of the output file print the minimal possible total length of the highways to be built. On the second line print S1 , E1 , S2 and E2 --- the numbers of the cities to connect by the first and the second highway, respectively.
Note that highways are one-way and must run from S1 to E1 and from S2 to E2 .

Sample Input

4
3 5 10

Sample Output

12
3 1 4 2

题意是有N个城市在一条快速公路上，这条快速公路是一条直线。可是这条快速公路是单向的，人们去的时候能够走快速公路。回来的时候又仅仅能走country road了。

所以新上任的市长打算在回去的方向上建立两条路(事实上一条整个回去的路就足够了。可是市长任性，就两条)。满足路上的城市都能来回都走上快速公路，问修这两条路的最短距离是多少。

要在回去的方向上修两条可以在全部城市都能互相来回，说明这两条路必定反复了一段距离。那既然必定要反复一段距离的话，又要修这两条路的距离最短，自然要覆盖那个两个城市之间最短距离的那个了。

这个题 题意比题都难理解。另外尽管是水题。仅仅须要找这些线段中的最短线段。但我自己还是WA了几次，原因是要考虑到第一条和最后一条线段是不能被选择为反复的。原因题目中说了： Each highway would connect two different cities.

代码：

#include <iostream>
#include <algorithm>
#include <cmath>
#include <vector>
#include <string>
#include <cstring>
#pragma warning(disable:4996)
using namespace std;

int dis[50002];

int main()
{
	int n,i,min,min_x;
	cin>>n;

	dis[0]=0;
	min=1000000000;

	cin>>dis[1];

	for(i=2;i<n-1;i++)//得考虑到不是第一条线段和最后一条线段的情况
	{
		cin>>dis[i];
		if(dis[i]-dis[i-1]<min)
		{
			min=dis[i]-dis[i-1];
			min_x=i;
		}
	}
	cin>>dis[n-1];

	if(n>=4)
	{
		cout<<min+dis[n-1]<<endl;
		cout<<min_x+1<<" "<<1<<" "<<n<<" "<<min_x<<endl;
	}
	else
	{
		cout<<0<<endl;
	}
	return 0;
}