西南交通大学第十三届ACM决赛 E.Shortest Path【思维+Dfs】

题目描述

Today HH becomes a designer, and he faces a problem so he asks you for help.

Treeisland is a country with n cities and n−1 two-way road and from any city you can go to any other cities.

HH the designer is going to design a plan to divide n city into n/2 pairs so that the sum of the length between the n/2 pairs city is minimum.

Now HH has finished it but he doesn't know whether it's true so he ask you to calculate it together.

It's guaranteed that n is even.

输入描述:

The first line contains an positive integer T(1≤T≤100), represents there are T test cases. 

For each test case: The first line contains an positive integer n(1≤n≤10 4), represents the number of cities in Treeisland, it's guarantee that n is even. 

Then n−1 lines followed. Each line contains three positive integer u, v and len, (u≠v,1≤u≤n,1≤v≤n,1≤len≤10 9)indicating there is a road of length len between u and v. 

It's guarantee you can get to any city from any city.

输出描述:

For each test case, output in one line an integer, represent the minimum sum of length.

示例1

输入

2
4
1 2 5
2 3 8
3 4 6
6
1 3 5
3 2 3
4 5 4
4 3 9
4 6 10

输出

11
31

说明

In the first example, you can divide them into (1,2), and (3,4), then the minimum sum of length is 5+6=11

In the second example, you can divide them into (1,3),(2,4),(5,6), hen the minimum sum of length is 5+(3+9)+(10+4)=31

 

题目大意：

给出N个点，让我们将其分成n/2对，每对点的贡献值为两点距离，求最小距离和。

思路：

①我们可以YY一下，对于很多种分配方案，我们可以很容易找到一种情况，就是一条边要么对答案有贡献，要么就是没贡献（也就是求两点距离的时候不会走过这样一条边）。

②题目又是在一棵树上做文章，那么我们肯定要想O（n）的复杂度去Dfs怎么做一做能够得到解。

对于一个点u来讲，如果以这个点u作为根的子树的点的个数为奇数的话，我们知道其子树中肯定有一个点，要和外边一个点相配对才行，那么对应从父亲到当前节点u这条边就一定会有贡献。

③那么过程维护一下，对应到一个点的时候，去判定子树的size是否为奇数即可。

Ac代码：

#include
#include
using namespace std;
#define ll long long int
struct node
{
    int from;
    int to;
    int w;
    int next;
}e[350000];
int cont;
int head[150000];
int size[150000];
ll output;
void add(int from,int to,int w)
{
    e[cont].to=to;
    e[cont].w=w;
    e[cont].next=head[from];
    head[from]=cont++;
}
void Dfs(int u,int from,int prew)
{
    size[u]=1;
    for(int i=head[u];i!=-1;i=e[i].next)
    {
        int v=e[i].to;
        int w=e[i].w;
        if(v==from)continue;
        Dfs(v,u,w);
        size[u]+=size[v];
    }
    if(size[u]%2==1)output+=prew;
}
int main()
{
    int n;
    int t;scanf("%d",&t);
    while(t--)
    {
        output=0,cont=0;
        scanf("%d",&n);
        memset(head,-1,sizeof(head));
        for(int i=1;i<=n-1;i++)
        {
            int x,y,w;scanf("%d%d%d",&x,&y,&w);
            add(x,y,w);add(y,x,w);
        }
        Dfs(1,-1,0);
        printf("%lld\n",output);
    }
}