Zoj3659 conquer a new region

Conquer a new region

Time Limit: 5 seconds
Memory limit: 32768 KB

The wheel of the History rolling forward, our King conquered a new region in a distant continent.

There are n towns (numbered from 1 to n) in this region connected by several roads. it's confirmed that there is exact one route between any two towns. traffic is important while controlled colonies are far away from the local country. we define the capacity
C (I, j) of a road indicating it is allowed to transport at most C (I, j) goods between town I and town J if there is a road between them. and for a route between I and j, we define a value S (I, j) indicating the maximum traffic capacity between I and j which
Is equal to the minimum capacity of the roads on the route.

Our King wants to select a center town to restore his war-resources in which the total traffic capacities from the center to the other n-1 towns is maximized. now, you, the best programmer in the Kingdom, shocould help our king to select this center.

Input

There are multiple test cases.

The first line of each case contains an integer n. (1 ≤ n ≤ 200,000)

The next n-1 lines each contains three integers a, B, c indicating there is a road between town a and town B whose capacity is C. (1 ≤ a, B ≤ n, 1 ≤ C ≤ 100,000)

Output

For each test case, output an integer indicating the total traffic capacity of the chosen center town.

Sample Input

41 2 22 4 12 3 141 2 12 4 12 3 1

Sample output

43

It is indeed very good to use and check the set for this question. At that time, there was a kind of network stream feeling, which had been stuck there. In fact, we can find that, this is a tree, so there is only one path between the two points, that is, this important nature. We can use and query the set. We sort the order from big to small, for two sets of A and B, we have two merge methods. If we compare A to B or B to A, we only need to merge them in the largest way, you can get the maximum value! Because there is only one edge between two points!
#include <iostream>#include <stdio.h>#include <algorithm>#include <string.h>using namespace std;#define MAXN 200050struct node {    int s,e,c;    bool operator <(node a)const{return c>a.c;}}edge[MAXN];long long sum[MAXN];int no[MAXN],father[MAXN];bool cmp(node a,node b){    return a<b;}int find(int x){    if(father[x]!=x)        father[x]=find(father[x]);    return father[x];}int main(){   int n,i;   long long  tempa,tempb;   while(scanf("%d",&n)!=EOF)   {       for(i=0;i<=n;i++)       {           no[i]=1,sum[i]=0,father[i]=i;       }       for(i=1;i<=n-1;i++)       {          scanf("%d%d%d",&edge[i].s,&edge[i].e,&edge[i].c);       }       sort(edge+1,edge+n,cmp);       for(i=1;i<=n-1;i++)       {           int a=find(edge[i].s);           int b=find(edge[i].e);           if(a!=b)           {               tempa=(long long )edge[i].c*no[b]+sum[a];               tempb=(long long )edge[i].c*no[a]+sum[b];               if(tempa>tempb)               {                   father[b]=a,sum[a]=tempa,no[a]+=no[b];               }               else               {                   father[a]=b,sum[b]=tempb,no[b]+=no[a];               }           }        }        int a=find(1);        printf("%lld\n",sum[a]);   }    return 0;}