zoj 3659 Conquer a New Region 並查集+貪心

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點擊開啟連結題目連結

Conquer a New RegionTime 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, should 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

Contest: The 2012 ACM-ICPC Asia Changchun Regional Contest

聽學長說是地區賽水題  

這就是傳說中的地區賽簽到題嗎 

好啊不看題解我真的不會做

有一種“最大產生樹”的感覺

不過百度了下最大產生樹沒有這道題

題意：給出n-1條邊 問從一個點出發到其他點的邊權的和最大是多少（到其他點的邊權由路徑上最小的邊權決定）

思路：先按照給出的邊從大到小排序 然後貪心

#include<cstdio>#include<cstring>#include<iostream>#include<algorithm>using namespace std;struct Edge{    int s,t;    int len;}edge[200200];int cmp(Edge a,Edge b){    return a.len>b.len;}struct Node{    int all;    long long int sum;}node[200200];int father[200200];int find(int x){    if(father[x]!=x)        father[x]=find(father[x]);    return father[x];}int n;int main(){    int i;    long long int ans;    while(scanf("%d",&n)!=EOF)    {        ans=0;        for(i=1;i<n;i++)        {            scanf("%d %d %d",&edge[i].s,&edge[i].t,&edge[i].len);        }        sort(edge+1,edge+n,cmp);        for(i=1;i<=n;i++)        {            father[i]=i;            node[i].all=1;            node[i].sum=0;        }        for(i=1;i<n;i++)        {            int fa=find(edge[i].s);            int fb=find(edge[i].t);            long long int s1=node[fb].sum+(long long int)edge[i].len*node[fa].all;            long long int s2=node[fa].sum+(long long int)edge[i].len*node[fb].all;            if(s1>=s2)            {                node[fa].sum=s1;                node[fa].all+=node[fb].all;                father[fb]=fa;                if(ans<s1)                    ans=s1;            }            else            {                node[fb].sum=s2;                node[fb].all+=node[fa].all;                father[fa]=fb;                if(ans<s2)                    ans=s2;            }        }        printf("%lld\n",ans);    }    return 0;}

Conquer a New RegionTime 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, should 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

Contest: The 2012 ACM-ICPC Asia Changchun Regional Contest