poj 1655 Balancing Act

Posted 2020-09-28 Nico&11101001

Balancing Act Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 14066   Accepted: 5937 Description Consider a tree T with N (1 <= N <= 20,000) nodes numbered 1...N. Deleting any node from the tree yields a forest: a collection of one or more trees. Define the balance of a node to be the size of the largest tree in the forest T created by deleting that node from T.  For example, consider the tree:  Deleting node 4 yields two trees whose member nodes are {5} and {1,2,3,6,7}. The larger of these two trees has five nodes, thus the balance of node 4 is five. Deleting node 1 yields a forest of three trees of equal size: {2,6}, {3,7}, and {4,5}. Each of these trees has two nodes, so the balance of node 1 is two.  For each input tree, calculate the node that has the minimum balance. If multiple nodes have equal balance, output the one with the lowest number.  Input The first line of input contains a single integer t (1 <= t <= 20), the number of test cases. The first line of each test case contains an integer N (1 <= N <= 20,000), the number of congruence. The next N-1 lines each contains two space-separated node numbers that are the endpoints of an edge in the tree. No edge will be listed twice, and all edges will be listed. Output For each test case, print a line containing two integers, the number of the node with minimum balance and the balance of that node. Sample Input 1 7 2 6 1 2 1 4 4 5 3 7 3 1 Sample Output 1 2 Source POJ Monthly--2004.05.15 IOI 2003 sample ta

树的重心

#include<cstdio>
#include<iostream>
#include<cstring>
#include<algorithm>
using namespace std;
const int maxn =  20003;
int m;
struct node{
    int v,next;
}edge[100000];int head[maxn],num;
void add_edge(int x ,int y)
{
    edge[++num].v=y;edge[num].next=head[x];head[x]=num;
}
bool vis[maxn];int son[maxn];
int siz=0x7fffffff,ans;
void dfs(int x)
{
    vis[x]=1;
    son[x]=0;
    int tmp=0;
    for(int i=head[x];i;i=edge[i].next)
    {
        int v=edge[i].v;
        if(vis[v])continue;
        dfs(v);
        son[x]+=(son[v]+1);
        tmp=max(son[v]+1,tmp);
    }
    tmp=max(tmp,m-son[x]-1);
    if(tmp<siz || tmp==siz && ans>x)
    {
        ans=x;
        siz=tmp;
    }
    
}
int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        memset(vis,0,sizeof vis);num=0;siz=0x7fffffff;ans=0;
        memset(head,0,sizeof(head));
        scanf("%d",&m);
        int a,b;
        for(int i=1;i<m;i++)
        {
            scanf("%d%d",&a,&b);
            add_edge(a,b);add_edge(b,a);
        }
        dfs(1);
        printf("%d %d\n",ans,siz);
    }
    return 0;
}