Sgu149 Computer Network

题目描述

给你一棵N（N<=10000）个节点的树，求每个点到其他点的最大距离。

不难想到一个节点到其他点的最大距离为：max(以它为根的子树的最大深度，根节点到它的距离+根节点的另外所有的子树(没有这个点的子树)的最大深度)。

我们不妨分两次求解出上面的两个答案的元素。显然第一个很好求，我们直接看第二个。

设整棵树的最大深度为dep1，次大深度为dep2，根节点为r。如果当前节点u不在最大深度的那棵子树上，那么它的第二个答案元素的最大距离就为：dis(r,u)+dep1，其中dis(i,j)为i到j的距离，即i的深度减j的深度的绝对值。否则，最大距离就为：dis(r,u)+dep2。

次大距离可以在求第一个元素的时候算一下。

 
 
 
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#include<iostream>
#include<cstring>
#include<cstdio>
#define maxn 10001
using namespace std;


inline int read(){


    register int x(0),f(1); register char c(getchar());


    while(c<'0'||'9'<c){ if(c=='-') f=-1; c=getchar(); }


    while('0'<=c&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar();


    return x*f;


}




struct edge{


    int to,next;


    edge(){}


    edge(const int &_to,const int &_next){


        to=_to,next=_next;


    }


}e[maxn<<1];


int head[maxn],k;


inline void add(const int &u,const int &v){


    e[k]=edge(v,head[u]);


    head[u]=k++;


}




int dp[maxn][2],n;//dp[i][0]是最大距离，dp[i][1]是次大距离


void dfs1(int u,int pre){


    for(register int i=head[u];~i;i=e[i].next){


        int v=e[i].to;


        if(v==pre) continue;


        dfs1(v,u);


        int tmp=dp[v][0]+1;


        if(tmp>dp[u][0]) swap(tmp,dp[u][0]);




 


 


        if(tmp>dp[u][1]) swap(tmp,dp[u][1]);//次大距离




    }


}


void dfs2(int u,int pre){


    for(register int i=head[u];~i;i=e[i].next){


        int v=e[i].to;


        if(v==pre) continue;


        int tmp;


        if(dp[u][0]==dp[v][0]+1) tmp=dp[u][1]+1;


        else tmp=dp[u][0]+1;


        if(tmp>dp[v][0]) swap(tmp,dp[v][0]);


        if(tmp>dp[v][1]) swap(tmp,dp[v][1]);


        dfs2(v,u);


    }


}




int main(){


    memset(head,-1,sizeof head);


    n=read();


    for(register int i=1;i<n;i++){


        int u=read(),v=read();


        add(u,v),add(v,u);


    }




    dfs1(1,0);//以它为根的子树的最大深度






    dfs2(1,0);//根节点到它的距离+根节点的另外所有的子树(没有这个点的子树)的最大深度




    for(register int i=1;i<=n;i++) printf("%d\n",dp[i][0]);


    return 0;




}














 


 








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