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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