Sgu149 Computer Network
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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