Sgu149 Computer Network

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。

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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。

xxxxxxxxxx

#include

#include

#include

#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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