SPOJ913 Query on a tree II

Posted 2020-08-20 SilverNebula

Time Limit: 433MS

Memory Limit: 1572864KB

64bit IO Format: %lld & %llu

Description

You are given a tree (an undirected acyclic connected graph) with N nodes, and edges numbered 1, 2, 3...N-1. Each edge has an integer value assigned to it, representing its length.

We will ask you to perfrom some instructions of the following form:

• DIST a b : ask for the distance between node a and node b
  or
• KTH a b k : ask for the k-th node on the path from node a to node b

Example:
N = 6 
1 2 1 // edge connects node 1 and node 2 has cost 1 
2 4 1 
2 5 2 
1 3 1 
3 6 2 

Path from node 4 to node 6 is 4 -> 2 -> 1 -> 3 -> 6 
DIST 4 6 : answer is 5 (1 + 1 + 1 + 2 = 5) 
KTH 4 6 4 : answer is 3 (the 4-th node on the path from node 4 to node 6 is 3) 

Input

The first line of input contains an integer t, the number of test cases (t <= 25). t test cases follow.

For each test case:

• In the first line there is an integer N (N <= 10000)
• In the next N-1 lines, the i-th line describes the i-th edge: a line with three integers a b c denotes an edge between a, b of cost c (c <= 100000)
• The next lines contain instructions "DIST a b" or "KTH a b k"
• The end of each test case is signified by the string "DONE".

There is one blank line between successive tests.

Output

For each "DIST" or "KTH" operation, write one integer representing its result.

Print one blank line after each test.

Example

Input:
1

6
1 2 1
2 4 1
2 5 2
1 3 1
3 6 2
DIST 4 6
KTH 4 6 4
DONE

Output:
5
3

Hint

Added by:	Thanh-Vy Hua
Date:	2006-08-27
Time limit:	0.433s
Source limit:	15000B
Memory limit:	1536MB
Cluster:	Cube (Intel G860)
Languages:	All except: ERL JS NODEJS PERL 6 VB.net
Resource:	Special thanks to Ivan Krasilnikov for his alternative solution

 

 

有两种操作，一是求两点间距离，二是求一点到另一点路径上的第k个点。

LCA妥妥的。

 

  1 /*by SilverN*/
  2 #include<algorithm>
  3 #include<iostream>
  4 #include<cstring>
  5 #include<cstdio>
  6 #include<cmath>
  7 #include<vector>
  8 using namespace std;
  9 const int mxn=10010;
 10 int read(){
 11     int x=0,f=1;char ch=getchar();
 12     while(ch<‘0‘ || ch>‘9‘){if(ch==‘-‘)f=-1;ch=getchar();}
 13     while(ch>=‘0‘ && ch<=‘9‘){x=x*10+ch-‘0‘;ch=getchar();}
 14     return x*f;
 15 }
 16 struct edge{
 17     int v,nxt,dis;
 18 }e[mxn<<1];
 19 int hd[mxn],mct=0;
 20 void add_edge(int u,int v,int d){
 21     e[++mct].v=v;e[mct].nxt=hd[u];e[mct].dis=d;hd[u]=mct;return;
 22 }
 23 int T,n;
 24 int fa[mxn][15];
 25 int dep[mxn];
 26 int dis[mxn];
 27 void init(){memset(hd,0,sizeof hd);memset(fa,0,sizeof fa);mct=0;}
 28 void DFS(int u,int f){
 29     dep[u]=dep[f]+1;
 30     for(int i=1;i<15;i++)fa[u][i]=fa[fa[u][i-1]][i-1];
 31     for(int i=hd[u];i;i=e[i].nxt){
 32         int v=e[i].v;
 33         if(v==f)continue;
 34         fa[v][0]=u;
 35         dis[v]=dis[u]+e[i].dis;
 36         DFS(v,u);
 37     }
 38     return;
 39 }
 40 int LCA(int x,int y){
 41     if(dep[x]<dep[y])swap(x,y);
 42     for(int i=14;i>=0;i--)
 43         if(dep[fa[x][i]]>=dep[y])x=fa[x][i];
 44     if(x==y)return y;
 45     for(int i=14;i>=0;i--){
 46         if(fa[x][i]!=fa[y][i])x=fa[x][i],y=fa[y][i];
 47     }
 48     return fa[x][0];
 49 }
 50 inline int dist(int x,int y){//求距离 
 51     int tmp=LCA(x,y);
 52     return dis[x]+dis[y]-dis[tmp]*2;
 53 }
 54 inline int find(int x,int k){//上溯 
 55     for(int i=14;i>=0;i--){
 56         if(k&(1<<i))x=fa[x][i];
 57     }
 58     return x;
 59 }
 60 inline int solve(int x,int y,int k){//查询从x到y路径上第k个结点 
 61     int tmp=LCA(x,y);
 62     int mid=dep[x]-dep[tmp]+1;
 63     if(k==mid)return tmp;
 64     if(k>mid){
 65         int dd=dep[y]-dep[tmp]+1;
 66         mid=k-mid+1;
 67         k=dd-mid;
 68         return find(y,k);
 69     }
 70     else
 71         return find(x,k-1);
 72 }
 73 int main(){
 74     T=read();
 75     int i,j,x,y,d;
 76     while(T--){
 77         init();
 78         n=read();
 79         for(i=1;i<n;i++){
 80             x=read();y=read();d=read();
 81             add_edge(x,y,d);
 82             add_edge(y,x,d);
 83         }
 84         int rt=n/2+1;
 85         dis[rt]=0;
 86         DFS(rt,0);
 87         char op[10];
 88         while(scanf("%s",op) && (op[0]!=‘D‘ || op[1]!=‘O‘)){
 89             if(op[0]==‘K‘){
 90                 x=read();y=read();d=read();
 91                 printf("%d\n",solve(x,y,d));
 92             }
 93             if(op[0]==‘D‘){
 94                 x=read();y=read();
 95                 printf("%d\n",dist(x,y));
 96             }
 97         }
 98     }
 99     return 0;
100 }