10628. Count on a treeProblem code: COT |
You are given a tree with N nodes.The tree nodes are numbered from 1 to N.Each node has an integer weight.
We will ask you to perform the following operation:
- u v k : ask for the kth minimum weight on the path from node u to node v
Input
In the first line there are two integers N and M.(N,M<=100000)
In the second line there are N integers.The ith integer denotes the weight of the ith node.
In the next N-1 lines,each line contains two integers u v,which describes an edge (u,v).
In the next M lines,each line contains three integers u v k,which means an operation asking for the kth minimum weight on the path from node u to node v.
Output
For each operation,print its result.
Example
Input:
8 5
8 5
105 2 9 3 8 5 7 7
1 2
1 3
1 4
3 5
3 6
3 7
4 8
2 5 1
2 5 2
2 5 3
2 5 4
7 8 2
Output:
2
8
9
105
7
在树上建立主席树。
然后求LCA
/* ***********************************************
Author :kuangbin
Created Time :2013-9-5 10:31:57
File Name :F:\2013ACM练习\专题学习\主席树\SPOJ_COT.cpp
************************************************ */ #include <stdio.h>
#include <string.h>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <math.h>
#include <stdlib.h>
#include <time.h>
using namespace std; //主席树部分 *****************8
const int MAXN = ;
const int M = MAXN * ;
int n,q,m,TOT;
int a[MAXN], t[MAXN];
int T[M], lson[M], rson[M], c[M]; void Init_hash()
{
for(int i = ; i <= n;i++)
t[i] = a[i];
sort(t+,t++n);
m = unique(t+,t+n+)-t-;
}
int build(int l,int r)
{
int root = TOT++;
c[root] = ;
if(l != r)
{
int mid = (l+r)>>;
lson[root] = build(l,mid);
rson[root] = build(mid+,r);
}
return root;
}
int hash(int x)
{
return lower_bound(t+,t++m,x) - t;
}
int update(int root,int pos,int val)
{
int newroot = TOT++, tmp = newroot;
c[newroot] = c[root] + val;
int l = , r = m;
while( l < r)
{
int mid = (l+r)>>;
if(pos <= mid)
{
lson[newroot] = TOT++; rson[newroot] = rson[root];
newroot = lson[newroot]; root = lson[root];
r = mid;
}
else
{
rson[newroot] = TOT++; lson[newroot] = lson[root];
newroot = rson[newroot]; root = rson[root];
l = mid+;
}
c[newroot] = c[root] + val;
}
return tmp;
}
int query(int left_root,int right_root,int LCA,int k)
{
int lca_root = T[LCA];
int pos = hash(a[LCA]);
int l = , r = m;
while(l < r)
{
int mid = (l+r)>>;
int tmp = c[lson[left_root]] + c[lson[right_root]] - *c[lson[lca_root]] + (pos >= l && pos <= mid);
if(tmp >= k)
{
left_root = lson[left_root];
right_root = lson[right_root];
lca_root = lson[lca_root];
r = mid;
}
else
{
k -= tmp;
left_root = rson[left_root];
right_root = rson[right_root];
lca_root = rson[lca_root];
l = mid + ;
}
}
return l;
} //LCA部分
int rmq[*MAXN];//rmq数组，就是欧拉序列对应的深度序列
struct ST
{
int mm[*MAXN];
int dp[*MAXN][];//最小值对应的下标
void init(int n)
{
mm[] = -;
for(int i = ;i <= n;i++)
{
mm[i] = ((i&(i-)) == )?mm[i-]+:mm[i-];
dp[i][] = i;
}
for(int j = ; j <= mm[n];j++)
for(int i = ; i + (<<j) - <= n; i++)
dp[i][j] = rmq[dp[i][j-]] < rmq[dp[i+(<<(j-))][j-]]?dp[i][j-]:dp[i+(<<(j-))][j-];
}
int query(int a,int b)//查询[a,b]之间最小值的下标
{
if(a > b)swap(a,b);
int k = mm[b-a+];
return rmq[dp[a][k]] <= rmq[dp[b-(<<k)+][k]]?dp[a][k]:dp[b-(<<k)+][k];
}
};
//边的结构体定义
struct Edge
{
int to,next;
};
Edge edge[MAXN*];
int tot,head[MAXN]; int F[MAXN*];//欧拉序列，就是dfs遍历的顺序，长度为2*n-1,下标从1开始
int P[MAXN];//P[i]表示点i在F中第一次出现的位置
int cnt; ST st;
void init()
{
tot = ;
memset(head,-,sizeof(head));
}
void addedge(int u,int v)//加边，无向边需要加两次
{
edge[tot].to = v;
edge[tot].next = head[u];
head[u] = tot++;
}
void dfs(int u,int pre,int dep)
{
F[++cnt] = u;
rmq[cnt] = dep;
P[u] = cnt;
for(int i = head[u];i != -;i = edge[i].next)
{
int v = edge[i].to;
if(v == pre)continue;
dfs(v,u,dep+);
F[++cnt] = u;
rmq[cnt] = dep;
}
}
void LCA_init(int root,int node_num)//查询LCA前的初始化
{
cnt = ;
dfs(root,root,);
st.init(*node_num-);
}
int query_lca(int u,int v)//查询u,v的lca编号
{
return F[st.query(P[u],P[v])];
} void dfs_build(int u,int pre)
{
int pos = hash(a[u]);
T[u] = update(T[pre],pos,);
for(int i = head[u]; i != -;i = edge[i].next)
{
int v = edge[i].to;
if(v == pre)continue;
dfs_build(v,u);
}
}
int main()
{
//freopen("in.txt","r",stdin);
//freopen("out.txt","w",stdout);
while(scanf("%d%d",&n,&q) == )
{
for(int i = ;i <= n;i++)
scanf("%d",&a[i]);
Init_hash();
init();
TOT = ;
int u,v;
for(int i = ;i < n;i++)
{
scanf("%d%d",&u,&v);
addedge(u,v);
addedge(v,u);
}
LCA_init(,n);
T[n+] = build(,m);
dfs_build(,n+);
int k;
while(q--)
{
scanf("%d%d%d",&u,&v,&k);
printf("%d\n",t[query(T[u],T[v],query_lca(u,v),k)]);
}
return ;
}
return ;
}