【BZOJ1803】Spoj1487 Query on a tree III 主席树+DFS序

【BZOJ1803】Spoj1487 Query on a tree III

Description

You are given a node-labeled rooted tree with n nodes. Define the query (x, k): Find the node whose label is k-th largest in the subtree of the node x. Assume no two nodes have the same labels.

Input

The first line contains one integer n (1 <= n <= 10^5). The next line contains n integers li (0 <= li <= 109) which denotes the label of the i-th node. Each line of the following n - 1 lines contains two integers u, v. They denote there is an edge between node u and node v. Node 1 is the root of the tree. The next line contains one integer m (1 <= m <= 10^4) which denotes the number of the queries. Each line of the next m contains two integers x, k. (k <= the total node number in the subtree of x)

Output

For each query (x, k), output the index of the node whose label is the k-th largest in the subtree of the node x.

Sample Input

5
1 3 5 2 7
1 2
2 3
1 4
3 5
4
2
3
4 1
3 2
3 2

Sample Output

5 4 5 5

题解：这样例你告诉我是求子树第k大？（the k_th largest）分明是第k小啊！

直接主席树+DFS序搞定。

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
const int maxn=100010;
int n,m,cnt,tot;
int to[maxn<<1],next[maxn<<1],head[maxn],v[maxn],p[maxn],q[maxn],rt[maxn];
int ls[maxn*30],rs[maxn*30],siz[maxn*30],s[maxn*30];
struct number
{
    int val,org;
}num[maxn];
bool cmp(number a,number b)
{
    return a.val<b.val;
}
void insert(int x,int &y,int l,int r,int a,int b)
{
    if(l>r)  return ;
    y=++tot,siz[y]=siz[x]+1;
    if(l==r)
    {
        s[y]=b;
        return ;
    }
    int mid=l+r>>1;
    if(a<=mid)   rs[y]=rs[x],insert(ls[x],ls[y],l,mid,a,b);
    else    ls[y]=ls[x],insert(rs[x],rs[y],mid+1,r,a,b);
}
int query(int a,int b,int l,int r,int c)
{
    if(l==r)    return s[a];
    int mid=l+r>>1,sm=siz[ls[a]]-siz[ls[b]];
    if(c<=sm)    return query(ls[a],ls[b],l,mid,c);
    else    return query(rs[a],rs[b],mid+1,r,c-sm);
}
void dfs(int x,int fa)
{
    p[x]=++p[0];
    insert(rt[p[0]-1],rt[p[0]],1,n,v[x],x);
    for(int i=head[x];i!=-1;i=next[i])  if(to[i]!=fa)   dfs(to[i],x);
    q[x]=p[0];
}
void add(int a,int b)
{
    to[cnt]=b,next[cnt]=head[a],head[a]=cnt++;
}
int main()
{
    scanf("%d",&n);
    int i,a,b;
    for(i=1;i<=n;i++)    scanf("%d",&num[i].val),num[i].org=i;
    sort(num+1,num+n+1,cmp);
    for(i=1;i<=n;i++)    v[num[i].org]=i;
    memset(head,-1,sizeof(head));
    for(i=1;i<n;i++)
    {
        scanf("%d%d",&a,&b);
        add(a,b),add(b,a);
    }
    dfs(1,0);
    scanf("%d",&m);
    for(i=1;i<=m;i++)
    {
        scanf("%d%d",&a,&b);
        printf("%d\n",query(rt[q[a]],rt[p[a]-1],1,n,b));
    }
    return 0;
}