bzoj 1803: Spoj1487 Query on a tree III（主席树）

1803: Spoj1487 Query on a tree III

Time Limit: 1 Sec  Memory Limit: 64 MB
Submit: 537  Solved: 241
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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

HINT

Amber的play with tree系列的题.... 

Source

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#include<iostream>#include<cstdio>#include<algorithm>#include<cstring>#include<cmath>#define N 200003using namespace std;int point[N],next[N],v[N],tot,n,num[N],m,cnt;int root[N],val[N],a[N],l[N],q[N],r[N],sz,pos[N],b[N];struct data{int l,r,w;}tree[N*20];void add(int x,int y){tot++; next[tot]=point[x]; point[x]=tot; v[tot]=y;tot++; next[tot]=point[y]; point[y]=tot; v[tot]=x;}int cmp(int x,int y){return a[x]<a[y];}void dfs(int x,int fa){q[++sz]=x; pos[x]=sz; l[x]=sz;for (int i=point[x];i;i=next[i]){if (v[i]==fa) continue;dfs(v[i],x);}r[x]=sz;}void insert(int &i,int l,int r,int v){tree[++sz]=tree[i]; i=sz;tree[i].w++;if (l==r) return;int mid=(l+r)/2;if (v<=mid) insert(tree[i].l,l,mid,v);else insert(tree[i].r,mid+1,r,v);}int query(int i,int j,int l,int r,int k){if (l==r) return l;int t=tree[tree[j].l].w-tree[tree[i].l].w;int mid=(l+r)/2;if (t>=k) return query(tree[i].l,tree[j].l,l,mid,k);else return query(tree[i].r,tree[j].r,mid+1,r,k-t);}int main(){freopen("a.in","r",stdin);scanf("%d",&n);for (int i=1;i<=n;i++) scanf("%d",&a[i]),b[i]=i;sort(b+1,b+n+1,cmp);val[b[1]]=++cnt; num[cnt]=b[1];for (int i=2;i<=n;i++)if (a[b[i]]!=a[b[i-1]])  val[b[i]]=++cnt,num[cnt]=b[i];    else val[b[i]]=cnt;    for (int i=1;i<n;i++){    int x,y; scanf("%d%d",&x,&y);    add(x,y);}dfs(1,0);sz=0;for (int i=1;i<=n;i++) {root[i]=root[i-1];insert(root[i],1,n,val[q[i]]);}scanf("%d",&m);for (int i=1;i<=m;i++) {int x,k; scanf("%d%d",&x,&k); int t=query(root[l[x]-1],root[r[x]],1,n,k);printf("%d\n",num[t]);}}