POJ Topic 2140 k-th Number (partition tree)

k-th number

Time Limit: 20000MS		Memory Limit: 65536K
Total Submissions: 42155		Accepted: 13855
Case Time Limit: 2000MS

Description

You is working for Macrohard company in data Structures Department. After failing your previous task on key insertion you were asked to write a new data structure that would being able to re Turn quickly k-th order statistics in the array segment.
That's, given an array A[1...N] of different integer numbers, your program must answer a series of questions Q (I, J, K) I n the form: "What would is the k-th number in A[I...J] segment, if this segment is sorted?"
For example, consider the array a = (1, 5, 2, 6, 3, 7, 4). Let the question is Q (2, 5, 3). The segment a[2...5] is (5, 2, 6, 3). If We sort this segment, we get (2, 3, 5, 6), the third number was 5, and therefore the answer to the question is 5.

Input

The first line of the input file contains n---the size of the array, and M---the number of questions to answer (1 < = N <=, 1 <= m <= 5 000).
The second line contains n different integer numbers not exceeding 109 by their absolute values---the array for which th E answers should be given.
The following m lines contain question descriptions, each description consists of three numbers:i, J, and K (1 <= i &L T;= j <= N, 1 <= k <= j-i + 1) and represents the question Q (I, J, K).

Output

For each question output of the answer to it---the k-th number in sorted A[I...J] segment.

Sample Input

7 31 5 2 6 3 7 42 5 34 4 11 7 3

Sample Output

563

Hint

This problem have huge input,so please use C-style input (scanf,printf), or your may got time limit exceed.

Source

Northeastern Europe 2004, Northern subregion

AC Code

#include <stdio.h> #include <string.h> #include <stdlib.h>int tree[30][100100],sorted[100010], Toleft[30][100010];int cmp (const void *a,const void *b) {return * (int *) a-* (int *) b;} void build (int l,int r,int dep) {if (l==r) {return;} int mid= (l+r) >>1;int same=mid-l+1;int i;for (i=l;i<=r;i++) if (Tree[dep][i]<sorted[mid]) Same--;int lpos=l ; int Rpos=mid+1;for (i=l;i<=r;i++) {if (Tree[dep][i]<sorted[mid]) {tree[dep+1][lpos++]=tree[dep][i];} ElseIf (tree[dep][i]==sorted[mid]&&same>0) {tree[dep+1][lpos++]=tree[dep][i];same--;} ELSETREE[DEP+1][RPOS++]=TREE[DEP][I];TOLEFT[DEP][I]=TOLEFT[DEP][L-1]+LPOS-L;//1 L Silly Division unclear}build (l,mid,dep+1);// It's 1 L, and I don't know. Build (mid+1,r,dep+1);} int query (int l,int r,int l,int r,int dep,int k) {if (l==r) {return tree[dep][l];} int mid= (L+R) >>1;int cnt=toleft[dep][r]-toleft[dep][l-1];if (cnt>=k) {int newl=l+toleft[dep][l-1]-toleft[ Dep][l-1];int newr=newl+cnt-1;return Query (l,mid,newl,newr,dep+1,k);} Else{int Newr=r+toleft[dep][r]-toleft[dep][r];iNT newl=newr-(r-l-cnt); return query (MID+1,R,NEWL,NEWR,DEP+1,K-CNT);}} int main () {int n,m;//while (scanf ("%d%d", &n,&m)!=eof)//{int i;scanf ("%d%d", &n,&m); Memset (tree,0, sizeof (tree)), for (i=1;i<=n;i++) {scanf ("%d", &tree[0][i]); sorted[i]=tree[0][i];} Qsort (Sorted+1,n,sizeof (sorted[1]), CMP), build (1,n,0), while (m--) {int a,b,k;scanf ("%d%d%d", &a,&b,&k); int Ans=query (1,n,a,b,0,k);p rintf ("%d\n", ans); //}}

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POJ Topic 2140 k-th Number (partition tree)