"POJ 2104" k-th number

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

Main topic:

Find the interval K small.

Analysis:

The line tree can be persisted to create a new version in the order of the numbers in the sequence, where each number is small in the number of all numbers in the segment tree.

Code:

1#include <cstdio>2#include <algorithm>3 4 Const intMax_n =2000000;5 6 structSegmenttree7 {8     intchild[2];9     intCount, number;Ten } Tree[max_n]; One  A intRoot[max_n], treeSize; - intNum[max_n], Id[max_n], back[max_n]; - intN, M, Qi, QJ, qk; the  - #defineMID ((left + right) >> 1) -  - intBuild (intLeftintRight ) + { -     inti = + +treeSize; +Tree[i]. Count =0; A     if(Left <Right ) at     { -Tree[i]. child[0] =Build (left, MID); -Tree[i]. child[1] = Build (MID +1, right); -     } -     returni; - } in  - intModify (intLeftintRightintPosintKeyintpre) to { +     inti = + +treeSize; -     if(Left <Right ) the     { *         intCH = (pos <= MID)?0:1; $Tree[i]. CHILD[!CH] = Tree[pre]. child[!CH];Panax NotoginsengCh? left = MID +1: right =MID; -Tree[i]. CHILD[CH] =Modify (left, right, POS, key, Tree[pre]. Child[ch]); theTree[i]. Count = Tree[tree[i]. child[0]]. Count + tree[tree[i]. child[1]]. Count; +}ElseTree[i]. Number = key, Tree[i]. Count =1; A     returni; the } +  - #defineLeftsize (Tree[tree[late]. Child[0]]. Count-tree[tree[early]. Child[0]]. Count) $  $ intQuery (intLeftintRightintEarlyintLate,intk) - { -     if(left = right)returnTree[late]. number; the     intch = (k <= leftsize)?0:1; -Ch? left = MID +1: right =MID;Wuyi     returnQuery (left, right, tree[early]. Child[ch], tree[late]. CHILD[CH], ch? Kleftsize:k); the } -  Wu BOOLCMP (intAintb) - { About     returnNum[a] <Num[b]; $ } -  - intMain () - { Ascanf ("%d%d", &n, &m); +      for(inti =1; I <= N; i++) thescanf ("%d", &num[i]), id[i] =i; -Std::sort (ID +1, ID + n +1, CMP); $root[0] = Build (1, n); the      for(inti =1; I <= N; i++) theBack[id[i]] =i; the      for(inti =1; I <= N; i++) theRoot[i] = Modify (1, N, Back[i], num[i], root[i-1]); -      for(inti =0; I < m; i++) in     { thescanf (" %d%d%d", &qi, &AMP;QJ, &qk); theprintf ("%d\n", Query (1, N, Root[qi-1], Root[qj], qk)); About     } the}

"POJ 2104" k-th number