You are working for Macrohard company in data structures department. After failing your previous task about key insertion you were asked to write a new data structure that would be able to return quickly k-th order statistics in the array segment.
That is, given an array a[1...n] of different integer numbers, your program must answer a series of questions Q(i, j, k) in the form: "What would be the k-th number in a[i...j] segment, if this segment was sorted?"
For example, consider the array a = (1, 5, 2, 6, 3, 7, 4). Let the question be 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 is 5, and therefore the answer to the question is 5.
That is, given an array a[1...n] of different integer numbers, your program must answer a series of questions Q(i, j, k) in the form: "What would be the k-th number in a[i...j] segment, if this segment was sorted?"
For example, consider the array a = (1, 5, 2, 6, 3, 7, 4). Let the question be 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 is 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 <= 100 000, 1 <= m <= 5 000).
The second line contains n different integer numbers not exceeding 10 9 by their absolute values --- the array for which the answers should be given.
The following m lines contain question descriptions, each description consists of three numbers: i, j, and k (1 <= i <= j <= n, 1 <= k <= j - i + 1) and represents the question Q(i, j, k).
The second line contains n different integer numbers not exceeding 10 9 by their absolute values --- the array for which the answers should be given.
The following m lines contain question descriptions, each description consists of three numbers: i, j, and k (1 <= i <= j <= n, 1 <= k <= j - i + 1) and represents the question Q(i, j, k).
Output
For each question output the answer to it --- the k-th number in sorted a[i...j] segment.
Sample Input
7 3 1 5 2 6 3 7 4 2 5 3 4 4 1 1 7 3
Sample Output
5 6 3
Hint
This problem has huge input,so please use c-style input(scanf,printf),or you may got time limit exceed.
. 1 #include <cstdio> 2 #include <Vector> . 3 #include <algorithm> . 4 the using namespace STD; . 5 . 6 const int N = 1E5 + . 5 ; . 7 int A [N]; /// input array . 8 int the root [N ]; /// the root [i] denotes the i-th segment tree before the array of elements of the root . 9 struct node { 10 int L, R & lt; /// left child node segment tree . 11 int SUM; /// statistics sub- number of elements in the tree 12 is } T [N * 40 ]; /// opening 20-fold or 40-fold 13 is int NUM = 0 ; /// node number 14 Vector < int > VEC; 15 16 int getId ( int K) { . 17 return lower_bound (vec.begin (), vec.end (), K) -vec.begin ( ) + . 1 ; 18 is } . 19 20 is void update ( int L, int R & lt, int & now, int BEF, int K) { /// update operation 21 is T [NUM ++] = T [BEF]; /// replicate a segment tree 22 is now NUM =;// Update the current root of the tree segment 23 is T [NUM] .sum ++ ; 24 IF (R & lt == L) return ; 25 int MID = (L + R & lt) >> . 1 ; 26 is IF (K <= MID) { 27 Update (L, MID, T [now] .L, T [BEF] .L, K); 28 } 29 the else { 30 Update (MID + . 1 , R & lt, T [now] .r, T [BEF]. R & lt, K); 31 is } 32 } 33 is 34 is int Query ( int L, int R & lt, int X, int Y,int k) { /// Query the interval [x, y] k-th largest numbers 35 IF (R & lt == L) return L; 36 int MID = (L + R & lt) >> . 1 ; 37 [ int CNT T = [T [y] .L] .sum-T [T [x] .L] .sum; /// y-x particles than the particles tree tree in the left subtree of the plurality of nodes 38 is IF (CNT> = K) { /// left subtree 39 return Query (L, MID, T [X] .L, T [Y] .L, K); 40 } 41 is the else { 42 is return Query (MID + . 1 , R & lt, T [ X] .r, T [Y] .r, - K- CNT); 43 is } 44 is } 45 46 is intmain () { 47 int n-, m; 48 Scanf ( " % D% D " , & n-, & m); 49 for ( int I = . 1 ; I <= n-; I ++ ) { 50 Scanf ( " % D " , a & [I]); 51 is vec.push_back (a [I]); 52 is } 53 is Sort (vec.begin (), vec.end ()); 54 is /// UNIQUE to return after the container is not re-repeat sequence the last element of the next element 55 /// ERASE deleted [left, right) of the element 56 is vec.erase (UNIQUE (vec.begin (), vec.end ()), vec.end ()); 57 is for (int i=1;i<=n;i++){ 58 update(1,n,root[i],root[i-1],getid(a[i])); 59 } 60 while(m--){ 61 int x,y,k; 62 scanf("%d%d%d",&x,&y,&k); 63 printf("%d\n",vec[query(1,n,root[x-1],root[y],k)-1]); 64 } 65 }