Algorithm
problem link- https://www.spoj.com/problems/MKTHNUM/
MKTHNUM - K-th Number
| English | Vietnamese |
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.
Input
The first line of the input contains n — the size of the array, and m — the number of questions to answer (1 ≤ n ≤ 100000, 1 ≤ m ≤ 5000).
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.
Example
Input: 7 3 1 5 2 6 3 7 4 2 5 3 4 4 1 1 7 3 Output: 5 6 3
Code Examples
#1 Code Example with C++ Programming
Code -
C++ Programming
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define MOD 1000000007LL
#define EPS 1e-9
#define io ios_base::sync_with_stdio(false);cin.tie(NULL);
#define M_PI 3.14159265358979323846
const int MAXN = 1e5+5;
int n, m;
vector<int> tree[4*MAXN];
vector<pair<int, int> > table;
int arr[MAXN];
void build(int node, int start, int end){
if(start > end) return;
if(start==end){
tree[node].push_back(table[start].second);
return;
}
int mid = (start + end) >> 1;
int left = node << 1, right = left + 1;
build(left, start, mid);
build(right, mid + 1, end);
merge(tree[left].begin(), tree[left].end(), tree[right].begin(), tree[right].end(), back_inserter(tree[node]));
}
int query(int node, int start, int end, int l, int r, int k){
if(start == end)
return tree[node][0];
int mid = (start + end) >> 1;
int left = node << 1, right = left + 1;
auto it = upper_bound(tree[left].begin(), tree[left].end(), r);
int total = it - lower_bound(tree[left].begin(), tree[left].end(), l);
if(total >= k){
return query(left, start, mid, l, r, k);
}else{
return query(right, mid + 1, end, l, r, k - total);
}
}
int main(){
io;
cin >> n >> m;
for(int i = 0; i < n; i++){
int x;
cin >> x;
arr[i] = x;
table.push_back({x, i});
}
sort(table.begin(), table.end());
build(1, 0, n - 1);
for(int i = 0; i < m; i++){
int l, r, k;
cin >> l >> r >> k;
--l, --r;
int idx = query(1, 0, n - 1, l, r, k);
cout << arr[idx] << endl;
}
return 0;
}Input
1 5 2 6 3 7 4
2 5 3
4 4 1
1 7 3
Output
6
3
Demonstration
SPOJ Solution-K-th Number-Solution in C, C++, Java, Python