Given an array of intervals arr[] of size N, the task is to find the Kth smallest element among all the elements within the intervals of the given array.
Examples:
_Input : _arr[] = {{5, 11}, {10, 15}, {12, 20}}, K =12
_Output: _13
_Explanation: _Elements in the given array of intervals are: {5, 6, 7, 8, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 17, 18, 19, 20}.
Therefore, the Kth(=12th) smallest element is 13.
_Input: _arr[] = {{5, 11}, {10, 15}, {12, 20}}, K = 7
Output:10
Recommended: Please try your approach on {IDE} first, before moving on to the solution.
**Naive Approach: **The simplest approach is to generate a new array consisting of all the elements from the array of intervals. Sort the new array. Finally, return the Kth smallest element of the array.
Time Complexity: O(X*Log(X)), where **X **is the total number of elements in the intervals.
Auxiliary Space: O(X*log(X))
Efficient approach: To optimize the above approach, the idea is to use MinHeap. Follow the steps below to solve the problem.
- Create a MinHeap, say **pq **to store all the intervals of the given array so that it returns the minimum element among all the elements of remaining intervals in O(1).
- Pop the minimum interval from the MinHeap and check if the minimum element of the popped interval is less than the maximum element of the popped interval. If found to be true, then insert a new interval {minimum element of popped interval + 1, maximum element of the popped interval}.
- Repeat the above step K – 1 times.
- Finally, return the minimum element of the popped interval.
Below is the implementation of the above approach:
- C++14
- Java
filter_none
edit
play_arrow
brightness_4
// C++ Program to implement
// the above approach
#include <bits/stdc++.h>
**using** **namespace** std;
// Function to get the Kth smallest
// element from an array of intervals
**int** KthSmallestNum(pair<``**int**``, **int**``> arr[],
**int** n, **int** k)
{
// Store all the intervals so that it
// returns the minimum element in O(1)
priority_queue<pair<``**int**``, **int**``>,
vector<pair<``**int**``, **int**``> >,
greater<pair<``**int**``, **int**``> > >
pq;
// Insert all Intervals into the MinHeap
**for** (``**int** i = 0; i < n; i++) {
pq.push({ arr[i].first,
arr[i].second });
}
// Stores the count of
// popped elements
**int** cnt = 1;
// Iterate over MinHeap
**while** (cnt < k) {
// Stores minimum element
// from all remaining intervals
pair<``**int**``, **int**``> interval
= pq.top();
// Remove minimum element
pq.pop();
// Check if the minimum of the current
// interval is less than the maximum
// of the current interval
**if** (interval.first < interval.second) {
// Insert new interval
pq.push(
{ interval.first + 1,
interval.second });
}
cnt++;
}
**return** pq.top().first;
}
// Driver Code
**int** main()
{
// Intervals given
pair<``**int**``, **int**``> arr[]
= { { 5, 11 },
{ 10, 15 },
{ 12, 20 } };
// Size of the arr
**int** n = **sizeof**``(arr) / **sizeof**``(arr[0]);
**int** k = 12;
cout << KthSmallestNum(arr, n, k);
}
#arrays #heap #mathematical #sorting #amazon #amazon-question #min-heap #priority-queue
