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Find k-th smallest element in given n ranges
• Difficulty Level : Medium
• Last Updated : 02 Mar, 2021

Given n and q, i.e, the number of ranges and number of queries, find the kth smallest element for each query (assume k>1).Print the value of kth smallest element if it exists, else print -1.

Examples :

```Input : arr[] = {{1, 4}, {6, 8}}
queries[] = {2, 6, 10};
Output : 2
7
-1
After combining the given ranges, the numbers
become 1 2 3 4 6 7 8. As here 2nd element is 2,
so we print 2. As 6th element is 7, so we print
7 and as 10th element doesn't exist, so we
print -1.

Input : arr[] = {{2, 6}, {5, 7}}
queries[] = {5, 8};
Output : 6
-1
After combining the given ranges, the numbers
become 2 3 4 5 6 7. As here 5th element is 6,
so we print 6 and as 8th element doesn't exist,
so we print -1.```

The idea is to first Prerequisite : Merge Overlapping Intervals and keep all intervals sorted in ascending order of start time. After merging in an array merged[], we use linear search to find kth smallest element.

Below is the implementation of the above approach :

## C++

 `// C++ implementation to solve k queries``// for given n ranges``#include ``using` `namespace` `std;` `// Structure to store the``// start and end point``struct` `Interval``{``    ``int` `s;``    ``int` `e;``};` `// Comparison function for sorting``bool` `comp(Interval a, Interval b)``{``    ``return` `a.s < b.s;``}` `// Function to find Kth smallest number in a vector``// of merged intervals``int` `kthSmallestNum(vector merged, ``int` `k)``{``    ``int` `n = merged.size();` `    ``// Traverse merged[] to find``    ``// Kth smallest element using Linear search.``    ``for` `(``int` `j = 0; j < n; j++)``    ``{``        ``if` `(k <= ``abs``(merged[j].e -``                     ``merged[j].s + 1))``            ``return` `(merged[j].s + k - 1);` `        ``k = k - ``abs``(merged[j].e -``                     ``merged[j].s + 1);``    ``}` `    ``if` `(k)``        ``return` `-1;``}` `// To combined both type of ranges,``// overlapping as well as non-overlapping.``void` `mergeIntervals(vector &merged,``                 ``Interval arr[], ``int` `n)``{``    ``// Sorting intervals according to start``    ``// time``    ``sort(arr, arr + n, comp);` `    ``// Merging all intervals into merged``    ``merged.push_back(arr);``    ``for` `(``int` `i = 1; i < n; i++)``    ``{``        ``// To check if starting point of next``        ``// range is lying between the previous``        ``// range and ending point of next range``        ``// is greater than the Ending point``        ``// of previous range then update ending``        ``// point of previous range by ending``        ``// point of next range.``        ``Interval prev = merged.back();``        ``Interval curr = arr[i];``        ``if` `((curr.s >= prev.s &&``             ``curr.s <= prev.e) &&``            ``(curr.e > prev.e))` `            ``merged.back().e = curr.e;` `        ``else``        ``{``            ``// If starting point of next range``            ``// is greater than the ending point``            ``// of previous range then store next range``            ``// in merged[].``            ``if` `(curr.s > prev.e)``                ``merged.push_back(curr);``        ``}``    ``}``}` `// Driver\'s Function``int` `main()``{``    ``Interval arr[] = {{2, 6}, {4, 7}};``    ``int` `n = ``sizeof``(arr)/``sizeof``(arr);``    ``int` `query[] = {5, 8};``    ``int` `q = ``sizeof``(query)/``sizeof``(query);` `    ``// Merge all intervals into merged[]``    ``vectormerged;``    ``mergeIntervals(merged, arr, n);` `    ``// Processing all queries on merged``    ``// intervals``    ``for` `(``int` `i = 0; i < q; i++)``        ``cout << kthSmallestNum(merged, query[i])``             ``<< endl;` `    ``return` `0;``}`

## Java

 `// Java implementation to solve k queries``// for given n ranges``import` `java.util.*;` `class` `GFG``{` `// Structure to store the``// start and end point``static` `class` `Interval``{``    ``int` `s;``    ``int` `e;``    ``Interval(``int` `a,``int` `b)``    ``{``        ``s = a;``        ``e = b;``    ``}``};``static` `class` `Sortby ``implements` `Comparator``{``    ``// Comparison function for sorting``    ``public` `int` `compare(Interval a, Interval b)``    ``{``        ``return` `a.s - b.s;``    ``}``}` `// Function to find Kth smallest number in a Vector``// of merged intervals``static` `int` `kthSmallestNum(Vector merged, ``int` `k)``{``    ``int` `n = merged.size();` `    ``// Traverse merged.get( )o find``    ``// Kth smallest element using Linear search.``    ``for` `(``int` `j = ``0``; j < n; j++)``    ``{``        ``if` `(k <= Math.abs(merged.get(j).e -``                    ``merged.get(j).s + ``1``))``            ``return` `(merged.get(j).s + k - ``1``);` `        ``k = k - Math.abs(merged.get(j).e -``                    ``merged.get(j).s + ``1``);``    ``}` `    ``if` `(k != ``0``)``        ``return` `-``1``;``    ``return` `0``;``}` `// To combined both type of ranges,``// overlapping as well as non-overlapping.``static` `Vector mergeIntervals(Vector merged,``                ``Interval arr[], ``int` `n)``{``    ``// Sorting intervals according to start``    ``// time``    ``Arrays.sort(arr, ``new` `Sortby());` `    ``// Merging all intervals into merged``    ``merged.add(arr[``0``]);``    ``for` `(``int` `i = ``1``; i < n; i++)``    ``{``        ``// To check if starting point of next``        ``// range is lying between the previous``        ``// range and ending point of next range``        ``// is greater than the Ending point``        ``// of previous range then update ending``        ``// point of previous range by ending``        ``// point of next range.``        ``Interval prev = merged.get(merged.size() - ``1``);``        ``Interval curr = arr[i];``        ``if` `((curr.s >= prev.s &&``            ``curr.s <= prev.e) &&``            ``(curr.e > prev.e))` `            ``merged.get(merged.size()-``1``).e = curr.e;` `        ``else``        ``{``            ``// If starting point of next range``            ``// is greater than the ending point``            ``// of previous range then store next range``            ``// in merged.get(.)         if (curr.s > prev.e)``                ``merged.add(curr);``        ``}``    ``}``    ``return` `merged;``}` `// Driver code``public` `static` `void` `main(String args[])``{``    ``Interval arr[] = {``new` `Interval(``2``, ``6``), ``new` `Interval(``4``, ``7``)};``    ``int` `n = arr.length;``    ``int` `query[] = {``5``, ``8``};``    ``int` `q = query.length;` `    ``// Merge all intervals into merged.get())``    ``Vector merged = ``new` `Vector();``    ``merged=mergeIntervals(merged, arr, n);` `    ``// Processing all queries on merged``    ``// intervals``    ``for` `(``int` `i = ``0``; i < q; i++)``        ``System.out.println( kthSmallestNum(merged, query[i]));``}``}` `// This code is contributed by Arnab Kundu`

## Python3

 `# Python3 implementation to solve k queries``# for given n ranges` `# Structure to store the``# start and end point``class` `Interval:``    ``def` `__init__(``self``, s, e):``        ``self``.s ``=` `s``        ``self``.e ``=` `e` `# Function to find Kth smallest number in a vector``# of merged intervals``def` `kthSmallestNum(merged: ``list``, k: ``int``) ``-``> ``int``:``    ``n ``=` `len``(merged)` `    ``# Traverse merged[] to find``    ``# Kth smallest element using Linear search.``    ``for` `j ``in` `range``(n):``        ``if` `k <``=` `abs``(merged[j].e ``-` `merged[j].s ``+` `1``):``            ``return` `merged[j].s ``+` `k ``-` `1` `        ``k ``=` `k ``-` `abs``(merged[j].e ``-` `merged[j].s ``+` `1``)` `    ``if` `k:``        ``return` `-``1` `# To combined both type of ranges,``# overlapping as well as non-overlapping.``def` `mergeIntervals(merged: ``list``, arr: ``list``, n: ``int``):` `    ``# Sorting intervals according to start``    ``# time``    ``arr.sort(key ``=` `lambda` `a: a.s)` `    ``# Merging all intervals into merged``    ``merged.append(arr[``0``])``    ``for` `i ``in` `range``(``1``, n):` `        ``# To check if starting point of next``        ``# range is lying between the previous``        ``# range and ending point of next range``        ``# is greater than the Ending point``        ``# of previous range then update ending``        ``# point of previous range by ending``        ``# point of next range.``        ``prev ``=` `merged[``-``1``]``        ``curr ``=` `arr[i]``        ``if` `curr.s >``=` `prev.s ``and` `curr.s <``=` `prev.e ``and``\``          ``curr.e > prev.e:``            ``merged[``-``1``].e ``=` `curr.e``        ``else``:` `            ``# If starting point of next range``            ``# is greater than the ending point``            ``# of previous range then store next range``            ``# in merged[].``            ``if` `curr.s > prev.e:``                ``merged.append(curr)` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:` `    ``arr ``=` `[Interval(``2``, ``6``), Interval(``4``, ``7``)]``    ``n ``=` `len``(arr)``    ``query ``=` `[``5``, ``8``]``    ``q ``=` `len``(query)` `    ``# Merge all intervals into merged[]``    ``merged ``=` `[]``    ``mergeIntervals(merged, arr, n)` `    ``# Processing all queries on merged``    ``# intervals``    ``for` `i ``in` `range``(q):``        ``print``(kthSmallestNum(merged, query[i]))` `# This code is contributed by``# sanjeev2552`

## C#

 `// C# implementation to solve k queries``// for given n ranges``using` `System;``using` `System.Collections;``using` `System.Collections.Generic;`` ` `class` `GFG{`` ` `// Structure to store the``// start and end point``public` `class` `Interval``{``    ``public` `int` `s;``    ``public` `int` `e;``    ` `    ``public` `Interval(``int` `a, ``int` `b)``    ``{``        ``s = a;``        ``e = b;``    ``}``};` `class` `sortHelper : IComparer``{``    ``int` `IComparer.Compare(``object` `a, ``object` `b)``    ``{``        ``Interval first = (Interval)a;``        ``Interval second = (Interval)b;``        ``return` `first.s - second.s;``    ``}``}` `// Function to find Kth smallest number in``// a Vector of merged intervals``static` `int` `kthSmallestNum(ArrayList merged, ``int` `k)``{``    ``int` `n = merged.Count;``    ` `    ``// Traverse merged.get( )o find``    ``// Kth smallest element using Linear search.``    ``for``(``int` `j = 0; j < n; j++)``    ``{``        ``if` `(k <= Math.Abs(((Interval)merged[j]).e -``                          ``((Interval)merged[j]).s + 1))``            ``return` `(((Interval)merged[j]).s + k - 1);`` ` `        ``k = k - Math.Abs(((Interval)merged[j]).e -``                         ``((Interval)merged[j]).s + 1);``    ``}`` ` `    ``if` `(k != 0)``        ``return` `-1;``        ` `    ``return` `0;``}`` ` `// To combined both type of ranges,``// overlapping as well as non-overlapping.``static` `ArrayList mergeIntervals(ArrayList merged,``                                ``Interval []arr, ``int` `n)``{``    ` `    ``// Sorting intervals according to start``    ``// time``    ``Array.Sort(arr, ``new` `sortHelper());``    ` `    ``// Merging all intervals into merged``    ``merged.Add((Interval)arr);``    ` `    ``for``(``int` `i = 1; i < n; i++)``    ``{``        ` `        ``// To check if starting point of next``        ``// range is lying between the previous``        ``// range and ending point of next range``        ``// is greater than the Ending point``        ``// of previous range then update ending``        ``// point of previous range by ending``        ``// point of next range.``        ``Interval prev = (Interval)merged[merged.Count - 1];``        ``Interval curr = arr[i];``        ` `        ``if` `((curr.s >= prev.s && curr.s <= prev.e) &&``            ``(curr.e > prev.e))``        ``{``            ``((Interval)merged[merged.Count - 1]).e = ((Interval)curr).e;``        ``}``        ``else``        ``{``            ` `            ``// If starting point of next range``            ``// is greater than the ending point``            ``// of previous range then store next range``            ``// in merged.get(.) if (curr.s > prev.e)``            ``merged.Add(curr);``        ``}``    ``}``    ``return` `merged;``}`` ` `// Driver code``public` `static` `void` `Main(``string` `[]args)``{``    ``Interval []arr = { ``new` `Interval(2, 6),``                       ``new` `Interval(4, 7) };``    ``int` `n = arr.Length;``    ``int` `[]query = { 5, 8 };``    ``int` `q = query.Length;``    ` `    ``// Merge all intervals into merged.get())``    ``ArrayList merged = ``new` `ArrayList();``    ` `    ``merged = mergeIntervals(merged, arr, n);``    ` `    ``// Processing all queries on merged``    ``// intervals``    ``for``(``int` `i = 0; i < q; i++)``        ``Console.WriteLine(kthSmallestNum(``            ``merged, query[i]));``}``}` `// This code is contributed by pratham76`

Output:

``` 6
-1```

Time Complexity : O(nlog(n))
Auxiliary Space: O(n)

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