# Kth largest even number in N intervals

Given a 2D array arr[] of N ranges, indicating integer intervals from L to R inclusive, and a number K, the task is to find Kth largest even number.

Examples:

Input: arr = {{12, 15}, {3, 9}, {2, 5}, {20, 25}, {16, 20}}, K = 9
Output: 6
Explanation: After merging, the ranges become {{2, 9}, {12, 25}} the, even numbers present in the ranges are {2, 4, 6, 8, 12, 14, 16, 18, 20, 22, 24} and the 9th largest even number is 6

Input: arr = {{2, 4}, {8, 12}}, K = 4
Output: 4

Approach: The given problem can be solved by using the approach of merging overlapping Intervals. The idea is to sort the intervals with respect to the lower limit of the range and merge them to remove repetition of the integers. Then the below steps can be followed to solve the problem:

• If K<=0 or N=0 then return -1
• Initialize, L = arr[i].first and R = arr[i].second
• Initialize a variable range, to store even numbers within the range
• Iterate in a loop from idx to 0
• If R is odd
• range = floor((R – L + 1) / 2)
• If, K > range K =  K – range
• Else return R – 2 * K + 1
• If R is even
• range = ceil((float)(R – L + 1) / 2)
• If, K > range K =  K – range
• Else, R – 2 * K + 2
• Return -1

Below is the implementation of the above approach:

## C++

 `// C++ implementation for the above approach` `#include ` `#include ` `using` `namespace` `std;`   `// Function to merge overlapping intervals` `// and return the Kth largest even number` `int` `calcEven(vector > V,` `             ``int` `N, ``int` `k)` `{`   `    ``// Base Case` `    ``if` `(k <= 0 || N == 0)` `        ``return` `-1;`   `    ``// Sort the intervals in increasing order` `    ``// according to their first element` `    ``sort(V.begin(), V.end());`   `    ``int` `i, idx = 0;`   `    ``// Merging the overlapping intervals` `    ``for` `(i = 1; i < N; i++) {`   `        ``// If it overlaps with` `        ``// the previous intervals` `        ``if` `((V[idx].second >= V[i].first)` `            ``|| (V[i].first == V[idx].second + 1)) {`   `            ``// Merge previous and current intervals` `            ``V[idx].second = max(V[idx].second,` `                                ``V[i].second);` `        ``}` `        ``else` `{`   `            ``// Increment the index` `            ``idx++;`   `            ``V[idx].second = V[i].second;` `            ``V[idx].first = V[i].first;` `        ``}` `    ``}`   `    ``// Find Kth largest even number` `    ``for` `(i = idx; i >= 0; i--) {`   `        ``// Initialize L and R` `        ``int` `L = V[i].first;` `        ``int` `R = V[i].second;`   `        ``// If R is odd` `        ``if` `(R & 1) {`   `            ``// Calculate number of even` `            ``// numbers within the range` `            ``int` `range = (R - L + 1) / 2;`   `            ``// if k > range then kth largest` `            ``// even number is not in this range` `            ``if` `(k > range) {`   `                ``k -= range;` `            ``}` `            ``else` `                ``return` `(R - 2 * k + 1);` `        ``}` `        ``else` `{`   `            ``// Calculate number of even` `            ``// numbers within the range` `            ``int` `range = ``ceil``((``float``)(R - L + 1) / 2);`   `            ``// if k > range then kth largest` `            ``// even number is not in this range` `            ``if` `(k > range) {`   `                ``k -= range;` `            ``}` `            ``else` `                ``return` `(R - 2 * k + 2);` `        ``}` `    ``}`   `    ``// No Kth even number in the range` `    ``// so return -1` `    ``return` `-1;` `}`   `// Driver Code` `int` `main()` `{`   `    ``// Initialize the ranges` `    ``vector > vec = { { 12, 15 },` `                                    ``{ 3, 9 },` `                                    ``{ 2, 5 },` `                                    ``{ 20, 25 },` `                                    ``{ 16, 20 } };`   `    ``int` `N = vec.size();`   `    ``// Initialize K` `    ``int` `K = 9;`   `    ``// Print the answer` `    ``cout << calcEven(vec, N, K);`   `    ``return` `0;` `}`

## Java

 `// Java implementation for the above approach` `import` `java.util.ArrayList;` `import` `java.util.Collections;` `import` `java.util.Comparator;`   `class` `GFG {`   `  ``static` `class` `Pair {` `    ``int` `first = ``0``;` `    ``int` `second = ``0``;`   `    ``public` `Pair(``int` `first, ``int` `second) {` `      ``this``.first = first;` `      ``this``.second = second;` `    ``}` `  ``}`   `  ``// Function to merge overlapping intervals` `  ``// and return the Kth largest even number` `  ``public` `static` `int` `calcEven(ArrayList V, ``int` `N, ``int` `k) {`   `    ``// Base Case` `    ``if` `(k <= ``0` `|| N == ``0``)` `      ``return` `-``1``;`   `    ``// Sort the intervals in increasing order` `    ``// according to their first element` `    ``Collections.sort(V, ``new` `Comparator() {` `      ``@Override` `      ``public` `int` `compare(Pair p1, Pair p2) {` `        ``return` `p1.first - p2.first;` `      ``}` `    ``});`   `    ``int` `i, idx = ``0``;`   `    ``// Merging the overlapping intervals` `    ``for` `(i = ``1``; i < N; i++) {`   `      ``// If it overlaps with` `      ``// the previous intervals` `      ``if` `((V.get(idx).second >= V.get(i).first) || (V.get(i).first == V.get(idx).second + ``1``)) {`   `        ``// Merge previous and current intervals` `        ``V.get(idx).second = Math.max(V.get(idx).second, V.get(i).second);` `      ``} ``else` `{`   `        ``// Increment the index` `        ``idx++;`   `        ``V.get(idx).second = V.get(i).second;` `        ``V.get(idx).first = V.get(i).first;` `      ``}` `    ``}`   `    ``// Find Kth largest even number` `    ``for` `(i = idx; i >= ``0``; i--) {`   `      ``// Initialize L and R` `      ``int` `L = V.get(i).first;` `      ``int` `R = V.get(i).second;`   `      ``// If R is odd` `      ``if` `((R & ``1``) > ``0``) {`   `        ``// Calculate number of even` `        ``// numbers within the range` `        ``int` `range = (R - L + ``1``) / ``2``;`   `        ``// if k > range then kth largest` `        ``// even number is not in this range` `        ``if` `(k > range) {`   `          ``k -= range;` `        ``} ``else` `          ``return` `(R - ``2` `* k + ``1``);` `      ``} ``else` `{`   `        ``// Calculate number of even` `        ``// numbers within the range` `        ``int` `range = (``int``) Math.ceil((R - L + ``1``) / ``2``);`   `        ``// if k > range then kth largest` `        ``// even number is not in this range` `        ``if` `(k > range) {`   `          ``k -= range;` `        ``} ``else` `          ``return` `(R - ``2` `* k + ``2``);` `      ``}` `    ``}`   `    ``// No Kth even number in the range` `    ``// so return -1` `    ``return` `-``1``;` `  ``}`   `  ``// Driver Code` `  ``public` `static` `void` `main(String args[]) {`   `    ``// Initialize the ranges` `    ``ArrayList vec = ``new` `ArrayList();`   `    ``vec.add(``new` `Pair(``12``, ``15``));` `    ``vec.add(``new` `Pair(``3``, ``9``));` `    ``vec.add(``new` `Pair(``2``, ``5``));` `    ``vec.add(``new` `Pair(``20``, ``25``));` `    ``vec.add(``new` `Pair(``16``, ``20``));`   `    ``int` `N = vec.size();`   `    ``// Initialize K` `    ``int` `K = ``9``;`   `    ``// Print the answer` `    ``System.out.println(calcEven(vec, N, K));` `  ``}` `}`   `// This code is contributed by gfgking.`

## Python3

 `# python implementation for the above approach` `import` `math`   `# Function to merge overlapping intervals` `# and return the Kth largest even number` `def` `calcEven(V, N, k):`   `    ``# Base Case` `    ``if` `(k <``=` `0` `or` `N ``=``=` `0``):` `        ``return` `-``1`   `    ``# Sort the intervals in increasing order` `    ``# according to their first element` `    ``V.sort()`   `    ``idx ``=` `0`   `    ``# Merging the overlapping intervals` `    ``for` `i ``in` `range``(``1``, N):`   `        ``# If it overlaps with` `        ``# the previous intervals` `        ``if` `((V[idx][``1``] >``=` `V[i][``0``]) ``or` `(V[i][``0``] ``=``=` `V[idx][``1``] ``+` `1``)):`   `            ``# Merge previous and current intervals` `            ``V[idx][``1``] ``=` `max``(V[idx][``1``], V[i][``1``])`   `        ``else``:`   `           ``# Increment the index` `            ``idx ``+``=` `1`   `            ``V[idx][``1``] ``=` `V[i][``1``]` `            ``V[idx][``0``] ``=` `V[i][``0``]`   `        ``# Find Kth largest even number` `    ``for` `i ``in` `range``(idx, ``-``1``, ``-``1``):`   `        ``# Initialize L and R` `        ``L ``=` `V[i][``0``]` `        ``R ``=` `V[i][``1``]`   `        ``# If R is odd` `        ``if` `(R & ``1``):`   `            ``# Calculate number of even` `            ``# numbers within the range` `            ``rng ``=` `(R ``-` `L ``+` `1``) ``/``/` `2`   `            ``# if k > range then kth largest` `            ``# even number is not in this range` `            ``if` `(k > rng):` `                ``k ``-``=` `rng`   `            ``else``:` `                ``return` `(R ``-` `2` `*` `k ``+` `1``)`   `        ``else``:`   `            ``# Calculate number of even` `            ``# numbers within the range` `            ``rng ``=` `math.ceil((R ``-` `L ``+` `1``) ``/` `2``)`   `            ``# if k > range then kth largest` `            ``# even number is not in this range` `            ``if` `(k > rng):` `                ``k ``-``=` `rng`   `            ``else``:` `                ``return` `(R ``-` `2` `*` `k ``+` `2``)`   `        ``# No Kth even number in the range` `        ``# so return -1` `    ``return` `-``1`   `# Driver Code` `if` `__name__ ``=``=` `"__main__"``:`   `   ``# Initialize the ranges` `    ``vec ``=` `[[``12``, ``15``], [``3``, ``9``], [``2``, ``5``], [``20``, ``25``], [``16``, ``20``]]`   `    ``N ``=` `len``(vec)`   `    ``# Initialize K` `    ``K ``=` `9`   `    ``# Print the answer` `    ``print``(calcEven(vec, N, K))`   `    ``# This code is contributed by rakeshsahni`

## Javascript

 ``

## C#

 `// C# implementation of the above approach` `using` `System;` `using` `System.Collections.Generic;` `using` `System.Linq;` `public` `class` `GFG` `{` `  ``static` `void` `Main(``string``[] args)` `  ``{` `    ``// Initialize the ranges` `    ``List> vec = ``new` `List> { ` `      ``Tuple.Create(12, 15),` `      ``Tuple.Create(3, 9),` `      ``Tuple.Create(2, 5),` `      ``Tuple.Create(20, 25),` `      ``Tuple.Create(16, 20) ` `      ``};`   `    ``int` `N = vec.Count;`   `    ``// Initialize K` `    ``int` `K = 9;`   `    ``// Print the answer` `    ``Console.WriteLine(CalcEven(vec, N, K));` `  ``}`   `  ``// Function to merge overlapping intervals` `  ``// and return the Kth largest even number` `  ``static` `int` `CalcEven(List> V, ``int` `N, ``int` `k)` `  ``{` `    ``// Base Case` `    ``if` `(k <= 0 || N == 0)` `      ``return` `-1;`   `    ``// Sort the intervals in increasing order` `    ``// according to their first element` `    ``V = V.OrderBy(x => x.Item1).ToList();`   `    ``int` `i, idx = 0;`   `    ``// Merging the overlapping intervals` `    ``for` `(i = 1; i < N; i++)` `    ``{` `      ``// If it overlaps with` `      ``// the previous intervals` `      ``if` `((V[idx].Item2 >= V[i].Item1)` `          ``|| (V[i].Item1 == V[idx].Item2 + 1))` `      ``{` `        ``// Merge previous and current intervals` `        ``V[idx] = Tuple.Create(V[idx].Item1, Math.Max(V[idx].Item2, V[i].Item2));` `      ``}` `      ``else` `      ``{` `        ``// Increment the index` `        ``idx++;`   `        ``V[idx] = Tuple.Create(V[i].Item1, V[i].Item2);` `      ``}` `    ``}`   `    ``// Find Kth largest even number` `    ``for` `(i = idx; i >= 0; i--)` `    ``{` `      ``// Initialize L and R` `      ``int` `L = V[i].Item1;` `      ``int` `R = V[i].Item2;`   `      ``// If R is odd` `      ``if` `(R % 2 != 0)` `      ``{` `        ``// Calculate number of even` `        ``// numbers within the range` `        ``int` `range = (R - L + 1) / 2;`   `        ``// if k > range then kth largest` `        ``// even number is not in this range` `        ``if` `(k > range)` `        ``{` `          ``k -= range;` `        ``}` `        ``else` `          ``return` `(R - 2 * k + 1);` `      ``}` `      ``else` `      ``{` `        ``// Calculate number of even` `        ``// numbers within the range` `        ``int` `range = (``int``)Math.Ceiling((``double``)(R - L + 1) / 2);`   `        ``// if k > range then kth largest` `        ``// even number is not in this range` `        ``if` `(k > range)` `        ``{` `          ``k -= range;` `        ``}` `        ``else` `          ``return` `(R - 2 * k +2);` `      ``}` `    ``}`   `    ``return` `-1 ;` `  ``}` `}`

Output

`6`

Time Complexity: O(N*log N)
Auxiliary Space: O(1)

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