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Find Non-overlapping intervals among a given set of intervals
• Last Updated : 28 Aug, 2020

Given N set of time intervals, the task is to find the intervals which don’t overlap with the given set of intervals.

Examples:

Input: interval arr[] = { {1, 3}, {2, 4}, {3, 5}, {7, 9} }
Output:
[5, 7]
Explanation:
The only interval which doesn’t overlaps with the other intervals is [5, 7].

Input: interval arr[] = { {1, 3}, {9, 12}, {2, 4}, {6, 8} }
Output:
[4, 6]
[8, 9]
Explanation:
There are two intervals which don’t overlap with other intervals are [4, 6], [8, 9].

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The idea is to sort the given time intervals according to starting time and if the consecutive intervals don’t overlap then the difference between them is the free interval.
Below are the steps:

1. Sort the given set of intervals according to starting time.
2. Traverse all the set of intervals and check whether the consecutive intervals overlaps or not.
3. If the intervals(say interval a & interval b) doesn’t overlap then the set of pairs form by [a.end, b.start] is the non-overlapping interval.
4. If the intervals overlaps, then check for next consecutive intervals.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach`` ` `#include "bits/stdc++.h"``using` `namespace` `std;`` ` `// interval with start time & end time``struct` `interval {``    ``int` `start, end;``};`` ` `// Comparator function to sort the given``// interval according to time``bool` `compareinterval(interval i1, interval i2)``{``    ``return` `(i1.start < i2.start);``}`` ` `// Function that find the free interval``void` `findFreeinterval(interval arr[], ``int` `N)``{`` ` `    ``// If there are no set of interval``    ``if` `(N <= 0) {``        ``return``;``    ``}`` ` `    ``// To store the set of free interval``    ``vector > P;`` ` `    ``// Sort the given interval according``    ``// starting time``    ``sort(arr, arr + N, compareinterval);`` ` `    ``// Iterate over all the interval``    ``for` `(``int` `i = 1; i < N; i++) {`` ` `        ``// Previous interval end``        ``int` `prevEnd = arr[i - 1].end;`` ` `        ``// Current interval start``        ``int` `currStart = arr[i].start;`` ` `        ``// If ending index of previous``        ``// is less than starting index``        ``// of current, then it is free``        ``// interval``        ``if` `(prevEnd < currStart) {``            ``P.push_back({ prevEnd,``                          ``currStart });``        ``}``    ``}`` ` `    ``// Print the free interval``    ``for` `(``auto``& it : P) {``        ``cout << ``"["` `<< it.first << ``", "``             ``<< it.second << ``"]"` `<< endl;``    ``}``}`` ` `// Driver Code``int` `main()``{`` ` `    ``// Given set of interval``    ``interval arr[] = { { 1, 3 },``                       ``{ 2, 4 },``                       ``{ 3, 5 },``                       ``{ 7, 9 } };`` ` `    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr[0]);`` ` `    ``// Function Call``    ``findFreeinterval(arr, N);``    ``return` `0;``}`

## Python3

 `# Python3 program for the above approach ``def` `findFreeinterval(arr, N):``     ` `    ``# If there are no set of interval``    ``if` `N < ``1``:``        ``return``     ` `    ``# To store the set of free interval``    ``P ``=` `[]``     ` `    ``# Sort the given interval according ``    ``# Starting time ``    ``arr.sort(key ``=` `lambda` `a:a[``0``])``     ` `    ``# Iterate over all the interval ``    ``for` `i ``in` `range``(``1``, N):``         ` `        ``# Previous interval end ``        ``prevEnd ``=` `arr[i ``-` `1``][``1``]``         ` `        ``# Current interval start ``        ``currStart ``=` `arr[i][``0``]``         ` `        ``# If Previous Interval is less ``        ``# than current Interval then we ``        ``# store that answer``        ``if` `prevEnd < currStart:``            ``P.append([prevEnd, currStart])``     ` `    ``# Print the intervals ``    ``for` `i ``in` `P:``        ``print``(i)``     ` `# Driver code ``if` `__name__ ``=``=` `"__main__"``:``     ` `    ``# Given List of intervals ``    ``arr ``=` `[ [ ``1``, ``3` `], [ ``2``, ``4` `],``            ``[ ``3``, ``5` `], [ ``7``, ``9` `] ]``     ` `    ``N ``=` `len``(arr)``     ` `    ``# Function call``    ``findFreeinterval(arr, N)``     ` `# This code is contributed by Tokir Manva`

## Java

 `// Java program for the above approach``import` `java.util.*;``class` `GFG {``     ` `// Interval with start time & end time``static` `class` `Interval``{``    ``int` `start, end;`` ` `    ``Interval(``int` `start, ``int` `end)``    ``{``        ``this``.start = start;``        ``this``.end = end;``    ``}``}`` ` `// Function that find the free interval``static` `void` `findFreeinterval(``int``[][] arr, ``int` `N)``{``    ``// If there are no set of interval``    ``if` `(N <= ``0``) ``    ``{``        ``return``;``    ``}`` ` `    ``// To store the set of free interval``    ``ArrayList p = ``new` `ArrayList<>();`` ` `    ``// Sort the given interval according``    ``// starting time``    ``Arrays.sort(arr, ``new` `Comparator<``int``[]>() ``    ``{``        ``public` `int` `compare(``int``[] a, ``int``[] b)``        ``{``            ``return` `a[``0``] - b[``0``];``        ``}``    ``});`` ` `    ``// Iterate over all the interval``    ``for` `(``int` `i = ``1``; i < N; i++) ``    ``{`` ` `        ``// Previous interval end``        ``int` `prevEnd = arr[i - ``1``][``1``];`` ` `        ``// Current interval start``        ``int` `currStart = arr[i][``0``];`` ` `        ``// If ending index of previous``        ``// is less than starting index``        ``// of current, then it is free``        ``// interval``        ``if` `(prevEnd < currStart) ``        ``{``            ``Interval interval = ``new` `Interval(prevEnd,``                                              ``currStart);``            ``p.add(interval);``        ``}``    ``}`` ` `    ``// Print the free interval``    ``for` `(``int` `i = ``0``; i < p.size(); i++)``    ``{``        ``System.out.println(``"["` `+ p.get(i).start + ``                          ``", "` `+ p.get(i).end + ``"]"``);``    ``}``}`` ` `// Driver code``public` `static` `void` `main(String[] args)``{`` ` `    ``// Given set of interval``    ``int``[][] arr = { { ``1``, ``3` `},``                    ``{ ``2``, ``4` `},``                    ``{ ``3``, ``5` `},``                    ``{ ``7``, ``9` `} };`` ` `    ``int` `N = arr.length;`` ` `    ``// Function Call``    ``findFreeinterval(arr, N);``}``}`` ` `// This code is contributed by offbeat`
Output:
```[5, 7]
```

Time Complexity: O(N*log N), where N is the number of set of intervals.

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