Check if any two intervals intersects among a given set of intervals

An interval is represented as a combination of start time and end time. Given a set of intervals, check if any two intervals intersect. 

Examples:

Input:  arr[] = {{1, 3}, {5, 7}, {2, 4}, {6, 8}}
Output: true
The intervals {1, 3} and {2, 4} overlap


Input:  arr[] = {{1, 3}, {7, 9}, {4, 6}, {10, 13}}
Output: false
No pair of intervals overlap. 

Expected time complexity is O(nLogn) where n is number of intervals.
We strongly recommend to minimize your browser and try this yourself first.
A Simple Solution is to consider every pair of intervals and check if the pair intersects or not. The time complexity of this solution is O(n²)

Method 1
A better solution is to Use Sorting. Following is complete algorithm. 
1) Sort all intervals in increasing order of start time. This step takes O(nLogn) time. 
2) In the sorted array, if start time of an interval is less than end of previous interval, then there is an overlap. This step takes O(n) time.
So overall time complexity of the algorithm is O(nLogn) + O(n) which is O(nLogn).

Below is the implementation of above idea.

C++

// A C++ program to check if any two intervals overlap
#include <algorithm>
#include <iostream>
using namespace std;

// An interval has start time and end time
struct Interval {
    int start;
    int end;
};

// Compares two intervals according to their starting time.
// This is needed for sorting the intervals using library
// function std::sort(). See http:// goo.gl/iGspV
bool compareInterval(Interval i1, Interval i2)
{
    return (i1.start < i2.start) ? true : false;
}

// Function to check if any two intervals overlap
bool isIntersect(Interval arr[], int n)
{
    // Sort intervals in increasing order of start time
    sort(arr, arr + n , compareInterval);

    // In the sorted array, if start time of an interval
    // is less than end of previous interval, then there
    // is an overlap
    for (int i = 1; i < n; i++)
        if (arr[i - 1].end > arr[i].start)
            return true;

    // If we reach here, then no overlap
    return false;
}

// Driver program
int main()
{
    Interval arr1[] = { { 1, 3 }, { 7, 9 }, { 4, 6 }, { 10, 13 } };
    int n1 = sizeof(arr1) / sizeof(arr1[0]);
    isIntersect(arr1, n1) ? cout << "Yes\n" : cout << "No\n";

    Interval arr2[] = { { 6, 8 }, { 1, 3 }, { 2, 4 }, { 4, 7 } };
    int n2 = sizeof(arr2) / sizeof(arr2[0]);
    isIntersect(arr2, n2) ? cout << "Yes\n" : cout << "No\n";

    return 0;
}

Java

// A Java program to check if any two intervals overlap
import java.io.*;
import java.lang.*;
import java.util.*;

class GFG{

// An interval has start time and end time
static class Interval
{
    int start;
    int end;

    public Interval(int start, int end)
    {
        super();
        this.start = start;
        this.end = end;
    }
};

// Function to check if any two intervals overlap
static boolean isIntersect(Interval arr[], int n)
{

    // Sort intervals in increasing order of start time
    Arrays.sort(arr, (i1, i2) -> {
        return i1.start - i2.start;
    });

    // In the sorted array, if start time of an interval
    // is less than end of previous interval, then there
    // is an overlap
    for(int i = 1; i < n; i++)
        if (arr[i - 1].end > arr[i].start)
            return true;

    // If we reach here, then no overlap
    return false;
}

// Driver code
public static void main(String[] args)
{
    Interval arr1[] = { new Interval(1, 3),
                        new Interval(7, 9),
                        new Interval(4, 6),
                        new Interval(10, 13) };
    int n1 = arr1.length;

    if (isIntersect(arr1, n1))
        System.out.print("Yes\n");
    else
        System.out.print("No\n");

    Interval arr2[] = { new Interval(6, 8),
                        new Interval(1, 3),
                        new Interval(2, 4),
                        new Interval(4, 7) };
    int n2 = arr2.length;

    if (isIntersect(arr2, n2))
        System.out.print("Yes\n");
    else
        System.out.print("No\n");
}
}

// This code is contributed by Kingash

Python3

# A Python program to check if any two intervals overlap

# An interval has start time and end time
class Interval:
    def __init__(self, start, end):
        self.start = start
        self.end = end

# Function to check if any two intervals overlap
def isIntersect(arr, n):

    # Sort intervals in increasing order of start time
    arr.sort(key=lambda x: x.start)

    # In the sorted array, if start time of an interval
    # is less than end of previous interval, then there
    # is an overlap
    for i in range(1, n):
        if (arr[i - 1].end > arr[i].start):
            return True

    # If we reach here, then no overlap
    return False

# Driver code
arr1 = [Interval(1, 3), Interval(7, 9), Interval(4, 6), Interval(10, 13)]
n1 = len(arr1)
if (isIntersect(arr1, n1)):
    print("Yes")
else:
    print("No")

arr2 = [Interval(6, 8), Interval(1, 3), Interval(2, 4), Interval(4, 7)]
n2 = len(arr2)

if (isIntersect(arr2, n2)):
    print("Yes")
else:
    print("No")

# This code is contributed by Saurabh Jaiswal

Javascript

<script>
// A Javascript program to check if any two intervals overlap

// An interval has start time and end time
class Interval
{
    constructor(start,end)
    {
        this.start = start;
        this.end = end;
    }
}

// Function to check if any two intervals overlap
function isIntersect(arr,n)
{
    // Sort intervals in increasing order of start time
    arr.sort(function(i1, i2){
        return i1.start - i2.start;
    });

    // In the sorted array, if start time of an interval
    // is less than end of previous interval, then there
    // is an overlap
    for(let i = 1; i < n; i++)
        if (arr[i - 1].end > arr[i].start)
            return true;

    // If we reach here, then no overlap
    return false;
}

// Driver code
let arr1=[new Interval(1, 3),
                        new Interval(7, 9),
                        new Interval(4, 6),
                        new Interval(10, 13) ];
let n1 = arr1.length;
if (isIntersect(arr1, n1))
    document.write("Yes<br>");
else
    document.write("No<br>");

let arr2 = [ new Interval(6, 8),
new Interval(1, 3),
new Interval(2, 4),
new Interval(4, 7) ];
let n2 = arr2.length;

if (isIntersect(arr2, n2))
    document.write("Yes<br>");
else
    document.write("No<br>");

// This code is contributed by rag2127
</script>

Output: 

No
Yes

Time Complexity:  O(nlogn)

Auxiliary Space: O(1)

Method 2: This approach is suggested by Anjali Agarwal. Following are the steps:  

1. Find the overall maximum element. Let it be max_ele 
2. Initialize an array of size max_ele with 0. 
3. For every interval [start, end], increment the value at index start, i.e. arr[start]++ and decrement the value at index (end + 1), i.e. arr[end + 1]- -. 
4. Compute the prefix sum of this array (arr[]). 
5. Every index, i of this prefix sum array will tell how many times i has occurred in all the intervals taken together. If this value is greater than 1, then it occurs in 2 or more intervals. 
6. So, simply initialize the result variable as false and while traversing the prefix sum array, change the result variable to true whenever the value at that index is greater than 1.  

Below is the implementation of this (Method 2) approach. 

C++

// A C++ program to check if any two intervals overlap
#include <algorithm>
#include <iostream>
using namespace std;

// An interval has start time and end time
struct Interval {
    int start;
    int end;
};

// Function to check if any two intervals overlap
bool isIntersect(Interval arr[], int n)
{

    int max_ele = 0;

    // Find the overall maximum element
    for (int i = 0; i < n; i++) {
        if (max_ele < arr[i].end)
            max_ele = arr[i].end;
    }

    // Initialize an array of size max_ele
    int aux[max_ele + 1] = { 0 };
    for (int i = 0; i < n; i++) {

        // starting point of the interval
        int x = arr[i].start;

        // end point of the interval
        int y = arr[i].end;
        aux[x]++, aux[y + 1]--;
    }
    for (int i = 1; i <= max_ele; i++) {
        // Calculating the prefix Sum
        aux[i] += aux[i - 1];

        // Overlap
        if (aux[i] > 1)
            return true;
    }

    // If we reach here, then no Overlap
    return false;
}

// Driver program
int main()
{
    Interval arr1[] = { { 1, 3 }, { 7, 9 }, { 4, 6 }, { 10, 13 } };
    int n1 = sizeof(arr1) / sizeof(arr1[0]);

    isIntersect(arr1, n1) ? cout << "Yes\n" : cout << "No\n";

    Interval arr2[] = { { 6, 8 }, { 1, 3 }, { 2, 4 }, { 4, 7 } };
    int n2 = sizeof(arr2) / sizeof(arr2[0]);
    isIntersect(arr2, n2) ? cout << "Yes\n" : cout << "No\n";

    return 0;
}
// This Code is written by Anjali Agarwal

Java

// A Java program to check if any two intervals overlap
class GFG
{

// An interval has start time and end time
static class Interval
{
    int start;
    int end;
    public Interval(int start, int end)
    {
        super();
        this.start = start;
        this.end = end;
    }
};

// Function to check if any two intervals overlap
static boolean isIntersect(Interval arr[], int n)
{

    int max_ele = 0;

    // Find the overall maximum element
    for (int i = 0; i < n; i++)
    {
        if (max_ele < arr[i].end)
            max_ele = arr[i].end;
    }

    // Initialize an array of size max_ele
    int []aux = new int[max_ele + 1];
    for (int i = 0; i < n; i++)
    {

        // starting point of the interval
        int x = arr[i].start;

        // end point of the interval
        int y = arr[i].end;
        aux[x]++;
        aux[y ]--;
    }
    for (int i = 1; i <= max_ele; i++)
    {
        // Calculating the prefix Sum
        aux[i] += aux[i - 1];

        // Overlap
        if (aux[i] > 1)
            return true;
    }

    // If we reach here, then no Overlap
    return false;
}

// Driver program
public static void main(String[] args)
{
    Interval arr1[] = { new Interval(1, 3), new Interval(7, 9),
                       new Interval(4, 6), new Interval(10, 13) };
    int n1 = arr1.length;

    if(isIntersect(arr1, n1))
        System.out.print("Yes\n");
    else
        System.out.print("No\n");

    Interval arr2[] = { new Interval(6, 8), new Interval(1, 3),
                        new Interval(2, 4), new Interval(4, 7) };
    int n2 = arr2.length;
    if(isIntersect(arr2, n2))
        System.out.print("Yes\n");
    else
        System.out.print("No\n");
}
}

// This code is contributed by 29AjayKumar

C#

// C# program to check if
// any two intervals overlap
using System;

class GFG
{

// An interval has start time and end time
class Interval
{
    public int start;
    public int end;
    public Interval(int start, int end)
    {
        this.start = start;
        this.end = end;
    }
};

// Function to check if
// any two intervals overlap
static bool isIntersect(Interval []arr, int n)
{
    int max_ele = 0;

    // Find the overall maximum element
    for (int i = 0; i < n; i++)
    {
        if (max_ele < arr[i].end)
            max_ele = arr[i].end;
    }

    // Initialize an array of size max_ele
    int []aux = new int[max_ele + 1];
    for (int i = 0; i < n; i++)
    {

        // starting point of the interval
        int x = arr[i].start;

        // end point of the interval
        int y = arr[i].end;
        aux[x]++;
        aux[y ]--;
    }

    for (int i = 1; i <= max_ele; i++)
    {
        // Calculating the prefix Sum
        aux[i] += aux[i - 1];

        // Overlap
        if (aux[i] > 1)
            return true;
    }

    // If we reach here, then no Overlap
    return false;
}

// Driver Code
public static void Main(String[] args)
{
    Interval []arr1 = { new Interval(1, 3),
                        new Interval(7, 9),
                        new Interval(4, 6),
                        new Interval(10, 13) };
    int n1 = arr1.Length;

    if(isIntersect(arr1, n1))
        Console.Write("Yes\n");
    else
        Console.Write("No\n");

    Interval []arr2 = { new Interval(6, 8),
                        new Interval(1, 3),
                        new Interval(2, 4),
                        new Interval(4, 7) };
    int n2 = arr2.Length;
    if(isIntersect(arr2, n2))
        Console.Write("Yes\n");
    else
        Console.Write("No\n");
}
}

// This code is contributed by Rajput-Ji

Javascript

<script>
// A Javascript program to check if any two intervals overlap

// An interval has start time and end time
class Interval
{
    constructor(start, end)
    {
        this.start = start;
        this.end = end;
    }
}

// Function to check if any two intervals overlap
function isIntersect(arr, n)
{
    let max_ele = 0;

    // Find the overall maximum element
    for (let i = 0; i < n; i++)
    {
        if (max_ele < arr[i].end)
            max_ele = arr[i].end;
    }

    // Initialize an array of size max_ele
    let aux = new Array(max_ele + 1);
    for(let i=0;i<(max_ele + 1);i++)
    {
        aux[i]=0;
    }
    for (let i = 0; i < n; i++)
    {

        // starting point of the interval
        let x = arr[i].start;

        // end point of the interval
        let y = arr[i].end;
        aux[x]++;
        aux[y ]--;
    }
    for (let i = 1; i <= max_ele; i++)
    {
        // Calculating the prefix Sum
        aux[i] += aux[i - 1];

        // Overlap
        if (aux[i] > 1)
            return true;
    }

    // If we reach here, then no Overlap
    return false;
}

// Driver program
let arr1 = [new Interval(1, 3), new Interval(7, 9),
                       new Interval(4, 6), new Interval(10, 13)];
let n1 = arr1.length;
if(isIntersect(arr1, n1))
        document.write("Yes<br>");
    else
        document.write("No<br>");

    let arr2 = [ new Interval(6, 8), new Interval(1, 3),
                        new Interval(2, 4), new Interval(4, 7) ];
    let n2 = arr2.length;
    if(isIntersect(arr2, n2))
        document.write("Yes<br>");
    else
        document.write("No<br>");

// This code is contributed by avanitrachhadiya2155
</script>

Output:

No
Yes

Time Complexity : O(max_ele + n) 

Auxiliary Space: O(max_ele)

Note: This method is more efficient than Method 1 if there are more number of intervals and at the same time maximum value among all intervals should be low, since time complexity is directly proportional to O(max_ele). 
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