Find if two rectangles overlap

• Difficulty Level : Easy
• Last Updated : 26 Oct, 2021

Given two rectangles, find if the given two rectangles overlap or not.
Note that a rectangle can be represented by two coordinates, top left and bottom right. So mainly we are given following four coordinates.
l1: Top Left coordinate of first rectangle.
r1: Bottom Right coordinate of first rectangle.
l2: Top Left coordinate of second rectangle.
r2: Bottom Right coordinate of second rectangle. We need to write a function bool doOverlap(l1, r1, l2, r2) that returns true if the two given rectangles overlap.

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

Note : It may be assumed that the rectangles are parallel to the coordinate axis.
One solution is to one by one pick all points of one rectangle and see if the point lies inside the other rectangle or not. This can be done using the algorithm discussed here
Following is a simpler approach. Two rectangles do not overlap if one of the following conditions is true.
1) One rectangle is above top edge of other rectangle.
2) One rectangle is on left side of left edge of other rectangle.
We need to check above cases to find out if given rectangles overlap or not. Following is the implementation of the above approach.

C++

// CPP program for the above approach
#include <bits/stdc++.h>

struct Point {
int x, y;
};

// Returns true if two rectangles (l1, r1) and (l2, r2)
// overlap
bool doOverlap(Point l1, Point r1, Point l2, Point r2)
{

// To check if either rectangle is actually a line
// For example :  l1 ={-1,0}  r1={1,1}  l2={0,-1}
// r2={0,1}

if (l1.x == r1.x || l1.y == r1.y || l2.x == r2.x
|| l2.y == r2.y) {
// the line cannot have positive overlap
return false;
}

// If one rectangle is on left side of other
if (l1.x >= r2.x || l2.x >= r1.x)
return false;

// If one rectangle is above other
if (r1.y >= l2.y || r2.y >= l1.y)
return false;

return true;
}

/* Driver program to test above function */
int main()
{
Point l1 = { 0, 10 }, r1 = { 10, 0 };
Point l2 = { 5, 5 }, r2 = { 15, 0 };
if (doOverlap(l1, r1, l2, r2))
printf("Rectangles Overlap");
else
printf("Rectangles Don't Overlap");
return 0;
}

Java

// Java program to check if rectangles overlap
class GFG {

static class Point {

int x, y;
}

// Returns true if two rectangles (l1, r1) and (l2, r2) overlap
static  boolean doOverlap(Point l1, Point r1, Point l2, Point r2) {

// To check if either rectangle is actually a line
// For example :  l1 ={-1,0}  r1={1,1}  l2={0,-1}  r2={0,1}

if (l1.x == r1.x || l1.y == r1.y || l2.x == r2.x || l2.y == r2.y)
{
// the line cannot have positive overlap
return false;
}

// If one rectangle is on left side of other
if (l1.x >= r2.x || l2.x >= r1.x) {
return false;
}

// If one rectangle is above other
if (r1.y >= l2.y || r2.y >= l1.y) {
return false;
}

return true;
}

/* Driver program to test above function */
public static void main(String[] args) {
Point l1 = new Point(),r1 = new Point(),
l2 = new Point(),r2 = new Point();
l1.x=0;l1.y=10; r1.x=10;r1.y=0;
l2.x=5;l2.y=5; r2.x=15;r2.y=0;

if (doOverlap(l1, r1, l2, r2)) {
System.out.println("Rectangles Overlap");
} else {
System.out.println("Rectangles Don't Overlap");
}
}
}
//this code contributed by PrinciRaj1992

Python3

# Python program to check if rectangles overlap
class Point:
def __init__(self, x, y):
self.x = x
self.y = y

# Returns true if two rectangles(l1, r1)
# and (l2, r2) overlap
def doOverlap(l1, r1, l2, r2):

# To check if either rectangle is actually a line
# For example  :  l1 ={-1,0}  r1={1,1}  l2={0,-1}  r2={0,1}

if (l1.x == r1.x or l1.y == r1.y or l2.x == r2.x or l2.y == r2.y):
# the line cannot have positive overlap
return False

# If one rectangle is on left side of other
if(l1.x >= r2.x or l2.x >= r1.x):
return False

# If one rectangle is above other
if(r1.y >= l2.y or r2.y >= l1.y):
return False

return True

# Driver Code
if __name__ == "__main__":
l1 = Point(0, 10)
r1 = Point(10, 0)
l2 = Point(5, 5)
r2 = Point(15, 0)

if(doOverlap(l1, r1, l2, r2)):
print("Rectangles Overlap")
else:
print("Rectangles Don't Overlap")

# This code is contributed by Vivek Kumar Singh

C#

// C# program to check if rectangles overlap
using System;

class GFG
{
class Point
{
public int x, y;
}

// Returns true if two rectangles (l1, r1)
// and (l2, r2) overlap
static bool doOverlap(Point l1, Point r1,
Point l2, Point r2)
{
// If one rectangle is on left side of other
if (l1.x >= r2.x || l2.x >= r1.x)
{
return false;
}

// If one rectangle is above other
if (r1.y >= l2.y || r2.y >= l1.y)
{
return false;
}
return true;
}

// Driver Code
public static void Main()
{
Point l1 = new Point(), r1 = new Point(),
l2 = new Point(), r2 = new Point();
l1.x = 0;l1.y = 10; r1.x = 10;r1.y = 0;
l2.x = 5;l2.y = 5; r2.x = 15;r2.y = 0;
if (doOverlap(l1, r1, l2, r2))
{
Console.WriteLine("Rectangles Overlap");
} else
{
Console.WriteLine("Rectangles Don't Overlap");
}
}
}

// This code is contributed by
// Rajput-Ji

Javascript

<script>

// JavaScript program to check if rectangles overlap
class Point {

constructor(val) {
this.x = val;
this.y = val;
}
}

// Returns true if two rectangles
// (l1, r1) and (l2, r2) overlap
function doOverlap( l1,  r1,  l2,  r2) {

// To check if either rectangle is actually a line
// For example : l1 ={-1,0} r1={1,1} l2={0,-1} r2={0,1}

if (l1.x == r1.x || l1.y == r1.y ||
l2.x == r2.x || l2.y == r2.y) {
// the line cannot have positive overlap
return false;
}

// If one rectangle is on left side of other
if (l1.x >= r2.x || l2.x >= r1.x) {
return false;
}

// If one rectangle is above other
if (r1.y >= l2.y || r2.y >= l1.y) {
return false;
}

return true;
}

/* Driver program to test above function */

var l1 = new Point(), r1 = new Point(),
l2 = new Point(), r2 = new Point();
l1.x = 0;
l1.y = 10;
r1.x = 10;
r1.y = 0;
l2.x = 5;
l2.y = 5;
r2.x = 15;
r2.y = 0;

if (doOverlap(l1, r1, l2, r2)) {
document.write("Rectangles Overlap");
} else {
document.write("Rectangles Don't Overlap");
}

// This code contributed by umadevi9616

</script>
Output
Rectangles Overlap

The Time Complexity of the above code is O(1) as the code doesn’t have any loop or recursion.

Auxiliary Space: O(1)