# Find if two rectangles overlap

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.

**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++

`#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) ` `{ ` ` ` `// 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` `(l1.y <= r2.y || l2.y <= r1.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; ` `}` |

*chevron_right*

*filter_none*

## 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) { ` ` ` `// 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` `(l1.y <= r2.y || l2.y <= r1.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 ` |

*chevron_right*

*filter_none*

## 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): ` ` ` ` ` `# 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` `(l1.y <` `=` `r2.y ` `or` `l2.y <` `=` `r1.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 ` |

*chevron_right*

*filter_none*

## 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` `(l1.y <= r2.y || l2.y <= r1.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. = 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 ` |

*chevron_right*

*filter_none*

**Output:**

Rectangles Overlap

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

This article is compiled by **Aman Gupta**. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.

## Recommended Posts:

- Find all rectangles filled with 0
- Find the minimum number of rectangles left after inserting one into another
- Find the number of rectangles of size 2*1 which can be placed inside a rectangle of size n*m
- Sum of Areas of Rectangles possible for an array
- Number of rectangles in N*M grid
- Total area of two overlapping rectangles
- Count Distinct Rectangles in N*N Chessboard
- Create a matrix with alternating rectangles of O and X
- Smallest square formed with given rectangles
- Number of rectangles in a circle of radius R
- Maximum given sized rectangles that can be cut out of a sheet of paper
- Minimum area of square holding two identical rectangles
- Number of unique rectangles formed using N unit squares
- Count of distinct rectangles inscribed in an equilateral triangle
- Intersecting rectangle when bottom-left and top-right corners of two rectangles are given
- Check if it is possible to rearrange rectangles in a non-ascending order of breadths
- Total number of unit cells covered by all given Rectangles
- Count of rectangles possible from N and M straight lines parallel to X and Y axis respectively
- Check if N rectangles of equal area can be formed from (4 * N) integers
- Count the number of rectangles such that ratio of sides lies in the range [a,b]