Total area of two overlapping rectangles
Given the coordinates of two rectangles in a 2D plane, the first rectangle is defined by its bottom-left corner (ax1, ay1) and its top-right corner (ax2, ay2) and the second rectangle is defined by its bottom-left corner (bx1, by1) and its top-right corner (bx2, by2). The task is to find the total area covered by the two rectangles.
Examples:
Input: L1= {2, 1}, R1={5, 5}, L2= {3, 2}, R2={5, 7}
Output: Total Area = 16
Explanation: In the below image we can observe that total area of two overlapping rectangles is 16 units.Input: L1= {-3, 0}, R1={3, 5}, L2= {0, -2}, R2={6, 3}
Output: Total Area = 51
Explanation: In the below image we can observe that total area of two overlapping rectangles is 51 units.
Total area of two overlapping rectangles using Inclusion-Exclusion Principle:
The area of any rectangle can be calculated using the formula: (x_distance) * (y_distance). Since the rectangles may overlap, we can use Inclusion Exclusion principle to calculate the area as follows:
Total Area = Area of Rectangle1 + Area of Rectangle2 – Intersecting area of both the rectangles
For Rectangle1:
- x_distance = abs(L1.x – R1.x)
- y_distance = abs(L1.y – R1.y)
- Area of Rectangle1 = x_distance * y_distance
For Rectangle2:
- x_distance = abs(L2.x – R2.x)
- y_distance = abs(L2.y – R2.y)
- Area of Rectangle2 = x_distance * y_distance
For area of overlapping Rectangle:
- x_distance = min(R1.x, R2.x) – max(L1.x, L2.x)
- y_distance = min(R1.y, R2.y) – max(L1.y, L2.y)
- Area of overlapping rectange = x_distance * y_distance
- If the x_distance or y_distance is negative, then the two rectangles do not intersect. In that case, overlapping area is 0.
Below is the implementation of the above approach:
C++
// C++ program to find total area of two // overlapping Rectangles #include <bits/stdc++.h> using namespace std; struct Point { int x, y; }; // Returns Total Area of two overlap // rectangles int overlappingArea(Point l1, Point r1, Point l2, Point r2) { // Area of 1st Rectangle int area1 = abs (l1.x - r1.x) * abs (l1.y - r1.y); // Area of 2nd Rectangle int area2 = abs (l2.x - r2.x) * abs (l2.y - r2.y); // Length of intersecting part i.e // start from max(l1.x, l2.x) of // x-coordinate and end at min(r1.x, // r2.x) x-coordinate by subtracting // start from end we get required // lengths int x_dist = min(r1.x, r2.x) - max(l1.x, l2.x); int y_dist = (min(r1.y, r2.y) - max(l1.y, l2.y)); int areaI = 0; if ( x_dist > 0 && y_dist > 0 ) { areaI = x_dist * y_dist; } return (area1 + area2 - areaI); } // Driver Code int main() { Point l1 = { 2, 2 }, r1 = { 5, 7 }; Point l2 = { 3, 4 }, r2 = { 6, 9 }; // Function Call cout << overlappingArea(l1, r1, l2, r2); return 0; } |
Java
// Java program to find total area of two // overlapping Rectangles class GFG { static class Point { int x, y; public Point( int x, int y) { this .x = x; this .y = y; } }; // Returns Total Area of two overlap // rectangles static int overlappingArea(Point l1, Point r1, Point l2, Point r2) { // Area of 1st Rectangle int area1 = Math.abs(l1.x - r1.x) * Math.abs(l1.y - r1.y); // Area of 2nd Rectangle int area2 = Math.abs(l2.x - r2.x) * Math.abs(l2.y - r2.y); // Length of intersecting part i.e // start from max(l1.x, l2.x) of // x-coordinate and end at min(r1.x, // r2.x) x-coordinate by subtracting // start from end we get required // lengths int x_dist = (Math.min(r1.x, r2.x) - Math.max(l1.x, l2.x); int y_dist = (Math.min(r1.y, r2.y) - Math.max(l1.y, l2.y); int areaI = 0 ; if ( x_dist > 0 && y_dist > 0 ) { areaI = x_dist * y_dist; } return (area1 + area2 - areaI); } // Driver Code public static void main(String[] args) { Point l1 = new Point( 2 , 2 ), r1 = new Point( 5 , 7 ); Point l2 = new Point( 3 , 4 ), r2 = new Point( 6 , 9 ); // Function Call System.out.println(overlappingArea(l1, r1, l2, r2)); } } // This code is contributed by PrinciRaj1992 |
Python3
# Python program to find total area of two # overlapping Rectangles # Returns Total Area of two overlap # rectangles def overlappingArea(l1, r1, l2, r2): x = 0 y = 1 # Area of 1st Rectangle area1 = abs (l1[x] - r1[x]) * abs (l1[y] - r1[y]) # Area of 2nd Rectangle area2 = abs (l2[x] - r2[x]) * abs (l2[y] - r2[y]) ''' Length of intersecting part i.e start from max(l1[x], l2[x]) of x-coordinate and end at min(r1[x], r2[x]) x-coordinate by subtracting start from end we get required lengths ''' x_dist = ( min (r1[x], r2[x]) - max (l1[x], l2[x])) y_dist = ( min (r1[y], r2[y]) - max (l1[y], l2[y])) areaI = 0 if x_dist > 0 and y_dist > 0 : areaI = x_dist * y_dist return (area1 + area2 - areaI) # Driver's Code l1 = [ 2 , 2 ] r1 = [ 5 , 7 ] l2 = [ 3 , 4 ] r2 = [ 6 , 9 ] # Function call print (overlappingArea(l1, r1, l2, r2)) # This code is contributed by Manisha_Ediga |
C#
// C# program to find total area of two // overlapping Rectangles using System; class GFG { public class Point { public int x, y; public Point( int x, int y) { this .x = x; this .y = y; } }; // Returns Total Area of two overlap // rectangles static int overlappingArea(Point l1, Point r1, Point l2, Point r2) { // Area of 1st Rectangle int area1 = Math.Abs(l1.x - r1.x) * Math.Abs(l1.y - r1.y); // Area of 2nd Rectangle int area2 = Math.Abs(l2.x - r2.x) * Math.Abs(l2.y - r2.y); // Length of intersecting part i.e // start from max(l1.x, l2.x) of // x-coordinate and end at min(r1.x, // r2.x) x-coordinate by subtracting // start from end we get required // lengths int x_dist = (Math.Min(r1.x, r2.x) - Math.Max(l1.x, l2.x)); int y_dist = (Math.Min(r1.y, r2.y) - Math.Max(l1.y, l2.y)); int areaI = 0; if (x_dist > 0 && y_dist > 0) { areaI = x_dist * y_dist; } return (area1 + area2 - areaI); } // Driver Code public static void Main(String[] args) { Point l1 = new Point(2, 2), r1 = new Point(5, 7); Point l2 = new Point(3, 4), r2 = new Point(6, 9); // Function Call Console.WriteLine(overlappingArea(l1, r1, l2, r2)); } } // This code is contributed by PrinciRaj1992 |
Javascript
<script> // Javascript program to find total area of two // overlapping Rectangles // Returns Total Area of two overlap // rectangles function overlappingArea(l1, r1, l2, r2) { let x = 0 let y = 1 // Area of 1st Rectangle let area1 = Math.abs(l1[x] - r1[x]) * Math.abs(l1[y] - r1[y]) // Area of 2nd Rectangle let area2 = Math.abs(l2[x] - r2[x]) * Math.abs(l2[y] - r2[y]) // Length of intersecting part i.e // start from max(l1[x], l2[x]) of // x-coordinate and end at min(r1[x], // r2[x]) x-coordinate by subtracting // start from end we get required // lengths let x_dist = (Math.min(r1[x], r2[x]) - Math.max(l1[x], l2[x])) let y_dist = (Math.min(r1[y], r2[y]) - Math.max(l1[y], l2[y])) let areaI = 0 if (x_dist > 0 && y_dist > 0) areaI = x_dist * y_dist return (area1 + area2 - areaI) } // Driver Code let l1 = [2, 2] let r1 = [5, 7] let l2 = [3, 4] let r2 = [6, 9] // Function call document.write(overlappingArea(l1, r1, l2, r2)) // This code is contributed by jana_sayantan. </script> |
24
Time complexity: O(1)
Auxiliary Space: O(1)
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