Rectangle Area

Problem Statement

Given the coordinates of two rectilinear rectangles in a 2D plane, return the total area covered by the two rectangles.

The first rectangle is defined by its bottom-left corner (ax1, ay1) and its top-right corner (ax2, ay2).

The second rectangle is defined by its bottom-left corner (bx1, by1) and its top-right corner (bx2, by2).

Leetcode link

Example 1:

Input: ax1 = -3, ay1 = 0, ax2 = 3, ay2 = 4, bx1 = 0, by1 = -1, bx2 = 9, by2 = 2
Output: 45

Example 2:

Input: ax1 = -2, ay1 = -2, ax2 = 2, ay2 = 2, bx1 = -2, by1 = -2, bx2 = 2, by2 = 2
Output: 16

Constraints:

• -10⁴ <= ax1 <= ax2 <= 10⁴
• -10⁴ <= ay1 <= ay2 <= 10⁴
• -10⁴ <= bx1 <= bx2 <= 10⁴
• -10⁴ <= by1 <= by2 <= 10⁴

Leetcode Link

Code

Python Code

class Solution:
    def computeArea(self, ax1: int, ay1: int, ax2: int, ay2: int, bx1: int, by1: int, bx2: int, by2: int) -> int:
        areaOf1stRectangle = (ax2 - ax1) * (ay2 - ay1);
        areaOf2ndRectangle = (bx2 - bx1) * (by2 - by1);

        xOverlap = min(ax2, bx2) - max(ax1, bx1);
        yOverlap = min(ay2, by2) - max(ay1, by1);
        areaOverlap = max(xOverlap,0) * max(yOverlap,0);

        return (areaOf1stRectangle + areaOf2ndRectangle - areaOverlap);

C++ Code

class Solution {
public:
    int computeArea(int ax1, int ay1, int ax2, int ay2, int bx1, int by1, int bx2, int by2) {

        int areaOf1stRectangle = (ax2 - ax1) * (ay2 - ay1);
        int areaOf2ndRectangle = (bx2 - bx1) * (by2 - by1);

        int xOverlap = min(ax2, bx2) - max(ax1, bx1);
        int yOverlap = min(ay2, by2) - max(ay1, by1);
        int areaOverlap = (xOverlap > 0 && yOverlap > 0) ? xOverlap * yOverlap : 0;

        return (areaOf1stRectangle + areaOf2ndRectangle - areaOverlap);
    }
};