Description
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).
Examples:
Example 1:
Rectangle Area
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: 16Solution in Python
Python
class Solution:
def computeArea(self, ax1: int, ay1: int, ax2: int, ay2: int,
bx1: int, by1: int, bx2: int, by2: int) -> int:
# Step 1: Calculate the area of both rectangles
area1 = (ax2 - ax1) * (ay2 - ay1) # Area of the first rectangle
area2 = (bx2 - bx1) * (by2 - by1) # Area of the second rectangle
# Step 2: Calculate the overlap between the two rectangles
overlap_x = max(0, min(ax2, bx2) - max(ax1, bx1)) # Overlap in x-axis
overlap_y = max(0, min(ay2, by2) - max(ay1, by1)) # Overlap in y-axis
overlap_area = overlap_x * overlap_y # Area of the overlap
# Step 3: Total area covered by both rectangles
total_area = area1 + area2 - overlap_area
return total_areaExplanation
- Area Calculation:
- For each rectangle, the area is computed as the product of the width (difference between the x-coordinates) and the height (difference between the y-coordinates).
- Finding the Overlap:
- The overlapping area is determined by finding the intersection of the x and y ranges of both rectangles. If the rectangles don’t overlap in either direction, the overlap is 0.
- Total Area:
- The total area is calculated by adding the areas of both rectangles and subtracting the overlapping area (if any).
Time Complexity
- O(1): This is a constant time solution since we are only performing a fixed number of arithmetic operations. The solution doesn’t depend on the input size because we’re given fixed values for the rectangle coordinates.
Solution in Javascript
JavaScript
var computeArea = function(ax1, ay1, ax2, ay2, bx1, by1, bx2, by2) {
// Step 1: Calculate the area of both rectangles
const area1 = (ax2 - ax1) * (ay2 - ay1); // Area of the first rectangle
const area2 = (bx2 - bx1) * (by2 - by1); // Area of the second rectangle
// Step 2: Calculate the overlap between the two rectangles
// Overlap in the x-axis (horizontal)
const overlap_x = Math.max(0, Math.min(ax2, bx2) - Math.max(ax1, bx1));
// Overlap in the y-axis (vertical)
const overlap_y = Math.max(0, Math.min(ay2, by2) - Math.max(ay1, by1));
// Area of the overlap (if any)
const overlapArea = overlap_x * overlap_y;
// Step 3: Total area covered by both rectangles
// Total area is the sum of the two rectangle areas minus the overlapping area
return area1 + area2 - overlapArea;
};Solution in Java
Java
class Solution {
public int computeArea(int ax1, int ay1, int ax2, int ay2,
int bx1, int by1, int bx2, int by2) {
// Step 1: Calculate the area of both rectangles
int area1 = (ax2 - ax1) * (ay2 - ay1); // Area of the first rectangle
int area2 = (bx2 - bx1) * (by2 - by1); // Area of the second rectangle
// Step 2: Calculate the overlap between the two rectangles
// Overlap in the x-axis (horizontal)
int overlap_x = Math.max(0, Math.min(ax2, bx2) - Math.max(ax1, bx1));
// Overlap in the y-axis (vertical)
int overlap_y = Math.max(0, Math.min(ay2, by2) - Math.max(ay1, by1));
// Area of the overlap (if any)
int overlapArea = overlap_x * overlap_y;
// Step 3: Total area covered by both rectangles
// Total area is the sum of the two rectangle areas minus the overlapping area
return area1 + area2 - overlapArea;
}
}Solution in C#
C#
public class Solution {
public int ComputeArea(int ax1, int ay1, int ax2, int ay2,
int bx1, int by1, int bx2, int by2) {
// Step 1: Calculate the area of both rectangles
int area1 = (ax2 - ax1) * (ay2 - ay1); // Area of the first rectangle
int area2 = (bx2 - bx1) * (by2 - by1); // Area of the second rectangle
// Step 2: Calculate the overlap in both x and y directions
// Overlap in the x-axis (horizontal overlap)
int overlap_x = Math.Max(0, Math.Min(ax2, bx2) - Math.Max(ax1, bx1));
// Overlap in the y-axis (vertical overlap)
int overlap_y = Math.Max(0, Math.Min(ay2, by2) - Math.Max(ay1, by1));
// Overlap area (if any overlap exists)
int overlapArea = overlap_x * overlap_y;
// Step 3: Total area covered by both rectangles
// Sum of the areas minus the overlap area
return area1 + area2 - overlapArea;
}
}