836. Rectangle Overlap

1. Description

An axis-aligned rectangle is represented as a list [x1, y1, x2, y2], where (x1, y1) is the coordinate of its bottom-left corner, and (x2, y2) is the coordinate of its top-right corner. Its top and bottom edges are parallel to the X-axis, and its left and right edges are parallel to the Y-axis.
Two rectangles overlap if the area of their intersection is positive. To be clear, two rectangles that only touch at the corner or edges do not overlap.
Given two axis-aligned rectangles rec1 and rec2, return true if they overlap, otherwise return false.

2. Example

Example 1:
Input: rec1 = [0,0,2,2], rec2 = [1,1,3,3]
Output: true

Example 2:
Input: rec1 = [0,0,1,1], rec2 = [1,0,2,1]
Output: false

Example 3:
Input: rec1 = [0,0,1,1], rec2 = [2,2,3,3]
Output: false

3. Constraints

• rec1.length == 4
• rec2.length == 4
• $-10^9$ <= rec1[i], rec2[i] <= $10^9$
• rec1 and rec2 represent a valid rectangle with a non-zero area.

4. Solutions

Geometry

Time complexity: O(1)
Space complexity: O(1)

class Solution {
public:
    bool isRectangleOverlap(vector<int>& rec1, vector<int>& rec2) {
        return (min(rec1[2], rec2[2]) > max(rec1[0], rec2[0]) &&
                min(rec1[3], rec2[3]) > max(rec1[1], rec2[1]));
    }
};