# 836. Rectangle Overlap

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.

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

# Solution

Approach 1: use 1D overlap.

# Code (Python)

Approach 1:

class Solution:
    def isRectangleOverlap(self, rec1: List[int], rec2: List[int]) -> bool:
        return self._linear_overlap([rec1[0], rec1[2]], [rec2[0], rec2[2]]) and self._linear_overlap([rec1[1], rec1[3]], [rec2[1], rec2[3]])
    def _linear_overlap(self, line1, line2):
        if line1[0] <= line2[0]:
            return line1[1] > line2[0]
            return self._linear_overlap(line2, line1)

# Code (C++)

Approach 1:

Approach 2: