#### Approach #1: Check Position [Accepted]

Intuition

If the rectangles do not overlap, then rec1 must either be higher, lower, to the left, or to the right of rec2.

Algorithm

The answer for whether they don't overlap is LEFT OR RIGHT OR UP OR DOWN, where OR is the logical OR, and LEFT is a boolean that represents whether rec1 is to the left of rec2. The answer for whether they do overlap is the negation of this.

The condition "rec1 is to the left of rec2" is rec1 <= rec2, that is the right-most x-coordinate of rec1 is left of the left-most x-coordinate of rec2. The other cases are similar.

Complexity Analysis

• Time and Space Complexity: .

#### Approach #2: Check Area [Accepted]

Intuition

If the rectangles overlap, they have positive area. This area must be a rectangle where both dimensions are positive, since the boundaries of the intersection are axis aligned.

Thus, we can reduce the problem to the one-dimensional problem of determining whether two line segments overlap.

Algorithm

Say the area of the intersection is width * height, where width is the intersection of the rectangles projected onto the x-axis, and height is the same for the y-axis. We want both quantities to be positive.

The width is positive when min(rec1, rec2) > max(rec1, rec2), that is when the smaller of (the largest x-coordinates) is larger than the larger of (the smallest x-coordinates). The height is similar.

Complexity Analysis

• Time and Space Complexity: .