#### 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[2] <= rec2[0]`

, 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[2], rec2[2]) > max(rec1[0], rec2[0])`

, 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: .