836. Rectangle Overlap

A rectangle is represented as a list [x1, y1, x2, y2], where (x1, y1) are the coordinates of its bottom-left corner, and (x2, y2) are the coordinates of its top-right corner.

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, return whether they overlap.

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

De Morgan's Law tells us that the following are equivalent. An easy way to remember De Morgan's is by the saying to split the bar and change the operation; that is to distribute negation and change the boolean operator in this example.

    public boolean isRectangleOverlap(int[] rec1, int[] rec2) {
        return !(rec1[2] <= rec2[0] ||   // left
                 rec1[3] <= rec2[1] ||   // bottom
                 rec1[0] >= rec2[2] ||   // right
                 rec1[1] >= rec2[3]);    // top
    }
    public boolean isRectangleOverlap(int[] rec1, int[] rec2) {
        return   rec1[2] > rec2[0] &&   // left
                 rec1[3] > rec2[1] &&   // bottom
                 rec1[0] < rec2[2] &&   // right
                 rec1[1] < rec2[3];     // top
    }