Algorithm Questions: how to determine rectangle is inside the another rectangle?

Question

Given a list of tuples (including x, y, width, height which four values define a rectangle in two-dimension coordination). The goal is to check in the original list, whether one rectangle is inside another rectangle (if it is, only take the smaller one, larger one is discarded)

Answer 1

The most obvious solution, if it isn't too slow, is to define rect1.contains(rect2) as:

rect1.x <= rect2.x && rect1.y <= rect2.y && rect1.x + rect1.width >= rect2.x + rect2.width && rect1.y + rect1.height >= rect2.y + rect2.height

and then check every rect in the list to see if it contains any others. (Don't check it against itself, though!)

Answer 2

Check on this:

http://www.jstor.org/stable/2691523?seq=1#page_scan_tab_contents

and

Find out if a rectangle is inside another rectangle [C]