Finding overlapping rectangles

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This is a classic quick programming puzzle: write a function that, given two rectangles, will determine if the triangles overlap. I found this puzzle over on http://leetcode.com/2011/05/determine-if-two-rectangles-overlap.html, and thought it was worth talking about because the solution is wrong, and it was interesting to me because it shows how thinking about a domain can influence your implementation of behaviour.

The mistake made by the original author is with one of the assumptions / interpretations made during their reasoning process. They said “when two rectangles overlap, one rectangle’s corner point(s) must [be contained within] the other rectangle”. This appears reasonable, given the example below:

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