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A crack team of love scientists from OkEros (a hot new dating site) have devised a way to represent dating profiles as rectangles on a two-dimensional plane.

They need help writing an algorithm to find the intersection of two users' love rectangles. They suspect finding that intersection is the key to a matching algorithm so powerful it will cause an immediate acquisition by Google or Facebook or Obama or something.

Two rectangles overlapping a little. It must be love.

Write a function to find the rectangular intersection of two given love rectangles.

As with the example above, love rectangles are always "straight" and never "diagonal." More rigorously: each side is parallel with either the x-axis or the y-axis.

They are defined as instances of the Rectangle structure:

struct Rectangle: CustomStringConvertible { // coordinates of bottom left corner let leftX: Int let bottomY: Int // dimensions let width: Int let height: Int var description: String { return "(\(leftX), \(bottomY), \(width), \(height))" } }

Your output rectangle should be a Rectangle structure as well.

What if there is no intersection? Does your function do something reasonable in that case?

What if one rectangle is entirely contained in the other? Does your function do something reasonable in that case?

What if the rectangles don't really intersect but share an edge? Does your function do something reasonable in that case?

Do some parts of your function seem very similar? Can they be refactored so you repeat yourself less?

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time and space.

What if we had an array of rectangles and wanted to find all the rectangular overlaps between all possible pairs of two rectangles within the array? Note that we'd be returning an array of rectangles.

What if we had an array of rectangles and wanted to find the overlap between all of them, if there was one? Note that we'd be returning a single rectangle.

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