Swift Xcode implementation of InterviewCake 'Rectangle Intersection' with linear intersection (not range) performing in O(1). ⚠️ Spoiler alert: this is an actual answer to the https://www.interviewcake.com/question/swift/rectangular-love? question, so no peeking!

InterviewCake-RectangleLove.swift

//
//  RectangleLove.swift
//
//  Copyright © 2018 Xavier Schott
//  Permission is hereby granted, free of charge, to any person obtaining a copy
//  of this software and associated documentation files (the "Software"), to deal
//  in the Software without restriction, including without limitation the rights
//  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
//  copies of the Software, and to permit persons to whom the Software is
//  furnished to do so, subject to the following conditions:
//
//  The above copyright notice and this permission notice shall be included in
//  all copies or substantial portions of the Software.
//
//  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
//  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
//  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
//  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
//  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
//  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
//  THE SOFTWARE.
//

import Foundation

struct Rectangle: CustomStringConvertible {

    // coordinates of bottom left corner
    let leftX: Int
    let bottomY: Int

    // dimensions
    let width: Int
    let height: Int

    init(leftX: Int, bottomY: Int, width: Int, height: Int) {
        self.leftX = leftX
        self.bottomY = bottomY
        self.width = width
        self.height = height
    }

    init() {
        self.init(leftX: 0, bottomY: 0, width: 0, height: 0)
    }

    var description: String {
        return String(format: "(%d, %d, %d, %d)", leftX, bottomY, width, height)
    }
}

extension Rectangle: Equatable {
    public static func == (lhs: Rectangle, rhs: Rectangle) -> Bool {
        return
            lhs.leftX == rhs.leftX &&
            lhs.bottomY == rhs.bottomY &&
            lhs.width == rhs.width &&
            lhs.height == rhs.height
    }
}

extension Rectangle {
    init(leftX: Int, rightX: Int, bottomY: Int, topY: Int) {
        if rightX <= leftX || topY <= bottomY {
            self.init(leftX: 0, bottomY: 0, width: 0, height: 0)
        } else {
            self.init(leftX: leftX, bottomY: bottomY, width: rightX - leftX, height: topY - bottomY)
        }
    }
}

class RectangleLove
{
    func intersection(a: Rectangle, b: Rectangle) -> Rectangle {
        let x1 = max(a.leftX, b.leftX)
        let x2 = min(a.leftX + a.width, b.leftX + b.width)
        let y1 = max(a.bottomY, b.bottomY)
        let y2 = min(a.bottomY + a.height, b.bottomY + b.height)
        return Rectangle(leftX: x1,
                         rightX: x2,
                         bottomY: y1,
                         topY: y2)
    }
}

InterviewCake-RectangleLoveTests.swift

//
//  RectangleLoveTests.swift
//
//  Copyright © 2018 Xavier Schott
//  Permission is hereby granted, free of charge, to any person obtaining a copy
//  of this software and associated documentation files (the "Software"), to deal
//  in the Software without restriction, including without limitation the rights
//  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
//  copies of the Software, and to permit persons to whom the Software is
//  furnished to do so, subject to the following conditions:
//
//  The above copyright notice and this permission notice shall be included in
//  all copies or substantial portions of the Software.
//
//  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
//  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
//  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
//  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
//  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
//  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
//  THE SOFTWARE.
//

import XCTest

class RectangleLoveTests: XCTestCase {
    func testRectangleLoveQuestion() {
        let a = Rectangle(leftX: 1, bottomY: 1, width: 6, height: 3)
        let b = Rectangle(leftX: 5, bottomY: 2, width: 3, height: 6)
        let expected = Rectangle(leftX: 5, bottomY: 2, width: 2, height: 2)
        let result = RectangleLove().intersection(a: a, b: b)
        XCTAssertEqual(expected, result)
    }

    func testRectangleLoveNegative() {
        let a = Rectangle(leftX: -9, bottomY: 1, width: 6, height: 3)
        let b = Rectangle(leftX: -5, bottomY: 2, width: 3, height: 6)
        let expected = Rectangle(leftX: -5, bottomY: 2, width: 2, height: 2)
        let result = RectangleLove().intersection(a: a, b: b)
        XCTAssertEqual(expected, result)
    }

    func testRectangleLoveNoIntersection() {
        let a = Rectangle(leftX: 1, bottomY: 1, width: 6, height: 3)
        let b = Rectangle(leftX: 7, bottomY: 2, width: 3, height: 6)
        let expected = Rectangle()
        let result = RectangleLove().intersection(a: a, b: b)
        XCTAssertEqual(expected, result)
    }

    func testRectangleLoveInside() {
        let a = Rectangle(leftX: 1, bottomY: 1, width: 6, height: 6)
        let b = Rectangle(leftX: 2, bottomY: 2, width: 3, height: 3)
        let expected = Rectangle(leftX: 2, bottomY: 2, width: 3, height: 3)
        let result = RectangleLove().intersection(a: a, b: b)
        XCTAssertEqual(expected, result)
    }

    func testRectangleLoveEdge() {
        let a = Rectangle(leftX: 1, bottomY: 1, width: 6, height: 6)
        let b = Rectangle(leftX: 7, bottomY: 2, width: 3, height: 3)
        let expected = Rectangle()
        let result = RectangleLove().intersection(a: a, b: b)
        XCTAssertEqual(expected, result)
    }

    func testRectangleLoveCorner() {
        let a = Rectangle(leftX: 1, bottomY: 1, width: 6, height: 6)
        let b = Rectangle(leftX: 7, bottomY: 7, width: 3, height: 3)
        let expected = Rectangle()
        let result = RectangleLove().intersection(a: a, b: b)
        XCTAssertEqual(expected, result)
    }

    func testRectangleLovePerformance() {
        var lotsOfRanctangles = [Rectangle]()
        for _ in 0 ..< 1000000 {
            lotsOfRanctangles.append(Rectangle(leftX: Int(arc4random_uniform(1024)),
                                               bottomY: Int(arc4random_uniform(1024)),
                                               width: Int(arc4random_uniform(1024)),
                                               height: Int(arc4random_uniform(1024))))
        }
        let r = RectangleLove()

        self.measure {
            var aRectangle = lotsOfRanctangles[0]
            for i in 1 ..< lotsOfRanctangles.count {
                let bRectangle = lotsOfRanctangles[i]
                _ = r.intersection(a: aRectangle, b: bRectangle)
                aRectangle = bRectangle
            }
        }
    }
    
}

Even though the Rectangle structure contains an origin and a size, naturally leading to range intersections on the horizontal and vertical axis, the proposed solution uses linear min and max by calculating the top-right coordinates. This makes for a very compact solution in the intersection method.

The Rectangle validity is left to a new init(leftX: Int, rightX: Int, bottomY: Int, topY: Int) method, implemented as an extension, which guarantees the rectangle isn't negative.