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Swift Xcode implementation of InterviewCake 'Highest product of 3' using an `Array` extension, and a few fold faster than the accepted answer. ⚠️ Spoiler alert: this is an actual answer to the https://www.interviewcake.com/question/swift/highest-product-of-3 question, so no peeking!
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// | |
// Array+HighestProductOfIntegers.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 | |
extension Array where Element == Int | |
{ | |
// Single out the 3 lowest and the 3 highest numbers, then run a O(n3) algorithm on these 6 values | |
// Works great on very large sets | |
func highestProductOfIntegers() -> Double { | |
assert(count >= 3) | |
var smallPQ = [Int](repeatElement(Int.max, count: 3)) | |
var largePQ = [Int](repeatElement(Int.min, count: 3)) | |
for i in 0 ..< count { | |
// Keep an ascending array of small values by replacing the highest | |
if self[i] < smallPQ[2] { | |
smallPQ[2] = self[i] | |
smallPQ.sort() | |
} | |
// Keep an ascending array of large values by replacing the smallest | |
if self[i] > largePQ[0] { | |
largePQ[0] = self[i] | |
largePQ.sort() | |
} | |
} | |
// Combine the smallest and largest numbers into a single array, and run all combinations | |
smallPQ.append(contentsOf: largePQ) | |
return smallPQ.productOfIntegersN3() | |
} | |
private func productOfIntegersN3() -> Double { | |
let array = self | |
var result = -Double.greatestFiniteMagnitude | |
for indice0 in 0 ... count - 2 { | |
for indice1 in indice0 + 1 ..< count - 1 { | |
for indice2 in indice1 + 1 ..< count { | |
result = Swift.max(result, Double(array[indice0] * array[indice1] * array[indice2])) | |
} | |
} | |
} | |
return result | |
} | |
} |
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// | |
// HighestProductOfIntegersTests.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 HighestProductOfIntegersTests: XCTestCase { | |
func testHighestProductOfIntegers1to5() { | |
let sample = [1, 2, 3, 5, 4] | |
let result = sample.highestProductOfIntegers() | |
XCTAssertTrue(60.0 == result) | |
} | |
func testHighestProductOfIntegers0to5() { | |
let sample = [1, 2, 0, 3, 5, 4] | |
let result = sample.highestProductOfIntegers() | |
XCTAssertTrue(60.0 == result) | |
} | |
func testHighestProductOfIntegersSomeNegative() { | |
let sample:[Int] = [-10, 1, -20, 3, -5, 2] | |
let result = sample.highestProductOfIntegers() | |
XCTAssertTrue(600.0 == result) | |
} | |
func testHighestProductOfIntegersSomeNegativeAndZero() { | |
let sample:[Int] = [-10, 1, -20, 0, 3, -5, 2] | |
let result = sample.highestProductOfIntegers() | |
XCTAssertTrue(600.0 == result) | |
} | |
func testHighestProductOfIntegersAllNegative() { | |
let sample:[Int] = [-10, -20, -1, -3, -2] | |
let result = sample.highestProductOfIntegers() | |
XCTAssertTrue(-6 == result) | |
} | |
func testHighestProductOfIntegersAllNegativeAndZero() { | |
let sample:[Int] = [-10, -20, -1, 0, -3, -2] | |
let result = sample.highestProductOfIntegers() | |
XCTAssertTrue(0 == result) | |
} | |
func testHighestProductOfIntegersUsingSolution() { | |
let sample = [1, 10, -5, 1, -100] | |
let result = sample.highestProductOfIntegers() | |
XCTAssertTrue(5000.0 == result) | |
} | |
func testHighestProductOfIntegers() { | |
var largeArray = [Int](repeatElement(0, count: 32768)) // 0.001 sec | |
for i in 0 ..< largeArray.count { | |
largeArray[i] = Int(arc4random_uniform(65536)) - 32768 // balance positive and negative numbers | |
} | |
self.measure { | |
_ = largeArray.highestProductOfIntegers() | |
} | |
} | |
} |
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Proposed solution combines a brute-force algorithm (
productOfIntegersN3
) with a less than O(log n) algorithm (highestProductOfIntegers
).productOfIntegersN3
will only be used on the final array of 6 elementshighestProductOfIntegers
is linear, and is tasked to isolate the 3 lowest and 3 highest numbers in a single passThe performance on a random set of non-ordered vales is surprisingly good, since the 2 arrays of max and min are seldom modified.