Created
February 25, 2018 00:49
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Swift Xcode implementation of InterviewCake _Super Balanced Tree_ using a tight DFS in a `BinaryTreeNode` extension. ⚠️ Spoiler alert: this is an actual answer to the https://www.interviewcake.com/question/swift/balanced-binary-tree question, so no peeking!
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// | |
// BinaryTreeNode.swift | |
// | |
import Foundation | |
class BinaryTreeNode { | |
var value: Int | |
var left: BinaryTreeNode? | |
var right: BinaryTreeNode? | |
init(_ value: Int) { | |
self.value = value | |
} | |
func insert(leftValue: Int) -> BinaryTreeNode { | |
let left = BinaryTreeNode(leftValue) | |
self.left = left | |
return left | |
} | |
func insert(rightValue: Int) -> BinaryTreeNode { | |
let right = BinaryTreeNode(rightValue) | |
self.right = right | |
return right | |
} | |
} |
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// | |
// SuperBalanced.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 BinaryTreeNode { | |
private func visitDFS(depth: Int, minDepth: inout Int, maxDepth: inout Int ) { | |
if maxDepth - minDepth < 2 { // Short circuit | |
maxDepth = max(maxDepth, depth) // Any node will increase depth | |
if nil == left && nil == right { // Leaf | |
minDepth = min(minDepth, depth) // Shallowest leaf | |
} else { // Node, keep going | |
left?.visitDFS(depth: depth + 1, minDepth: &minDepth, maxDepth: &maxDepth) | |
right?.visitDFS(depth: depth + 1, minDepth: &minDepth, maxDepth: &maxDepth) | |
} | |
} | |
} | |
func superBalanced() -> Bool { | |
var minDepth = Int.max | |
var maxDepth = 0 | |
visitDFS(depth: 0, minDepth: &minDepth, maxDepth: &maxDepth) | |
return maxDepth - minDepth < 2 | |
} | |
} | |
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// | |
// SuperBalancedTests.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 SuperBalancedTests: XCTestCase { | |
func testBalancedTree() { | |
let node0 = BinaryTreeNode(0) | |
let node1 = BinaryTreeNode(1) | |
node0.left = node1 | |
let node2 = BinaryTreeNode(2) | |
node0.right = node2 | |
let node5 = BinaryTreeNode(5) | |
node2.left = node5 | |
let node6 = BinaryTreeNode(6) | |
node2.right = node6 | |
XCTAssertTrue(node0.superBalanced()) | |
} | |
func testSmallGoodRightTrees() { | |
let node0 = BinaryTreeNode(0) | |
XCTAssertTrue(node0.superBalanced()) | |
let node2 = BinaryTreeNode(2) | |
node0.right = node2 | |
XCTAssertTrue(node0.superBalanced()) | |
let node6 = BinaryTreeNode(6) | |
node2.right = node6 | |
XCTAssertTrue(node0.superBalanced()) | |
let node14 = BinaryTreeNode(14) | |
node6.right = node14 | |
XCTAssertTrue(node0.superBalanced()) | |
} | |
func testSmallGoodLefttTrees() { | |
let node0 = BinaryTreeNode(0) | |
XCTAssertTrue(node0.superBalanced()) | |
let node1 = BinaryTreeNode(1) | |
node0.left = node1 | |
XCTAssertTrue(node0.superBalanced()) | |
let node3 = BinaryTreeNode(3) | |
node1.left = node3 | |
XCTAssertTrue(node0.superBalanced()) | |
let node7 = BinaryTreeNode(7) | |
node3.left = node7 | |
XCTAssertTrue(node0.superBalanced()) | |
} | |
func testSingleBranchTrees() { | |
let node0 = BinaryTreeNode(0) | |
let node2 = BinaryTreeNode(2) | |
node0.right = node2 | |
let node6 = BinaryTreeNode(6) | |
node2.right = node6 | |
let node14 = BinaryTreeNode(14) | |
node6.right = node14 | |
XCTAssertTrue(node0.superBalanced()) | |
let node1 = BinaryTreeNode(1) | |
node0.left = node1 | |
XCTAssertFalse(node0.superBalanced()) | |
} | |
func testImbalancedBalancedTree() { | |
let node0 = BinaryTreeNode(0) | |
let node1 = BinaryTreeNode(1) | |
node0.left = node1 | |
let node2 = BinaryTreeNode(2) | |
node0.right = node2 | |
let node5 = BinaryTreeNode(5) | |
node2.left = node5 | |
let node6 = BinaryTreeNode(6) | |
node2.right = node6 | |
let node9 = BinaryTreeNode(9) | |
node5.left = node9 | |
XCTAssertFalse(node0.superBalanced()) | |
} | |
func testPerformanceExample() { | |
// This is an example of a performance test case. | |
self.measure { | |
// Put the code you want to measure the time of here. | |
} | |
} | |
} |
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Using a very short recursive DFS, combined with a shortcut exit.
This routines stops when nodes are too deep, not even looking for further leaves.