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算法基础(五)树综合

字数统计: 1.1k阅读时长: 6 min
2020/08/29

算法基础(五)树综合

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class TreeNode<T: Comparable & LosslessStringConvertible>  {
var value: T
var left: TreeNode<T>?
var right: TreeNode<T>?

init(_ value: T, left: TreeNode<T>? = nil, right: TreeNode<T>? = nil) {
self.value = value
self.left = left
self.right = right
}
}



class Tree<T: Comparable & LosslessStringConvertible> {
var head: TreeNode<T>?

init(_ head: TreeNode<T>) {
self.head = head
}

//通过前中遍历还原二叉树
init?(previous: [T], middle: [T]) {
guard previous.count == middle.count else {
return nil
}
guard let head = _init(previous: previous, middle: middle) else {
return nil
}
self.head = head
}

private func _init(previous: [T], middle: [T]) -> TreeNode<T>? {
guard !previous.isEmpty && !middle.isEmpty else {
return nil
}
let root = TreeNode<T>.init(previous.first!)
for (index, num) in middle.enumerated() {
if num == previous.first! {
root.left = _init(previous: Array(previous[1..<index+1]), middle: Array(middle[0..<index]))
root.right = _init(previous: Array(previous[index+1..<previous.count]), middle: Array(middle[index+1..<middle.count]))
}
}
return root
}

//依照前序遍历还原二叉树
init?(_ array: [String]) {
guard !array.isEmpty else {
return nil
}
var array = array
var index = 0
_init(&array, &self.head, &index)
}

private func _init(_ array: inout [String], _ node:inout TreeNode<T>?, _ index: inout Int) {
if array[index] == "#" {
node = nil
index += 1
} else {
node = TreeNode<T>.init(T.init(array[index])!)
index += 1
guard index < array.count else {
return
}
_init(&array, &node!.left, &index)
guard index < array.count else {
return
}
_init(&array, &node!.right, &index)
}
}

//二叉树的复制
static func copy(from head: TreeNode<T>) -> TreeNode<T> {
var node: TreeNode<T>?
var head: TreeNode<T>? = head
helper_copy(&head, &node)
return node!
}

static private func helper_copy(_ node: inout TreeNode<T>?, _ newNode: inout TreeNode<T>?) {
guard let node = node else {
newNode = nil
return
}
newNode = .init(node.value)
helper_copy(&node.left, &newNode!.left)
helper_copy(&node.right, &newNode!.right)
}

enum getStringOption: Int {
case previous
case middle
case behind
case level
}

//前、中、后、层次遍历二叉树
func getString(through option: getStringOption = .previous) -> String? {
guard head != nil else {
return nil
}
var string = ""
helper_getString(self.head, to: &string, option: option)
_ = string.removeLast()
return string
}

public struct Queue<T> {

// 数组用来存储数据元素
private var data = [T]()

// 将类型为T的数据元素添加到队列的末尾
public mutating func enqueue(element: T) {
data.append(element)
}

// 移除并返回队列中第一个元素
// 如果队列不为空,则返回队列中第一个类型为T的元素;否则,返回nil。
public mutating func dequeue() -> T? {
return data.removeFirst()
}

// 检查队列是否为空
// 如果队列为空,则返回true;否则,返回false
public func isEmpty() -> Bool {
return data.isEmpty
}
}

private func helper_getString(_ node: TreeNode<T>?,to string: inout String, option: getStringOption = .previous) {
guard let node = node else {
return
}
switch option {
case .previous:
string += String(node.value)+","
helper_getString(node.left, to: &string, option: .previous)
helper_getString(node.right, to: &string, option: .previous)
break
case .middle:
helper_getString(node.left, to: &string, option: .middle)
string += String(node.value)+","
helper_getString(node.right, to: &string, option: .middle)
break

case .behind:
helper_getString(node.left, to: &string, option: .behind)
helper_getString(node.right, to: &string, option: .behind)
string += String(node.value)+","
break
case .level:
var queue = Queue<TreeNode<T>>()
queue.enqueue(element: node)
while !queue.isEmpty() {
let n = queue.dequeue()!
string += String(n.value)+","
if (n.left != nil) {
queue.enqueue(element: n.left!)
}
if (n.right != nil) {
queue.enqueue(element: n.right!)
}
}
}
}


//二叉树深度
func getDepth() -> Int {
return helper_getDepth(self.head)
}

private func helper_getDepth(_ node: TreeNode<T>?) -> Int {
guard node != nil else {
return 0
}
let m = helper_getDepth(node?.left)
let n = helper_getDepth(node?.right)
return (m<n ? n+1:m+1)
}

//二叉树结点树
func getNodeCount() -> Int {
return helper_getNodeCount(self.head)
}

private func helper_getNodeCount(_ node: TreeNode<T>?) -> Int {
guard node != nil else {
return 0
}
return helper_getNodeCount(node?.left) + helper_getNodeCount(node?.right) + 1
}

//判断是否为平衡二叉树(自底向上的方式)
func isBalanced(_ root: TreeNode<T>?) -> Bool {
return helper_isBalanced(root) >= 0
// 由上向下的递归
// guard let root = root else {
// return true
// }
// if abs(helper_getDepth(root.left)-helper_getDepth(root.right)) > 1 {
// return false
// } else {
// return isBalanced(root.left) && isBalanced(root.right)
// }
}

private func helper_isBalanced(_ node: TreeNode<T>?) -> Int {
guard let node = node else {
return 0
}
let l = helper_isBalanced(node.left)
let r = helper_isBalanced(node.right)
if abs(l-r) > 1 || l == -1 || r == -1 {
return -1
}
return max(l, r) + 1

}
}



let head = TreeNode.init(10, left: .init(6, left: .init(4), right: .init(8)), right: .init(14, left: .init(12), right: .init(16)))
let tree = Tree.init(head)
tree.getString(through: .behind)
tree.getString(through: .level)
tree.getDepth()
tree.getNodeCount()

let string = "123##45#6##7###"
var array: [String] = string.map { (c) -> String in return String.init(c) }

let tree1 = Tree<Int>.init(array)
tree1?.getString()


let node = Tree<Int>.copy(from: head)

let tree2 = Tree<Int>.init(node)

tree2.getNodeCount()


let tree3 = Tree<Int>.init(previous: [3,9,20,15,7], middle: [9,3,15,20,7])
tree3?.getString()

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  1. 1. 算法基础(五)树综合