图 Trie 堆栈
图形
在计算机科学中，图形是一种抽象数据类型，旨在实现数学中的无向图和有向图概念。图形数据结构由有限（并且可能是可变的）顶点或节点或点组成，以及用于无向图的一组无序的这些顶点对或用于有向图的一组有序对。这些对被称为用于无向图的边，弧或线，以及用于有向图的箭头，有向边，有向弧或有向线。顶点可以是图结构的一部分，或者可以是由整数索引或引用表示的外部实体。图形数据结构还可以将每个边缘值与某个边缘值相关联，例如符号标签或数字属性（成本，容量，长度等）。 （维基百科，来源 ）
//
// GraphFactory.swift
// SwiftStructures
//
// Created by Wayne Bishop on 6/7/14.
// Copyright (c) 2014 Arbutus Software Inc. All rights reserved.
//
import Foundation
public class SwiftGraph {
//declare a default directed graph canvas
private var canvas: Array<Vertex>
public var isDirected: Bool
init() {
canvas = Array<Vertex>()
isDirected = true
}
//create a new vertex
func addVertex(key: String) -> Vertex {
//set the key
let childVertex: Vertex = Vertex()
childVertex.key = key
//add the vertex to the graph canvas
canvas.append(childVertex)
return childVertex
}
//add edge to source vertex
func addEdge(source: Vertex, neighbor: Vertex, weight: Int) {
//create a new edge
let newEdge = Edge()
//establish the default properties
newEdge.neighbor = neighbor
newEdge.weight = weight
source.neighbors.append(newEdge)
print("The neighbor of vertex: \(source.key as String!) is \(neighbor.key as String!)..")
//check condition for an undirected graph
if isDirected == false {
//create a new reversed edge
let reverseEdge = Edge()
//establish the reversed properties
reverseEdge.neighbor = source
reverseEdge.weight = weight
neighbor.neighbors.append(reverseEdge)
print("The neighbor of vertex: \(neighbor.key as String!) is \(source.key as String!)..")
}
}
/* reverse the sequence of paths given the shortest path.
process analagous to reversing a linked list. */
func reversePath(_ head: Path!, source: Vertex) -> Path! {
guard head != nil else {
return head
}
//mutated copy
var output = head
var current: Path! = output
var prev: Path!
var next: Path!
while(current != nil) {
next = current.previous
current.previous = prev
prev = current
current = next
}
//append the source path to the sequence
let sourcePath: Path = Path()
sourcePath.destination = source
sourcePath.previous = prev
sourcePath.total = nil
output = sourcePath
return output
}
//process Dijkstra's shortest path algorthim
func processDijkstra(_ source: Vertex, destination: Vertex) -> Path? {
var frontier: Array<Path> = Array<Path>()
var finalPaths: Array<Path> = Array<Path>()
//use source edges to create the frontier
for e in source.neighbors {
let newPath: Path = Path()
newPath.destination = e.neighbor
newPath.previous = nil
newPath.total = e.weight
//add the new path to the frontier
frontier.append(newPath)
}
//construct the best path
var bestPath: Path = Path()
while frontier.count != 0 {
//support path changes using the greedy approach
bestPath = Path()
var pathIndex: Int = 0
for x in 0..<frontier.count {
let itemPath: Path = frontier[x]
if (bestPath.total == nil) || (itemPath.total < bestPath.total) {
bestPath = itemPath
pathIndex = x
}
}
//enumerate the bestPath edges
for e in bestPath.destination.neighbors {
let newPath: Path = Path()
newPath.destination = e.neighbor
newPath.previous = bestPath
newPath.total = bestPath.total + e.weight
//add the new path to the frontier
frontier.append(newPath)
}
//preserve the bestPath
finalPaths.append(bestPath)
//remove the bestPath from the frontier
//frontier.removeAtIndex(pathIndex) - Swift2
frontier.remove(at: pathIndex)
} //end while
//establish the shortest path as an optional
var shortestPath: Path! = Path()
for itemPath in finalPaths {
if (itemPath.destination.key == destination.key) {
if (shortestPath.total == nil) || (itemPath.total < shortestPath.total) {
shortestPath = itemPath
}
}
}
return shortestPath
}
///an optimized version of Dijkstra's shortest path algorthim
func processDijkstraWithHeap(_ source: Vertex, destination: Vertex) -> Path! {
let frontier: PathHeap = PathHeap()
let finalPaths: PathHeap = PathHeap()
//use source edges to create the frontier
for e in source.neighbors {
let newPath: Path = Path()
newPath.destination = e.neighbor
newPath.previous = nil
newPath.total = e.weight
//add the new path to the frontier
frontier.enQueue(newPath)
}
//construct the best path
var bestPath: Path = Path()
while frontier.count != 0 {
//use the greedy approach to obtain the best path
bestPath = Path()
bestPath = frontier.peek()
//enumerate the bestPath edges
for e in bestPath.destination.neighbors {
let newPath: Path = Path()
newPath.destination = e.neighbor
newPath.previous = bestPath
newPath.total = bestPath.total + e.weight
//add the new path to the frontier
frontier.enQueue(newPath)
}
//preserve the bestPaths that match destination
if (bestPath.destination.key == destination.key) {
finalPaths.enQueue(bestPath)
}
//remove the bestPath from the frontier
frontier.deQueue()
} //end while
//obtain the shortest path from the heap
var shortestPath: Path! = Path()
shortestPath = finalPaths.peek()
return shortestPath
}
//MARK: traversal algorithms
//bfs traversal with inout closure function
func traverse(_ startingv: Vertex, formula: (_ node: inout Vertex) -> ()) {
//establish a new queue
let graphQueue: Queue<Vertex> = Queue<Vertex>()
//queue a starting vertex
graphQueue.enQueue(startingv)
while !graphQueue.isEmpty() {
//traverse the next queued vertex
var vitem: Vertex = graphQueue.deQueue() as Vertex!
//add unvisited vertices to the queue
for e in vitem.neighbors {
if e.neighbor.visited == false {
print("adding vertex: \(e.neighbor.key!) to queue..")
graphQueue.enQueue(e.neighbor)
}
}
/*
notes: this demonstrates how to invoke a closure with an inout parameter.
By passing by reference no return value is required.
*/
//invoke formula
formula(&vitem)
} //end while
print("graph traversal complete..")
}
//breadth first search
func traverse(_ startingv: Vertex) {
//establish a new queue
let graphQueue: Queue<Vertex> = Queue<Vertex>()
//queue a starting vertex
graphQueue.enQueue(startingv)
while !graphQueue.isEmpty() {
//traverse the next queued vertex
let vitem = graphQueue.deQueue() as Vertex!
guard vitem != nil else {
return
}
//add unvisited vertices to the queue
for e in vitem!.neighbors {
if e.neighbor.visited == false {
print("adding vertex: \(e.neighbor.key!) to queue..")
graphQueue.enQueue(e.neighbor)
}
}
vitem!.visited = true
print("traversed vertex: \(vitem!.key!)..")
} //end while
print("graph traversal complete..")
} //end function
//use bfs with trailing closure to update all values
func update(startingv: Vertex, formula:((Vertex) -> Bool)) {
//establish a new queue
let graphQueue: Queue<Vertex> = Queue<Vertex>()
//queue a starting vertex
graphQueue.enQueue(startingv)
while !graphQueue.isEmpty() {
//traverse the next queued vertex
let vitem = graphQueue.deQueue() as Vertex!
guard vitem != nil else {
return
}
//add unvisited vertices to the queue
for e in vitem!.neighbors {
if e.neighbor.visited == false {
print("adding vertex: \(e.neighbor.key!) to queue..")
graphQueue.enQueue(e.neighbor)
}
}
//apply formula..
if formula(vitem!) == false {
print("formula unable to update: \(vitem!.key)")
}
else {
print("traversed vertex: \(vitem!.key!)..")
}
vitem!.visited = true
} //end while
print("graph traversal complete..")
}
}
特里
在计算机科学中，trie，也称为数字树，有时候是基数树或前缀树（因为它们可以通过前缀搜索），是一种搜索树 - 一种有序的树数据结构，用于存储动态集或关联键通常是字符串的数组。 （维基百科，来源 ）
//
// Trie.swift
// SwiftStructures
//
// Created by Wayne Bishop on 10/14/14.
// Copyright (c) 2014 Arbutus Software Inc. All rights reserved.
//
import Foundation
public class Trie {
private var root: TrieNode!
init(){
root = TrieNode()
}
//builds a tree hierarchy of dictionary content
func append(word keyword: String) {
//trivial case
guard keyword.length > 0 else {
return
}
var current: TrieNode = root
while keyword.length != current.level {
var childToUse: TrieNode!
let searchKey = keyword.substring(to: current.level + 1)
//print("current has \(current.children.count) children..")
//iterate through child nodes
for child in current.children {
if (child.key == searchKey) {
childToUse = child
break
}
}
//new node
if childToUse == nil {
childToUse = TrieNode()
childToUse.key = searchKey
childToUse.level = current.level + 1
current.children.append(childToUse)
}
current = childToUse
} //end while
//final end of word check
if (keyword.length == current.level) {
current.isFinal = true
print("end of word reached!")
return
}
} //end function
//find words based on the prefix
func search(forWord keyword: String) -> Array<String>! {
//trivial case
guard keyword.length > 0 else {
return nil
}
var current: TrieNode = root
var wordList = Array<String>()
while keyword.length != current.level {
var childToUse: TrieNode!
let searchKey = keyword.substring(to: current.level + 1)
//print("looking for prefix: \(searchKey)..")
//iterate through any child nodes
for child in current.children {
if (child.key == searchKey) {
childToUse = child
current = childToUse
break
}
}
if childToUse == nil {
return nil
}
} //end while
//retrieve the keyword and any descendants
if ((current.key == keyword) && (current.isFinal)) {
wordList.append(current.key)
}
//include only children that are words
for child in current.children {
if (child.isFinal == true) {
wordList.append(child.key)
}
}
return wordList
} //end function
}
（GitHub，来源 ）
堆
在计算机科学中，堆栈是一种抽象数据类型，用作元素的集合，有两个主要操作：push，它向集合添加元素，pop，删除最近添加的尚未删除的元素。元素从堆栈中出现的顺序产生了其替代名称 LIFO（用于后进，先出）。另外，窥视操作可以在不修改堆栈的情况下访问顶部。 （维基百科，来源 ）
请参阅下面的许可证信息和原始代码源（ github ）
//
// Stack.swift
// SwiftStructures
//
// Created by Wayne Bishop on 8/1/14.
// Copyright (c) 2014 Arbutus Software Inc. All rights reserved.
//
import Foundation
class Stack<T> {
private var top: Node<T>
init() {
top = Node<T>()
}
//the number of items - O(n)
var count: Int {
//return trivial case
guard top.key != nil else {
return 0
}
var current = top
var x: Int = 1
//cycle through list
while current.next != nil {
current = current.next!
x += 1
}
return x
}
//add item to the stack
func push(withKey key: T) {
//return trivial case
guard top.key != nil else {
top.key = key
return
}
//create new item
let childToUse = Node<T>()
childToUse.key = key
//set new created item at top
childToUse.next = top
top = childToUse
}
//remove item from the stack
func pop() {
if self.count > 1 {
top = top.next
}
else {
top.key = nil
}
}
//retrieve the top most item
func peek() -> T! {
//determine instance
if let topitem = top.key {
return topitem
}
else {
return nil
}
}
//check for value
func isEmpty() -> Bool {
if self.count == 0 {
return true
}
else {
return false
}
}
}
麻省理工学院许可证（MIT）
版权所有（c）2015，Wayne Bishop＆Arbutus Software Inc.
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