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?微信公眾號：山青詠芝（shanqingyongzhi）
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There are a total of?n?courses you have to take, labeled from?0?to?n-1.

Some courses may have prerequisites, for example to take course 0 you have to first take course 1, which is expressed as a pair:?[0,1]

Given the total number of courses and a list of prerequisite?pairs, return the ordering of courses you should take to finish all courses.

There may be multiple correct orders, you just need to return one of them. If it is impossible to finish all courses, return an empty array.

Example 1:

Input: 2, [[1,0]] Output: [0,1] Explanation:?There are a total of 2 courses to take. To take course 1 you should have finished course 0. So the correct course order is [0,1] .

Example 2:

Input: 4, [[1,0],[2,0],[3,1],[3,2]] Output: [0,1,2,3] or [0,2,1,3] Explanation:?There are a total of 4 courses to take. To take course 3 you should have finished both courses 1 and 2. Both courses 1 and 2 should be taken after you finished course 0. So one correct course order is [0,1,2,3]. Another correct ordering is [0,2,1,3] .

Note:

The input prerequisites is a graph represented by?a list of edges, not adjacency matrices. Read more about?how a graph is represented.

You may assume that there are no duplicate edges in the input prerequisites.

---

現在你總共有?n?門課需要選，記為?0?到?n-1。

在選修某些課程之前需要一些先修課程。?例如，想要學習課程 0 ，你需要先完成課程?1 ，我們用一個匹配來表示他們:?[0,1]

給定課程總量以及它們的先決條件，返回你為了學完所有課程所安排的學習順序。

可能會有多個正確的順序，你只要返回一種就可以了。如果不可能完成所有課程，返回一個空數組。

示例?1:

輸入: 2, [[1,0]] 輸出: [0,1] 解釋:?總共有 2 門課程。要學習課程 1，你需要先完成課程 0。因此，正確的課程順序為 [0,1] 。

示例?2:

輸入: 4, [[1,0],[2,0],[3,1],[3,2]] 輸出: [0,1,2,3] or [0,2,1,3] 解釋:?總共有 4 門課程。要學習課程 3，你應該先完成課程 1 和課程 2。并且課程 1 和課程 2 都應該排在課程 0 之后。因此，一個正確的課程順序是?[0,1,2,3] 。另一個正確的排序是?[0,2,1,3] 。

說明:

輸入的先決條件是由邊緣列表表示的圖形，而不是鄰接矩陣。詳情請參見圖的表示法。

你可以假定輸入的先決條件中沒有重復的邊。

提示:

這個問題相當于查找一個循環是否存在于有向圖中。如果存在循環，則不存在拓撲排序，因此不可能選取所有課程進行學習。

通過 DFS 進行拓撲排序?- 一個關于Coursera的精彩視頻教程（21分鐘），介紹拓撲排序的基本概念。

拓撲排序也可以通過?BFS?完成。

---

104ms

1 class Edge { 2 3 let y: Int 4 var next: Edge? 5 6 init(_ y: Int) { 7 self.y = y 8 } 9 } 10 11 struct Graph { 12 13 var edges: [Edge?] 14 var indegree: [Int] 15 16 init(numOfVertices: Int) { 17 self.edges = [Edge?](repeating: nil, count: numOfVertices) 18 self.indegree = [Int](repeating: 0, count: numOfVertices) 19 } 20 21 mutating func insertEdge(_ x: Int, _ y: Int) { 22 23 let newEdge = Edge(y) 24 newEdge.next = edges[x] 25 26 edges[x] = newEdge 27 indegree[y] += 1 28 } 29 } 30 31 32 class Solution { 33 func findOrder(_ numCourses: Int, _ prerequisites: [[Int]]) -> [Int] { 34 35 var graph = createGraph(numCourses: numCourses, prerequisites: prerequisites) 36 37 var queue: [Int] = [] 38 for x in 0..<graph.indegree.count { 39 if graph.indegree[x] == 0 { 40 queue.append(x) 41 } 42 } 43 44 var order: [Int] = [] 45 46 while !queue.isEmpty { 47 48 var nextQueue: [Int] = [] 49 50 for x in queue { 51 order.append(x) 52 53 var edge = graph.edges[x] 54 while let _edge = edge { 55 let y = _edge.y 56 graph.indegree[y] -= 1 57 58 if graph.indegree[y] == 0 { 59 nextQueue.append(y) 60 } 61 62 edge = _edge.next 63 } 64 } 65 66 queue = nextQueue 67 } 68 69 return order.count == numCourses ? order : [] 70 } 71 72 func createGraph(numCourses: Int, prerequisites: [[Int]]) -> Graph { 73 74 var graph = Graph(numOfVertices: numCourses) 75 76 for pair in prerequisites { 77 let y = pair[0] 78 let x = pair[1] 79 80 graph.insertEdge(x,y) 81 } 82 83 return graph 84 } 85 86 }

---

108ms

1 class Solution { 2 func findOrder(_ numCourses: Int, _ prerequisites: [[Int]]) -> [Int] { 3 4 var graph = [[Int]](repeating:[Int](), count: numCourses) 5 var coursesIn = Array(repeating: 0, count: numCourses) 6 var res = [Int]() 7 for a in prerequisites { 8 graph[a[1]].append(a[0]) 9 coursesIn[a[0]] += 1 10 } 11 var q = [Int]() 12 for i in coursesIn.indices { 13 if coursesIn[i] == 0 { q.append(i) } 14 } 15 while !q.isEmpty { 16 var t = q.removeFirst() 17 res.append(t) 18 for a in graph[t] { 19 coursesIn[a] -= 1 20 21 if coursesIn[a] == 0 { q.append(a) } 22 23 } 24 } 25 if res.count != numCourses { res.removeAll() } 26 return res 27 } 28 }

---

108ms

1 class Solution { 2 func findOrder(_ numCourses: Int, _ prerequisites: [[Int]]) -> [Int] { 3 var res:[Int] = [Int]() 4 var graph:[[Int]] = [[Int]](repeating:[Int](),count:numCourses) 5 var ins:[Int] = [Int](repeating:0,count:numCourses) 6 for a in prerequisites 7 { 8 graph[a[1]].append(a[0]) 9 ins[a[0]] += 1 10 } 11 var q:[Int] = [Int]() 12 for i in 0..<numCourses 13 { 14 if ins[i] == 0 15 { 16 q.append(i) 17 } 18 } 19 while(!q.isEmpty) 20 { 21 var t:Int = q.first! 22 res.append(t) 23 q.removeFirst() 24 for num in graph[t] 25 { 26 ins[num] -= 1 27 if ins[num] == 0 28 { 29 q.append(num) 30 } 31 } 32 } 33 if res.count != numCourses 34 { 35 res.removeAll() 36 } 37 return res 38 } 39 }

---

112ms

1 class Solution { 2 func findOrder(_ numCourses: Int, _ prerequisites: [[Int]]) -> [Int] { 3 if numCourses == 0 { 4 return [] 5 } else if numCourses == 1 { 6 return [0] 7 } 8 9 var inDegree = Array(repeating: 0, count: numCourses) 10 var graph = [Int: [Int]]() 11 for prerequisite in prerequisites { 12 inDegree[prerequisite[0]] += 1 13 graph[prerequisite[1], default: [Int]()].append(prerequisite[0]) 14 } 15 var queue = [Int]() 16 for course in 0 ..< numCourses where inDegree[course] == 0{ 17 queue.append(course) 18 } 19 var result = [Int]() 20 while !queue.isEmpty { 21 let course = queue.removeFirst() 22 result.append(course) 23 if let courses = graph[course] { 24 for course in courses { 25 inDegree[course] -= 1 26 if inDegree[course] == 0 { 27 queue.append(course) 28 } 29 } 30 } 31 } 32 return result.count == numCourses ? result : [] 33 } 34 }

---

116ms

1 class Course { 2 let number: Int 3 var dependents: [Int: Course] 4 var numberOfPrereq: Int 5 6 init(number: Int) { 7 self.number = number 8 dependents = [Int: Course]() 9 numberOfPrereq = 0 10 } 11 } 12 13 class Solution { 14 func findOrder(_ numCourses: Int, _ prerequisites: [[Int]]) -> [Int] { 15 var courses = [Course]() 16 17 for courseNumber in 0..<numCourses { 18 courses.append(Course(number: courseNumber)) 19 } 20 21 // Build the graph 22 for prerequisite in prerequisites { 23 let courseNum = prerequisite[0] 24 let prerequisiteNum = prerequisite[1] 25 26 let course = courses[courseNum] 27 let pre = courses[prerequisiteNum] 28 course.numberOfPrereq += 1 29 30 // Add an edge 31 pre.dependents[course.number] = course 32 } 33 34 var result = [Int]() 35 36 var stack = [Course]() 37 for courseNumber in 0..<numCourses { 38 let course = courses[courseNumber] 39 if course.numberOfPrereq == 0 { 40 stack.append(course) 41 } 42 } 43 44 while !stack.isEmpty { 45 let c = stack.removeLast() 46 47 // Add to result 48 result.append(c.number) 49 50 for el in c.dependents { 51 // Remove edge 52 c.dependents.removeValue(forKey: el.value.number) 53 el.value.numberOfPrereq -= 1 54 if el.value.numberOfPrereq == 0 { 55 stack.append(el.value) 56 } 57 } 58 } 59 60 // Should have no edge left, otherwise we have a cycle 61 for course in courses { 62 if course.numberOfPrereq != 0 { 63 return [] 64 } 65 } 66 67 return result 68 } 69 }

---

120ms

1 class Solution { 2 func findOrder(_ total: Int, _ courses: [[Int]]) -> [Int] { 3 var dict: [Int: [Int]] = [:] 4 var prev: [Int] = Array(repeating: 0, count: total) 5 for course in courses { 6 prev[course.first!] += 1 7 dict[course.last!, default: []].append(course.first!) 8 } 9 var count = 0 10 var queue: [Int] = [] 11 for (index, num) in prev.enumerated() { 12 if num == 0 { 13 queue.append(index) 14 } 15 } 16 var res: [Int] = [] 17 while !queue.isEmpty { 18 let num = queue.first! 19 queue.removeFirst() 20 res.append(num) 21 if let nextCourses = dict[num], !courses.isEmpty { 22 for course in nextCourses { 23 prev[course] -= 1 24 if prev[course] == 0 { 25 queue.append(course) 26 } 27 } 28 } 29 } 30 if res.count != total { 31 return [] 32 } 33 return res 34 } 35 }

---

128ms

1 class Edge { 2 3 let y: Int 4 var next: Edge? 5 6 init(y: Int) { 7 self.y = y 8 } 9 } 10 11 struct Graph { 12 var edges: [Edge?] 13 var edgeCount: [Int] 14 var indegree: [Int] 15 16 init(vertexCount: Int) { 17 self.edges = [Edge?](repeating: nil, count: vertexCount) 18 self.edgeCount = [Int](repeating: 0, count: vertexCount) 19 self.indegree = [Int](repeating: 0, count: vertexCount) 20 } 21 } 22 23 class Solution { 24 25 func findOrder(_ numCourses: Int, _ prerequisites: [[Int]]) -> [Int] { 26 guard numCourses > 0 else { 27 return [] 28 } 29 guard numCourses > 1 else { 30 return [0] 31 } 32 33 34 var graph = graphFrom(numCourses: numCourses, prerequisites: prerequisites) 35 var courseOrder: [Int] = [] 36 37 var queue: [Int] = [] 38 for x in 0..<graph.edges.count { 39 if graph.indegree[x] == 0 { 40 queue.append(x) 41 } 42 } 43 44 while !queue.isEmpty { 45 46 var nextQueue: [Int] = [] 47 48 for x in queue { 49 courseOrder.append(x) 50 51 var edge = graph.edges[x] 52 while let _edge = edge { 53 let y = _edge.y 54 graph.indegree[y] -= 1 55 56 if graph.indegree[y] == 0 { 57 nextQueue.append(y) 58 } 59 60 edge = _edge.next 61 } 62 } 63 64 queue = nextQueue 65 } 66 67 68 return courseOrder.count == numCourses ? courseOrder : [] 69 } 70 71 72 73 func graphFrom(numCourses: Int, prerequisites: [[Int]]) -> Graph { 74 var graph = Graph(vertexCount: numCourses) 75 76 for pair in prerequisites { 77 78 let x = pair[1] 79 let y = pair[0] 80 81 let newEdge = Edge(y: y) 82 newEdge.next = graph.edges[x] 83 84 graph.edges[x] = newEdge 85 graph.edgeCount[x] += 1 86 graph.indegree[y] += 1 87 } 88 89 return graph 90 } 91 }

---

132ms

1 class Solution { 2 class Node: Hashable { 3 static func == (lhs: Node, rhs: Node) -> Bool { 4 return lhs.val == rhs.val 5 } 6 7 var val: Int 8 var indegree: Set<Node> 9 var outdegree: Set<Node> 10 11 init(_ val: Int) { 12 self.val = val 13 self.indegree = Set<Node>() 14 self.outdegree = Set<Node>() 15 } 16 17 public var hashValue: Int { 18 return val 19 } 20 } 21 22 23 func findOrder(_ numCourses: Int, _ prerequisites: [[Int]]) -> [Int] { 24 guard numCourses > 0 else { 25 return [Int]() 26 } 27 28 var map = [Int: Node]() 29 var queue = [Node]() 30 var set = Set<Node>() 31 var res = [Int]() 32 33 for num in 0..<numCourses { 34 map[num] = Node(num) 35 } 36 37 for pair in prerequisites { 38 map[pair[0]]?.indegree.insert(map[pair[1]]!) 39 map[pair[1]]?.outdegree.insert(map[pair[0]]!) 40 } 41 42 for (_, node) in map { 43 if node.indegree.count == 0 { 44 queue.append(node) 45 set.insert(node) 46 res.append(node.val) 47 } 48 } 49 50 while !queue.isEmpty { 51 let curr = queue.removeFirst() 52 for node in curr.outdegree { 53 node.indegree.remove(curr) 54 55 if node.indegree.count == 0, !set.contains(node) { 56 queue.append(node) 57 set.insert(node) 58 res.append(node.val) 59 } 60 } 61 } 62 63 return res.count == numCourses ? res : [Int]() 64 } 65 }

---

160ms

1 class Solution { 2 func findOrder(_ n: Int, _ prerequisites: [[Int]]) -> [Int] { 3 var indegree = [Int](repeating: 0 , count: n) 4 var adjMap = [Int: Set<Int>]() 5 for prerequisite in prerequisites { 6 let first = prerequisite[1] 7 let second = prerequisite[0] 8 indegree[second] += 1 9 var newSet : Set<Int> 10 if let s = adjMap[first]{ 11 newSet = s 12 }else { 13 newSet = Set<Int>() 14 } 15 newSet.insert(second) 16 adjMap[first] = newSet 17 } 18 var queue = [Int]() 19 for i in 0 ..< n{ 20 if indegree[i] == 0{ 21 queue.append(i) 22 } 23 } 24 var res = [Int]() 25 while !queue.isEmpty{ 26 let cur = queue.removeFirst() 27 res.append(cur) 28 if let map = adjMap[cur]{ 29 for adj in map{ 30 indegree[adj] -= 1 31 if indegree[adj] == 0{ 32 queue.append(adj) 33 } 34 } 35 } 36 } 37 if res.count != n { 38 return [Int]() 39 } 40 return res 41 } 42 }

---

184ms

1 class Solution { 2 struct Node{ 3 var nodes: [Int] = [Int]() 4 var isSeen: Bool = false 5 } 6 var graph: [Node] = [Node]() 7 var order: [Int] = [Int]() 8 var graphHasCycle: Bool = false 9 var isInStack: [Bool] = [Bool]() 10 func dfs(_ node: Int){ 11 isInStack[node] = true 12 graph[node].isSeen = true 13 for to in graph[node].nodes{ 14 if !graph[to].isSeen{ 15 dfs(to) 16 }else{ 17 if isInStack[to] { 18 graphHasCycle = true 19 } 20 } 21 } 22 isInStack[node] = false 23 order.append(node) 24 } 25 func addEdge(_ from: Int , _ to: Int){ 26 graph[from].nodes.append(to) 27 } 28 func findOrder(_ numCourses: Int, _ prerequisites: [[Int]]) -> [Int] { 29 for i in 0...numCourses - 1{ 30 graph.append(Node()) 31 isInStack.append(false) 32 } 33 var from : Int? 34 var to : Int? 35 for edge in prerequisites { 36 from = edge[0] 37 to = edge[1] 38 addEdge(from!,to!) 39 } 40 for i in 0...numCourses - 1 { 41 if !graph[i].isSeen{ 42 dfs(i) 43 } 44 } 45 if graphHasCycle { 46 return [] 47 } 48 return order 49 } 50 }

?

轉載于:https://www.cnblogs.com/strengthen/p/10197798.html

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