[DFS] Add a solution to Course Schedule

DFS/CourseSchedule.swift

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+/**
+ * Question Link: https://leetcode.com/problems/course-schedule/
+ * Primary idea: Kahn's Algorithms
+ * 1) Create the graph
+ * 2) Decorate each vertex with its in-degree
+ * 3) Create a set of all sources
+ * 4) While the set isn’t empty,
+ *     i. Remove a vertex from the set and add it to the sorted list
+ *     ii. For every edge from that vertex:
+ *         - Decrement the in-degree of the destination node
+ *         - Check all of its destination vertices and add them to the set if they have no incoming edges
+ * Time Complexity: O(|E| + |V|), Space Complexity: O(n^2)
+ * Recommand Reading: http://cs.brown.edu/courses/csci0160/lectures/14.pdf
+ */
+class Solution {
+    func canFinish(_ numCourses: Int, _ prerequisites: [[Int]]) -> Bool {
+        // ATTENTION: if graph use [[Int]], will get 'memory limited exceed'
+        var graph = [[UInt8]](repeatElement([UInt8](repeatElement(0, count: numCourses)), count: numCourses))
+        var indegree = [Int](repeatElement(0, count: numCourses))
+
+        // 1. Create the graph
+        for i in 0 ..< prerequisites.count {
+            let course = prerequisites[i][0]
+            let pre = prerequisites[i][1]
+
+            // 2. Decorate each vertex with its in-degree
+            // Eliminate duplicate case
+            if graph[pre][course] == 0 {
+                indegree[course] += 1
+            }
+            graph[pre][course] = 1
+        }
+
+        // 3. Create a array of sources
+        var sources = [Int]()
+        for i in 0 ..< numCourses {
+            if indegree[i] == 0 {
+                sources.append(i)
+            }
+        }
+
+        //var topoSortedList = [Int]()
+        var count = 0
+        while !sources.isEmpty {
+            // 4.i. Remove a vertex from the set and add it to the sorted list
+            let source = sources.popLast()
+            //topoSortedList.append(source!)
+            count += 1
+
+            // 4.ii. Decrement the in-degree of the destination node
+            for i in 0 ..< numCourses {
+                if graph[source!][i] == 1 {
+                    indegree[i] -= 1
+                    // Check all of its destination vertices and add them to the set if they have no incoming edges
+                    if indegree[i] == 0 {
+                        sources.append(i)
+                    }
+                }
+            }
+        }
+
+        //return topoSortedList.count == numCourses
+        return count == numCourses
+    }
+}