Parallel Course DFS with 2 phase

Graph/ParallelCourse.cpp

@@ -0,0 +1,124 @@
+/*
+
+You are given an integer n, which indicates that there are n courses labeled from 1 to n. You are also given an array relations where relations[i] = [prevCoursei, nextCoursei], representing a prerequisite relationship between course prevCoursei and course nextCoursei: course prevCoursei has to be taken before course nextCoursei.
+
+In one semester, you can take any number of courses as long as you have taken all the prerequisites in the previous semester for the courses you are taking.
+
+Return the minimum number of semesters needed to take all courses. If there is no way to take all the courses, return -1.
+
+
+
+
+ Input: n = 3, relations = [[1,3],[2,3]]
+Output: 2
+Explanation: The figure above represents the given graph.
+In the first semester, you can take courses 1 and 2.
+In the second semester, you can take course 3.
+
+
+
+
+
+*/
+
+
+class Solution {
+public:
+    int minimumSemesters(int n, vector<vector<int>>& relations) {
+
+        // build the graph 
+
+        vector<int> indegree (n+1, 0);
+        vector<vector<int>> graph(n+1);
+
+        // Build graph
+        for (auto temp : relations) {
+            graph[temp[0]].push_back(temp[1]);
+            indegree[temp[1]]++;
+        }
+
+        // mark node as unvisited
+        vector<int> visited(n+1,0);
+
+     // run dfs for every node to check the cycle
+
+        for(int node = 1; node < n+1; node++) {
+
+
+
+            if(isCycle(node, visited, graph) == -1) {
+                // cycle so not possible
+                return -1;
+            }
+        }
+
+        // if no cycle is detected then find the longest path to get the value of number of semester required
+
+
+        vector<int> visitedLength (n+1,0);
+
+
+        int maxLength = 1;
+        for(int node = 1; node < n+1; node++) {
+
+            maxLength = max(maxLength, getDfsMaxLength(node, visitedLength, graph)) ;
+
+        }
+
+        return maxLength;
+
+    }
+
+
+    // dp approach
+    int getDfsMaxLength(int node, vector<int> & visitedLength, vector<vector<int>> & graph) {
+        // if already calculated then return the   longest path length
+
+        // if != 0. then it is already computed
+        if(visitedLength[node] != 0 ) {
+            return visitedLength[node];
+        }
+
+        int maxLength = 1;
+
+        for(auto &endNode :  graph[node]) {
+            int l = getDfsMaxLength ( endNode, visitedLength, graph);
+            maxLength = max(maxLength, l+1);
+
+        }
+
+        // cache it
+        visitedLength[node] = maxLength;
+        return maxLength;
+
+    }
+
+
+
+    // check the cycle in graph
+    int isCycle(int node, vector<int> & visited, vector<vector<int>> & graph ) {
+
+
+        // if already visited
+
+        if(visited[node] != 0) {
+            return visited[node];
+        }else{
+
+            // visiting state
+            visited[node] = -1;
+        }
+
+        for(auto & endNode : graph[node]) {
+            if(isCycle(endNode, visited, graph) == -1) {
+                return -1;
+            }
+        }
+
+        // visited state
+
+        visited[node] = 1;
+
+        return 1;
+    }
+};