Create Day 29 Course Schedule.cpp

Author: tusharjaiswal123

Day 29 Course Schedule.cpp

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+PROBLEM:
+
+
+
+
+There are a total of numCourses courses you have to take, labeled from 0 to numCourses-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, is it possible for you to finish all courses?
+
+ 
+Example 1:
+Input: numCourses = 2, prerequisites = [[1,0]]
+Output: true
+Explanation: There are a total of 2 courses to take. 
+             To take course 1 you should have finished course 0. So it is possible.
+
+Example 2:
+Input: numCourses = 2, prerequisites = [[1,0],[0,1]]
+Output: false
+Explanation: There are a total of 2 courses to take. 
+             To take course 1 you should have finished course 0, and to take course 0 you should
+             also have finished course 1. So it is impossible.
+ 
+
+Constraints:
+
+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.
+1. 1 <= numCourses <= 10^5
+
+
+
+
+
+SOLUTION:
+
+
+//Detect cycle in directed graph(using dfs/kahn's algo)
+
+
+
+class Solution {
+public:
+    
+    bool dfs(vector<int> adj[],vector<bool>& vis,vector<bool>& ancestor,int s)
+    {
+        vis[s]=true;
+        ancestor[s]=true;
+        
+        for(auto k:adj[s])
+        {
+            if(!vis[k])
+            {
+                if(dfs(adj,vis,ancestor,k))
+                    return true;
+            }
+            
+            else if(vis[k]==true && ancestor[k]==true)
+                return true;
+        }
+        
+        ancestor[s]=false;
+        return false;
+    }
+    
+    bool canFinish(int numCourses, vector<vector<int>>& prerequisites) {
+        
+        int i,n,a,b;
+        vector<int> adj[numCourses];
+        vector<bool> vis(numCourses,false);
+        vector<bool> ancestor(numCourses,false);
+        
+        n=prerequisites.size();
+        
+        for(i=0;i<n;i++)
+        {
+            a=prerequisites[i][0];
+            b=prerequisites[i][1];
+            
+            adj[b].push_back(a);
+        }
+        
+        for(i=0;i<numCourses;i++)
+        {
+            if(!vis[i])
+            {
+                if(dfs(adj,vis,ancestor,i))
+                    return false;
+            }
+        }
+        
+        return true;
+        
+        
+    }
+};