From 28fdd13ec6583281002102108476af755fb43fe0 Mon Sep 17 00:00:00 2001
From: Harshita Patidar <harshitapatidar257@gmail.com>
Date: Sat, 4 Oct 2025 13:55:57 +0530
Subject: [PATCH 1/2] Create 207. Course Schedule.cpp

---
 207. Course Schedule.cpp | 102 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 102 insertions(+)
 create mode 100644 207. Course Schedule.cpp

diff --git a/207. Course Schedule.cpp b/207. Course Schedule.cpp
new file mode 100644
index 0000000..f2cf1e9
--- /dev/null
+++ b/207. Course Schedule.cpp	
@@ -0,0 +1,102 @@
+/*
+207. Course Schedule
+Medium
+
+There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1. 
+You are given an array prerequisites where prerequisites[i] = [ai, bi] indicates that 
+you must take course bi first if you want to take course ai.
+
+For example:
+- [0, 1] means: to take course 0 you must finish course 1 first.
+
+Return true if you can finish all courses. Otherwise, return false.
+
+
+---------------- Example 1 ----------------
+Input: numCourses = 2, prerequisites = [[1,0]]
+Output: true
+Explanation: To take course 1 you must finish course 0 → possible.
+
+---------------- Example 2 ----------------
+Input: numCourses = 2, prerequisites = [[1,0],[0,1]]
+Output: false
+Explanation: Cycle exists (0 requires 1 and 1 requires 0) → impossible.
+
+
+Constraints:
+1 <= numCourses <= 2000
+0 <= prerequisites.length <= 5000
+prerequisites[i].length == 2
+0 <= ai, bi < numCourses
+All pairs prerequisites[i] are unique.
+*/
+
+
+// ---------------- Approach ----------------
+//
+// This is a **cycle detection in a directed graph** problem.
+// - Each course is a node.
+// - A prerequisite pair [a, b] represents a directed edge b → a.
+// - If there is a cycle in this graph, it means courses are interdependent 
+//   and cannot all be finished.
+//
+// We use DFS with two arrays:
+// - visited[node]: to mark nodes that have been fully processed.
+// - pathVisit[node]: to mark nodes in the current DFS recursion stack.
+//
+// If during DFS we encounter a node that is already in the current path (pathVisit),
+// it means we found a cycle → return false.
+
+
+// ---------------- Intuition ----------------
+//
+// - Think of prerequisites as a graph of dependencies.
+// - If a cycle exists, some course depends on itself indirectly → impossible to finish.
+// - If no cycle exists, we can always complete courses in a valid topological order.
+
+
+// ---------------- Solution in Code ----------------
+
+class Solution {
+public:
+    bool dfs(vector<vector<int>> &adj, vector<int> &visited, vector<int> &pathVisit, int node) {
+        visited[node] = 1;
+        pathVisit[node] = 1;
+
+        for (int neighbor : adj[node]) {
+            if (!visited[neighbor]) {
+                if (dfs(adj, visited, pathVisit, neighbor)) {
+                    return true; // cycle detected
+                }
+            }
+            else if (pathVisit[neighbor]) {
+                return true; // back edge → cycle
+            }
+        }
+
+        pathVisit[node] = 0; // backtrack
+        return false;
+    }
+
+    bool canFinish(int numCourses, vector<vector<int>>& prerequisites) {
+        // Build adjacency list from prerequisites
+        vector<vector<int>> adj(numCourses);
+        for (auto &edge : prerequisites) {
+            int a = edge[0], b = edge[1];
+            adj[b].push_back(a);
+        }
+
+        vector<int> visited(numCourses, 0);
+        vector<int> pathVisit(numCourses, 0);
+
+        // Run DFS from each unvisited node
+        for (int i = 0; i < numCourses; i++) {
+            if (!visited[i]) {
+                if (dfs(adj, visited, pathVisit, i)) {
+                    return false; // cycle found
+                }
+            }
+        }
+        return true;
+    }
+};

From 68aa1bda63ff50400cae7ea15edbcfd8c34c117f Mon Sep 17 00:00:00 2001
From: SjxSubham <sjxsubham@gmail.com>
Date: Sat, 4 Oct 2025 22:42:08 +0530
Subject: [PATCH 2/2] Remove problem description and examples from Course
 Schedule

Removed problem statement and example comments from the Course Schedule file.
---
 207. Course Schedule.cpp | 34 ----------------------------------
 1 file changed, 34 deletions(-)

diff --git a/207. Course Schedule.cpp b/207. Course Schedule.cpp
index f2cf1e9..bd1fe4a 100644
--- a/207. Course Schedule.cpp	
+++ b/207. Course Schedule.cpp	
@@ -1,37 +1,3 @@
-/*
-207. Course Schedule
-Medium
-
-There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1. 
-You are given an array prerequisites where prerequisites[i] = [ai, bi] indicates that 
-you must take course bi first if you want to take course ai.
-
-For example:
-- [0, 1] means: to take course 0 you must finish course 1 first.
-
-Return true if you can finish all courses. Otherwise, return false.
-
-
----------------- Example 1 ----------------
-Input: numCourses = 2, prerequisites = [[1,0]]
-Output: true
-Explanation: To take course 1 you must finish course 0 → possible.
-
----------------- Example 2 ----------------
-Input: numCourses = 2, prerequisites = [[1,0],[0,1]]
-Output: false
-Explanation: Cycle exists (0 requires 1 and 1 requires 0) → impossible.
-
-
-Constraints:
-1 <= numCourses <= 2000
-0 <= prerequisites.length <= 5000
-prerequisites[i].length == 2
-0 <= ai, bi < numCourses
-All pairs prerequisites[i] are unique.
-*/
-
-
 // ---------------- Approach ----------------
 //
 // This is a **cycle detection in a directed graph** problem.