From a13ce0b5d544f2472e81f861801ff3aa3e0f811e Mon Sep 17 00:00:00 2001
From: Evan Ferrao <evanferrao@gmail.com>
Date: Sun, 15 Feb 2026 17:47:11 +0530
Subject: [PATCH] add directed cycle detection and bipartite graphs

---
 Graphs/BipartiteGraphUsingBFSandDFS.java   | 134 ++++++++++++++++++++
 Graphs/CycleDetectionDirectedGraphDFS.java | 136 +++++++++++++++++++++
 2 files changed, 270 insertions(+)
 create mode 100644 Graphs/BipartiteGraphUsingBFSandDFS.java
 create mode 100644 Graphs/CycleDetectionDirectedGraphDFS.java

diff --git a/Graphs/BipartiteGraphUsingBFSandDFS.java b/Graphs/BipartiteGraphUsingBFSandDFS.java
new file mode 100644
index 0000000..13b2be0
--- /dev/null
+++ b/Graphs/BipartiteGraphUsingBFSandDFS.java
@@ -0,0 +1,134 @@
+// https://leetcode.com/problems/is-graph-bipartite/
+
+import java.util.*;
+import java.io.*;
+
+class BipartiteGraphUsingBFSandDFS {
+
+    // BFS
+    public static boolean bfs(int node, int color, int colorArray[], ArrayList<ArrayList<Integer>> adj){
+        Queue<Integer> q = new LinkedList<>();
+
+        q.add(node);
+        colorArray[node] = color;
+
+        while(!q.isEmpty()){
+            Integer currNodeode = q.poll();
+
+            for(Integer it : adj.get(currNodeode)){
+                // if(!visited[it]){
+                //     visited[it] = true;
+                //     q.add(it);
+                // }
+                if (colorArray[it]==-1){ // not colored yet (not visited basically)
+                    colorArray[it] = 1 - colorArray[currNodeode];
+                    q.add(it);
+                } else if (colorArray[it]==colorArray[currNodeode]){
+                    return false;
+                }
+            }
+        }
+
+        return true;
+    }
+
+
+    // DFS
+    public static boolean dfs(int node, int color, int colorArray[], ArrayList<ArrayList<Integer>> adj){
+        colorArray[node] = color;
+
+        for (Integer it: adj.get(node)){
+            if (colorArray[it]==-1){ // not colored yet (not visited basically)
+                if (dfs(it,1-color, colorArray, adj)==false) return false;
+            } else if (colorArray[it]==color){
+                return false;
+            }
+        }
+        return true;
+    }
+
+
+    public static boolean isBipartite(int graph[][]){
+
+        int V = graph.length;
+
+        ArrayList<ArrayList<Integer>> adj = new ArrayList<>();
+        for(int i=0;i<V;i++) adj.add(new ArrayList<>());
+
+        for(int u=0; u<V; u++){
+            for(int v : graph[u]){
+                adj.get(u).add(v);
+            }
+        }
+
+        int colorArray[] = new int[V];
+        Arrays.fill(colorArray, -1);
+
+        for(int i=0;i<V;i++){
+            if(colorArray[i] == -1){
+
+                // choose one
+                if(dfs(i, 0, colorArray, adj)==false) return false;
+                // if(!bfs(i, 0, colorArray, adj)) return false;
+            }
+        }
+
+        return true;
+    }
+
+
+    //  DRIVER
+    public static void main(String args[]){
+
+        // ============ CASE 1 ============
+        {
+            int graph[][] = {
+                {1,2,3},
+                {0,2},
+                {0,1,3},
+                {0,2}
+            };
+
+            System.out.printf("Case 1: %s\n",
+                isBipartite(graph) ? "Bipartite" : "Not Bipartite");
+        }
+
+        // ============ CASE 2 ============
+        {
+            int graph[][] = {
+                {1,3},
+                {0,2},
+                {1,3},
+                {0,2}
+            };
+
+            System.out.printf("Case 2: %s\n",
+                isBipartite(graph) ? "Bipartite" : "Not Bipartite");
+        }
+
+        // ============ CASE 3 ============
+        {
+            int graph[][] = {
+                {1},
+                {0,2},
+                {1,3},
+                {2}
+            };
+
+            System.out.printf("Case 3: %s\n",
+                isBipartite(graph) ? "Bipartite" : "Not Bipartite");
+        }
+
+        // ============ CASE 4 ============
+        {
+            int graph[][] = {
+                {},
+                {},
+                {}
+            };
+
+            System.out.printf("Case 4: %s\n",
+                isBipartite(graph) ? "Bipartite" : "Not Bipartite");
+        }
+    }
+}
diff --git a/Graphs/CycleDetectionDirectedGraphDFS.java b/Graphs/CycleDetectionDirectedGraphDFS.java
new file mode 100644
index 0000000..6a42aa9
--- /dev/null
+++ b/Graphs/CycleDetectionDirectedGraphDFS.java
@@ -0,0 +1,136 @@
+import java.util.*;
+import java.io.*;
+
+class CycleDetectionDirectedGraphDFS {
+
+    // DFS
+    public static boolean dfsCheck(int node, boolean visited[],
+                              boolean pathVis[],
+                              ArrayList<ArrayList<Integer>> adj){
+
+        visited[node] = true;
+        pathVis[node] = true;
+
+        for(int next : adj.get(node)){
+
+            if(!visited[next]){
+                if(dfsCheck(next, visited, pathVis, adj)) return true;
+            }
+            else if(pathVis[next]){
+                return true;
+            }
+        }
+
+        pathVis[node] = false;
+        return false;
+    }
+
+
+    public static boolean isCyclic(int V, ArrayList<ArrayList<Integer>> adj){
+
+        boolean visited[] = new boolean[V];
+        boolean pathVis[] = new boolean[V];
+
+        for(int i=0;i<V;i++){
+            if(!visited[i]){
+                if(dfsCheck(i, visited, pathVis, adj)) return true;
+            }
+        }
+
+        return false;
+    }
+
+
+    // helper to create adjacency list
+    public static ArrayList<ArrayList<Integer>> makeGraph(int V){
+        ArrayList<ArrayList<Integer>> adj = new ArrayList<>();
+        for(int i=0;i<V;i++) adj.add(new ArrayList<>());
+        return adj;
+    }
+
+
+    // DRIVER
+    public static void main(String args[]){
+
+        // ================= CASE 1 =================
+        {
+            int V = 6;
+            ArrayList<ArrayList<Integer>> adj = makeGraph(V);
+
+            /*
+                0 → 1 → 2 → 3
+                    ↑     ↓
+                    └─────┘
+                4 → 5
+            */
+
+            adj.get(0).add(1);
+            adj.get(1).add(2);
+            adj.get(2).add(3);
+            adj.get(3).add(1);
+            adj.get(4).add(5);
+
+            System.out.printf("Case 1: %s\n",
+                isCyclic(V, adj) ? "Cycle detected" : "No cycle");
+        }
+
+
+        // ================= CASE 2 =================
+        {
+            int V = 4;
+            ArrayList<ArrayList<Integer>> adj = makeGraph(V);
+
+            /*
+                0 → 1 → 2 → 3
+                No cycle
+            */
+
+            adj.get(0).add(1);
+            adj.get(1).add(2);
+            adj.get(2).add(3);
+
+            System.out.printf("Case 2: %s\n",
+                isCyclic(V, adj) ? "Cycle detected" : "No cycle");
+        }
+
+
+        // ================= CASE 3 =================
+        {
+            int V = 3;
+            ArrayList<ArrayList<Integer>> adj = makeGraph(V);
+
+            /*
+                0 → 1
+                1 → 2
+                2 → 0
+            */
+
+            adj.get(0).add(1);
+            adj.get(1).add(2);
+            adj.get(2).add(0);
+
+            System.out.printf("Case 3: %s\n",
+                isCyclic(V, adj) ? "Cycle detected" : "No cycle");
+        }
+
+
+        // ================= CASE 4 =================
+        {
+            int V = 5;
+            ArrayList<ArrayList<Integer>> adj = makeGraph(V);
+
+            /*
+                disconnected, no cycle
+                0 → 1
+                2 → 3
+                4 alone
+            */
+
+            adj.get(0).add(1);
+            adj.get(2).add(3);
+
+            System.out.printf("Case 4: %s\n",
+                isCyclic(V, adj) ? "Cycle detected" : "No cycle");
+        }
+    }
+}