Create TreeCheck.java

Added a Java program to check if an undirected graph is a tree using DFS and adjacency matrix. Verifies connectivity and absence of cycles.

Author: amankumar100

src/main/java/com/thealgorithms/tree/GraphTreeCheck.java

@@ -0,0 +1,69 @@
+package com.thealgorithms.tree;
+
+import java.util.Scanner;
+
+class GraphTreeCheck {
+
+    private static final int MAX = 10;
+    private int[][] adjMatrix = new int[MAX][MAX];
+    private boolean[] visited = new boolean[MAX];
+    private int nodes;
+
+    public static void main(String[] args) {
+        Scanner in = new Scanner(System.in);
+        GraphTreeCheck graph = new GraphTreeCheck();
+
+        System.out.print("Enter the number of nodes: ");
+        graph.nodes = in.nextInt();
+
+        System.out.println("Enter the Adjacency Matrix (1 -> PATH, 0 -> NO PATH):");
+        for (int i = 1; i <= graph.nodes; i++) {
+            for (int j = 1; j <= graph.nodes; j++) {
+                graph.adjMatrix[i][j] = in.nextInt();
+                if (i == j) {
+                    graph.adjMatrix[i][j] = 0; // No self loops
+                }
+            }
+        }
+
+        if (graph.isTree()) {
+            System.out.println("The graph is a TREE.");
+        } else {
+            System.out.println("The graph is NOT a tree.");
+        }
+    }
+
+    public boolean isTree() {
+        // Check for cycles using DFS
+        if (hasCycle(1, -1)) {
+            return false;
+        }
+
+        // Check for connectivity
+        for (int i = 1; i <= nodes; i++) {
+            if (!visited[i]) {
+                return false;
+            }
+        }
+
+        return true;
+    }
+
+    private boolean hasCycle(int current, int parent) {
+        visited[current] = true;
+
+        for (int neighbor = 1; neighbor <= nodes; neighbor++) {
+            if (adjMatrix[current][neighbor] == 1) {
+                if (!visited[neighbor]) {
+                    if (hasCycle(neighbor, current)) {
+                        return true;
+                    }
+                } else if (neighbor != parent) {
+                    // Found a back edge indicating a cycle
+                    return true;
+                }
+            }
+        }
+        return false;
+    }
+}