Create Depth_first_search.md

java/Depth_first_search.md

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+---
+id: DFS
+sidebar_position: 3
+title: Depth-First Search
+sidebar_label: DFS
+description: DFS algorithm implementation in Java.
+tags: [java, searching, graph traversal]
+---
+
+##*Description*
+
+Depth-First Search (DFS) is a graph traversal algorithm that explores nodes in a depthward motion. It starts at a selected node (root) and explores as far as possible along each branch before backtracking.
+
+##*Java implementation*
+
+```
+public class DFS {
+    public static void search(int[][] graph, int start) {
+        boolean[] visited = new boolean[graph.length];
+        dfs(graph, start, visited);
+    }
+
+    private static void dfs(int[][] graph, int node, boolean[] visited) {
+        visited[node] = true;
+        System.out.print(node + " ");
+        for (int neighbor : graph[node]) {
+            if (!visited[neighbor]) {
+                dfs(graph, neighbor, visited);
+            }
+        }
+    }
+
+    public static void main(String[] args) {
+        int[][] graph = {{1, 2}, {0, 3}, {0, 4}, {1}, {2}};
+        int start = 0;
+        search(graph, start);
+    }
+}
+```
+
+#*Complexity*
+
+- Time Complexity: O(V + E), where V is vertices and E is edges.
+- Space Complexity: O(V), for visited array and recursive stack.
+
+#*Use Cases for example*
+
+- Traversing social networks.
+- Web crawlers.
+- Finding connected components.
+
+#*Variants of this algorithm include:*
+
+- Pre-order DFS (current node before neighbors).
+- Post-order DFS (current node after neighbors).
+- In-order DFS (current node between neighbors).
+
+## Conclusion
+In this article, we learned about Depth first search and implemented it in Java.