Rename dfs to depth_first_search.:

graph/depth_first_search.cpp

@@ -0,0 +1,133 @@
+/**
+ *
+ * \file
+ * \brief [Depth First Search Algorithm
+ * (Depth First Search)](https://en.wikipedia.org/wiki/Depth-first_search)
+ *
+ * \author [Ayaan Khan](http://github.com/ayaankhan98)
+ *
+ * \details
+ * Depth First Search also quoted as DFS is a Graph Traversal Algorithm.
+ * Time Complexity O(|V| + |E|) where V is number of vertices and E
+ * is number of edges in graph.
+ *
+ * Application of Depth First Search are
+ *
+ * 1. Finding connected components
+ * 2. Finding 2-(edge or vertex)-connected components.
+ * 3. Finding 3-(edge or vertex)-connected components.
+ * 4. Finding the bridges of a graph.
+ * 5. Generating words in order to plot the limit set of a group.
+ * 6. Finding strongly connected components.
+ *
+ * And there are many more...
+ *
+ * <h4>Working</h4>
+ * 1. Mark all vertices as unvisited first
+ * 2. start exploring from some starting vertex.
+ *
+ *      While exploring vertex we mark the vertex as visited
+ *      and start exploring the vertices connected to this
+ *      vertex in recursive way.
+ *
+ */
+
+#include <algorithm>
+#include <iostream>
+#include <vector>
+
+/**
+ *
+ * \namespace graph
+ * \brief Graph Algorithms
+ *
+ */
+namespace graph {
+/**
+ * \brief
+ * Adds and edge between two vertices of graph say u and v in this
+ * case.
+ *
+ * @param adj Adjacency list representation of graph
+ * @param u first vertex
+ * @param v second vertex
+ *
+ */
+void addEdge(std::vector<std::vector<size_t>> *adj, size_t u, size_t v) {
+    /**
+     *
+     * Here we are considering undirected graph that's the
+     * reason we are adding v to the adjacency list representation of u
+     * and also adding u to the adjacency list representation of v
+     *
+     */
+    (*adj)[u - 1].push_back(v - 1);
+    (*adj)[v - 1].push_back(u - 1);
+}
+
+/**
+ *
+ * \brief
+ * Explores the given vertex, exploring a vertex means traversing
+ * over all the vertices which are connected to the vertex that is
+ * currently being explored.
+ *
+ * @param adj garph
+ * @param v vertex to be explored
+ * @param visited already visited vertices
+ *
+ */
+void explore(const std::vector<std::vector<size_t>> &adj, size_t v,
+             std::vector<bool> *visited) {
+    std::cout << v + 1 << " ";
+    (*visited)[v] = true;
+    for (auto x : adj[v]) {
+        if (!(*visited)[x]) {
+            explore(adj, x, visited);
+        }
+    }
+}
+
+/**
+ * \brief
+ * initiates depth first search algorithm.
+ *
+ * @param adj adjacency list of graph
+ * @param start vertex from where DFS starts traversing.
+ *
+ */
+void depth_first_search(const std::vector<std::vector<size_t>> &adj,
+                        size_t start) {
+    size_t vertices = adj.size();
+
+    std::vector<bool> visited(vertices, false);
+    explore(adj, start, &visited);
+}
+}  // namespace graph
+
+/** Main function */
+int main() {
+    size_t vertices = 0, edges = 0;
+    std::cout << "Enter the Vertices : ";
+    std::cin >> vertices;
+    std::cout << "Enter the Edges : ";
+    std::cin >> edges;
+
+    /// creating graph
+    std::vector<std::vector<size_t>> adj(vertices, std::vector<size_t>());
+
+    /// taking input for edges
+    std::cout << "Enter the vertices which have edges between them : "
+              << std::endl;
+    while (edges--) {
+        size_t u = 0, v = 0;
+        std::cin >> u >> v;
+        graph::addEdge(&adj, u, v);
+    }
+
+    /// running depth first search over graph
+    graph::depth_first_search(adj, 2);
+
+    std::cout << std::endl;
+    return 0;
+}