docs, test: Fit Topological Sort algorithm to contributing guidelines (#2835)

* Modified docs,test of topological sort algorithm

* Update topological_sort.cpp

* Add class "Graph"

* Update graph/topological_sort.cpp

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

* Add namespace topological_sort

---------

Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>

graph/topological_sort.cpp

@@ -1,50 +1,189 @@
-#include <algorithm>
-#include <iostream>
-#include <vector>
+/**
+ * @file
+ * @brief [Topological Sort
+ * Algorithm](https://en.wikipedia.org/wiki/Topological_sorting)
+ * @details
+ * Topological sorting of a directed graph is a linear ordering or its vertices
+ * such that for every directed edge (u,v) from vertex u to vertex v, u comes
+ * before v in the oredering.
+ *
+ * A topological sort is possible only in a directed acyclic graph (DAG).
+ * This file contains code of finding topological sort using Kahn's Algorithm
+ * which involves using Depth First Search technique
+ */
 
-int number_of_vertices,
-    number_of_edges;  // For number of Vertices (V) and number of edges (E)
-std::vector<std::vector<int>> graph;
-std::vector<bool> visited;
-std::vector<int> topological_order;
+#include <algorithm>  // For std::reverse
+#include <cassert>    // For assert
+#include <iostream>   // For IO operations
+#include <stack>      // For std::stack
+#include <stdexcept>  // For std::invalid_argument
+#include <vector>     // For std::vector
 
-void dfs(int v) {
-    visited[v] = true;
-    for (int u : graph[v]) {
-        if (!visited[u]) {
-            dfs(u);
+/**
+ * @namespace graph
+ * @brief Graph algorithms
+ */
+namespace graph {
+
+/**
+ * @namespace topological_sort
+ * @brief Topological Sort Algorithm
+ */
+namespace topological_sort {
+/**
+ * @class Graph
+ * @brief Class that represents a directed graph and provides methods for
+ * manipulating the graph
+ */
+class Graph {
+ private:
+    int n;                              // Number of nodes
+    std::vector<std::vector<int>> adj;  // Adjacency list representation
+
+ public:
+    /**
+     * @brief Constructor for the Graph class
+     * @param nodes Number of nodes in the graph
+     */
+    Graph(int nodes) : n(nodes), adj(nodes) {}
+
+    /**
+     * @brief Function that adds an edge between two nodes or vertices of graph
+     * @param u Start node of the edge
+     * @param v End node of the edge
+     */
+    void addEdge(int u, int v) { adj[u].push_back(v); }
+
+    /**
+     * @brief Get the adjacency list of the graph
+     * @returns A reference to the adjacency list
+     */
+    const std::vector<std::vector<int>>& getAdjacencyList() const {
+        return adj;
+    }
+
+    /**
+     * @brief Get the number of nodes in the graph
+     * @returns The number of nodes
+     */
+    int getNumNodes() const { return n; }
+};
+
+/**
+ * @brief Function to perform Depth First Search on the graph
+ * @param v Starting vertex for depth-first search
+ * @param visited Array representing whether each node has been visited
+ * @param graph Adjacency list of the graph
+ * @param s Stack containing the vertices for topological sorting
+ */
+void dfs(int v, std::vector<int>& visited,
+         const std::vector<std::vector<int>>& graph, std::stack<int>& s) {
+    visited[v] = 1;
+    for (int neighbour : graph[v]) {
+        if (!visited[neighbour]) {
+            dfs(neighbour, visited, graph, s);
         }
     }
-    topological_order.push_back(v);
+    s.push(v);
 }
 
-void topological_sort() {
-    visited.assign(number_of_vertices, false);
-    topological_order.clear();
-    for (int i = 0; i < number_of_vertices; ++i) {
+/**
+ * @brief Function to get the topological sort of the graph
+ * @param g Graph object
+ * @returns A vector containing the topological order of nodes
+ */
+std::vector<int> topologicalSort(const Graph& g) {
+    int n = g.getNumNodes();
+    const auto& adj = g.getAdjacencyList();
+    std::vector<int> visited(n, 0);
+    std::stack<int> s;
+
+    for (int i = 0; i < n; i++) {
         if (!visited[i]) {
-            dfs(i);
+            dfs(i, visited, adj, s);
         }
     }
-    reverse(topological_order.begin(), topological_order.end());
-}
-int main() {
-    std::cout
-        << "Enter the number of vertices and the number of directed edges\n";
-    std::cin >> number_of_vertices >> number_of_edges;
-    int x = 0, y = 0;
-    graph.resize(number_of_vertices, std::vector<int>());
-    for (int i = 0; i < number_of_edges; ++i) {
-        std::cin >> x >> y;
-        x--, y--;  // to convert 1-indexed to 0-indexed
-        graph[x].push_back(y);
+
+    std::vector<int> ans;
+    while (!s.empty()) {
+        int elem = s.top();
+        s.pop();
+        ans.push_back(elem);
     }
-    topological_sort();
-    std::cout << "Topological Order : \n";
-    for (int v : topological_order) {
-        std::cout << v + 1
-                  << ' ';  // converting zero based indexing back to one based.
+
+    if (ans.size() < n) {  // Cycle detected
+        throw std::invalid_argument("cycle detected in graph");
+    }
+    return ans;
+}
+}  // namespace topological_sort
+}  // namespace graph
+
+/**
+ * @brief Self-test implementation
+ * @returns void
+ */
+static void test() {
+    // Test 1
+    std::cout << "Testing for graph 1\n";
+    int n_1 = 6;
+    graph::topological_sort::Graph graph1(n_1);
+    graph1.addEdge(4, 0);
+    graph1.addEdge(5, 0);
+    graph1.addEdge(5, 2);
+    graph1.addEdge(2, 3);
+    graph1.addEdge(3, 1);
+    graph1.addEdge(4, 1);
+    std::vector<int> ans_1 = graph::topological_sort::topologicalSort(graph1);
+    std::vector<int> expected_1 = {5, 4, 2, 3, 1, 0};
+    std::cout << "Topological Sorting Order: ";
+    for (int i : ans_1) {
+        std::cout << i << " ";
     }
     std::cout << '\n';
+    assert(ans_1 == expected_1);
+    std::cout << "Test Passed\n\n";
+
+    // Test 2
+    std::cout << "Testing for graph 2\n";
+    int n_2 = 5;
+    graph::topological_sort::Graph graph2(n_2);
+    graph2.addEdge(0, 1);
+    graph2.addEdge(0, 2);
+    graph2.addEdge(1, 2);
+    graph2.addEdge(2, 3);
+    graph2.addEdge(1, 3);
+    graph2.addEdge(2, 4);
+    std::vector<int> ans_2 = graph::topological_sort::topologicalSort(graph2);
+    std::vector<int> expected_2 = {0, 1, 2, 4, 3};
+    std::cout << "Topological Sorting Order: ";
+    for (int i : ans_2) {
+        std::cout << i << " ";
+    }
+    std::cout << '\n';
+    assert(ans_2 == expected_2);
+    std::cout << "Test Passed\n\n";
+
+    // Test 3 - Graph with cycle
+    std::cout << "Testing for graph 3\n";
+    int n_3 = 3;
+    graph::topological_sort::Graph graph3(n_3);
+    graph3.addEdge(0, 1);
+    graph3.addEdge(1, 2);
+    graph3.addEdge(2, 0);
+    try {
+        graph::topological_sort::topologicalSort(graph3);
+    } catch (std::invalid_argument& err) {
+        assert(std::string(err.what()) == "cycle detected in graph");
+    }
+    std::cout << "Test Passed\n";
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run self test implementations
     return 0;
 }