chore: import upstream snapshot with attribution

graph/connected_components.cpp

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+/**
+ *
+ * \file
+ * \brief [Graph Connected Components
+ * (Connected Components)]
+ * (https://en.wikipedia.org/wiki/Component_(graph_theory))
+ *
+ * \author [Ayaan Khan](http://github.com/ayaankhan98)
+ *
+ * \details
+ * A graph is a collection of nodes also called vertices and these vertices
+ * are connected by edges. A connected component in a graph refers to a set of
+ * vertices which are reachable form one another.
+ *
+ * <pre>
+ * Example - Here is graph with 3 connected components
+ *
+ *      1   4           5               8
+ *     / \ /           / \             / \
+ *    2---3           6   7           9   10
+ *
+ *    first          second           third
+ *    component      component        component
+ * </pre>
+ *
+ */
+
+#include <algorithm>
+#include <cassert>
+#include <iostream>
+#include <vector>
+
+/**
+ * @namespace graph
+ * @brief Graph Algorithms
+ */
+
+namespace graph {
+/**
+ * @brief Function that add edge between two nodes or vertices of graph
+ *
+ * @param adj adjacency list of graph.
+ * @param u any node or vertex of graph.
+ * @param v any node or vertex of graph.
+ */
+void addEdge(std::vector<std::vector<int>> *adj, int u, int v) {
+    (*adj)[u - 1].push_back(v - 1);
+    (*adj)[v - 1].push_back(u - 1);
+}
+
+/**
+ * @brief Utility function for depth first seach algorithm
+ * this function explores the vertex which is passed into.
+ *
+ * @param adj adjacency list of graph.
+ * @param u vertex or node to be explored.
+ * @param visited already visited vertices.
+ */
+void explore(const std::vector<std::vector<int>> *adj, int u,
+             std::vector<bool> *visited) {
+    (*visited)[u] = true;
+    for (auto v : (*adj)[u]) {
+        if (!(*visited)[v]) {
+            explore(adj, v, visited);
+        }
+    }
+}
+
+/**
+ * @brief Function that perfoms depth first search algorithm on graph
+ * and calculated the number of connected components.
+ *
+ * @param adj adjacency list of graph.
+ *
+ * @return connected_components number of connected components in graph.
+ */
+int getConnectedComponents(const std::vector<std::vector<int>> *adj) {
+    int n = adj->size();
+    int connected_components = 0;
+    std::vector<bool> visited(n, false);
+
+    for (int i = 0; i < n; i++) {
+        if (!visited[i]) {
+            explore(adj, i, &visited);
+            connected_components++;
+        }
+    }
+    return connected_components;
+}
+}  // namespace graph
+
+/** Function to test the algorithm */
+void tests() {
+    std::cout << "Running predefined tests..." << std::endl;
+    std::cout << "Initiating Test 1..." << std::endl;
+    std::vector<std::vector<int>> adj1(9, std::vector<int>());
+    graph::addEdge(&adj1, 1, 2);
+    graph::addEdge(&adj1, 1, 3);
+    graph::addEdge(&adj1, 3, 4);
+    graph::addEdge(&adj1, 5, 7);
+    graph::addEdge(&adj1, 5, 6);
+    graph::addEdge(&adj1, 8, 9);
+
+    assert(graph::getConnectedComponents(&adj1) == 3);
+    std::cout << "Test 1 Passed..." << std::endl;
+
+    std::cout << "Innitiating Test 2..." << std::endl;
+    std::vector<std::vector<int>> adj2(10, std::vector<int>());
+    graph::addEdge(&adj2, 1, 2);
+    graph::addEdge(&adj2, 1, 3);
+    graph::addEdge(&adj2, 1, 4);
+    graph::addEdge(&adj2, 2, 3);
+    graph::addEdge(&adj2, 3, 4);
+    graph::addEdge(&adj2, 4, 8);
+    graph::addEdge(&adj2, 4, 10);
+    graph::addEdge(&adj2, 8, 10);
+    graph::addEdge(&adj2, 8, 9);
+    graph::addEdge(&adj2, 5, 7);
+    graph::addEdge(&adj2, 5, 6);
+    graph::addEdge(&adj2, 6, 7);
+
+    assert(graph::getConnectedComponents(&adj2) == 2);
+    std::cout << "Test 2 Passed..." << std::endl;
+}
+
+/** Main function */
+int main() {
+    /// running predefined tests
+    tests();
+
+    int vertices = int(), edges = int();
+    std::cout << "Enter the number of vertices : ";
+    std::cin >> vertices;
+    std::cout << "Enter the number of edges : ";
+    std::cin >> edges;
+
+    std::vector<std::vector<int>> adj(vertices, std::vector<int>());
+
+    int u = int(), v = int();
+    while (edges--) {
+        std::cin >> u >> v;
+        graph::addEdge(&adj, u, v);
+    }
+
+    int cc = graph::getConnectedComponents(&adj);
+    std::cout << cc << std::endl;
+    return 0;
+}