Merge remote-tracking branch 'upstream/fixgraph' into fixgraph

CMakeLists.txt

@@ -39,6 +39,7 @@ add_subdirectory(probability)
 add_subdirectory(data_structures)
 add_subdirectory(machine_learning)
 add_subdirectory(numerical_methods)
+add_subdirectory(graph)
 
 cmake_policy(SET CMP0054 NEW)
 cmake_policy(SET CMP0057 NEW)

graph/CMakeLists.txt

@@ -0,0 +1,20 @@
+# If necessary, use the RELATIVE flag, otherwise each source file may be listed
+# with full pathname. RELATIVE may makes it easier to extract an executable name
+# automatically.
+file( GLOB APP_SOURCES RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} *.cpp )
+# file( GLOB APP_SOURCES ${CMAKE_SOURCE_DIR}/*.c )
+# AUX_SOURCE_DIRECTORY(${CMAKE_CURRENT_SOURCE_DIR} APP_SOURCES)
+foreach( testsourcefile ${APP_SOURCES} )
+    # I used a simple string replace, to cut off .cpp.
+    string( REPLACE ".cpp" "" testname ${testsourcefile} )
+    add_executable( ${testname} ${testsourcefile} )
+
+    set_target_properties(${testname} PROPERTIES
+        LINKER_LANGUAGE CXX
+    )
+    if(OpenMP_CXX_FOUND)
+        target_link_libraries(${testname} OpenMP::OpenMP_CXX)
+    endif()
+    install(TARGETS ${testname} DESTINATION "bin/graph")
+
+endforeach( testsourcefile ${APP_SOURCES} )

graph/bfs.cpp

@@ -1,62 +1,196 @@
+/**
+ *
+ * \file
+ * \brief [Breadth First Search Algorithm
+ * (Breadth First Search)](https://en.wikipedia.org/wiki/Breadth-first_search)
+ *
+ * \author [Ayaan Khan](http://github.com/ayaankhan98)
+ *
+ * \details
+ * Breadth First Search also quoted as BFS is a Graph Traversal Algorithm.
+ * Time Complexity O(|V| + |E|) where V are the number of vertices and E
+ * are the number of edges in the graph.
+ *
+ * Applications of Breadth First Search are
+ *
+ * 1. Finding shortest path between two vertices say u and v, with path
+ *    length measured by number of edges (an advantage over depth first
+ *    search algorithm)
+ * 2. Ford-Fulkerson Method for computing the maximum flow in a flow network.
+ * 3. Testing bipartiteness of a graph.
+ * 4. Cheney's Algorithm, Copying garbage collection.
+ *
+ * And there are many more...
+ *
+ * <h4>working</h4>
+ * In the implementation below we first created a graph using the adjacency
+ * list representation of graph.
+ * Breadth First Search Works as follows
+ * it requires a vertex as a start vertex, Start vertex is that vertex
+ * from where you want to start traversing the graph.
+ * we maintain a bool array or a vector to keep track of the vertices
+ * which we have visited so that we do not traverse the visited vertices
+ * again and again and eventually fall into an infinite loop. Along with this
+ * boolen array we use a Queue.
+ *
+ * 1. First we mark the start vertex as visited.
+ * 2. Push this visited vertex in the Queue.
+ * 3. while the queue is not empty we repeat the following steps
+ *
+ *      1. Take out an element from the front of queue
+ *      2. start exploring the adjacency list of this vertex
+ *         if element in the adjacency list is not visited then we
+ *         push that element into the queue and mark this as visited
+ *
+ */
+#include <algorithm>
+#include <cassert>
 #include <iostream>
-using namespace std;
+#include <queue>
-class graph {
+#include <vector>
-    int v;
-    list<int> *adj;
 
- public:
+/**
-    graph(int v);
+ * \namespace graph
-    void addedge(int src, int dest);
+ * \brief Graph algorithms
-    void printgraph();
+ */
-    void bfs(int s);
+namespace graph {
-};
+/**
-graph::graph(int v) {
+ * \brief
-    this->v = v;
+ * Adds and edge between two vertices of graph say u and v in this
-    this->adj = new list<int>[v];
+ * case.
+ *
+ * @param adj Adjacency list representation of graph
+ * @param u first vertex
+ * @param v second vertex
+ *
+ */
+void addEdge(std::vector<std::vector<int>> *adj, int u, int v) {
+    /**
+     * Here we are considering directed graph that's the
+     * reason we are adding v to the adjacency list representation of u
+     * but not adding u to the adjacency list representation of v
+     *
+     * in case of a un-directed graph you can un comment the statement below.
+     */
+    (*adj)[u - 1].push_back(v - 1);
+    // adj[v - 1].push_back(u -1);
 }
-void graph::addedge(int src, int dest) {
+
-    src--;
+/**
-    dest--;
+ * \brief
-    adj[src].push_back(dest);
+ * Function performs the breadth first search algorithm over the graph
-    // adj[dest].push_back(src);
+ *
+ * @param adj Adjacency list representation of graph
+ * @param start vertex from where traversing starts
+ *
+ */
+std::vector<int> beadth_first_search(const std::vector<std::vector<int>> &adj,
+                                     int start) {
+    size_t vertices = adj.size();
+
+    std::vector<int> result;
+
+    /// vector to keep track of visited vertices
+    std::vector<bool> visited(vertices, 0);
+
+    std::queue<int> tracker;
+    /// marking the start vertex as visited
+    visited[start] = true;
+    tracker.push(start);
+    while (!tracker.empty()) {
+        size_t vertex = tracker.front();
+        tracker.pop();
+        result.push_back(vertex + 1);
+        for (auto x : adj[vertex]) {
+            /// if the vertex is not visited then mark this as visited
+            /// and push it to the queue
+            if (!visited[x]) {
+                visited[x] = true;
+                tracker.push(x);
+            }
+        }
+    }
+    return result;
 }
-void graph::printgraph() {
+}  // namespace graph
-    for (int i = 0; i < this->v; i++) {
+
-        cout << "Adjacency list of vertex " << i + 1 << " is \n";
+void tests() {
-        list<int>::iterator it;
+    std::cout << "Initiating Tests" << std::endl;
-        for (it = adj[i].begin(); it != adj[i].end(); ++it) {
+
-            cout << *it + 1 << " ";
+    /// Test 1 Begin
-        }
+    std::vector<std::vector<int>> graphData(4, std::vector<int>());
-        cout << endl;
+    graph::addEdge(&graphData, 1, 2);
-    }
+    graph::addEdge(&graphData, 1, 3);
-}
+    graph::addEdge(&graphData, 2, 3);
-void graph::bfs(int s) {
+    graph::addEdge(&graphData, 3, 1);
-    bool *visited = new bool[this->v + 1];
+    graph::addEdge(&graphData, 3, 4);
-    memset(visited, false, sizeof(bool) * (this->v + 1));
+    graph::addEdge(&graphData, 4, 4);
-    visited[s] = true;
+
-    list<int> q;
+    std::vector<int> returnedResult = graph::beadth_first_search(graphData, 2);
-    q.push_back(s);
+    std::vector<int> correctResult = {3, 1, 4, 2};
-    list<int>::iterator it;
+
-    while (!q.empty()) {
+    assert(std::equal(correctResult.begin(), correctResult.end(),
-        int u = q.front();
+                      returnedResult.begin()));
-        cout << u << " ";
+    std::cout << "Test 1 Passed..." << std::endl;
-        q.pop_front();
+
-        for (it = adj[u].begin(); it != adj[u].end(); ++it) {
+    /// Test 2 Begin
-            if (visited[*it] == false) {
+    /// clear data from previous test
-                visited[*it] = true;
+    returnedResult.clear();
-                q.push_back(*it);
+    correctResult.clear();
-            }
+
-        }
+    returnedResult = graph::beadth_first_search(graphData, 0);
-    }
+    correctResult = {1, 2, 3, 4};
+
+    assert(std::equal(correctResult.begin(), correctResult.end(),
+                      returnedResult.begin()));
+    std::cout << "Test 2 Passed..." << std::endl;
+
+    /// Test 3 Begins
+    /// clear data from previous test
+    graphData.clear();
+    returnedResult.clear();
+    correctResult.clear();
+
+    graphData.resize(6);
+    graph::addEdge(&graphData, 1, 2);
+    graph::addEdge(&graphData, 1, 3);
+    graph::addEdge(&graphData, 2, 4);
+    graph::addEdge(&graphData, 3, 4);
+    graph::addEdge(&graphData, 2, 5);
+    graph::addEdge(&graphData, 4, 6);
+
+    returnedResult = graph::beadth_first_search(graphData, 0);
+    correctResult = {1, 2, 3, 4, 5, 6};
+
+    assert(std::equal(correctResult.begin(), correctResult.end(),
+                      returnedResult.begin()));
+    std::cout << "Test 3 Passed..." << std::endl;
 }
+
+/** Main function */
 int main() {
-    graph g(4);
+    /// running predefined test cases
-    g.addedge(1, 2);
+    tests();
-    g.addedge(2, 3);
+
-    g.addedge(3, 4);
+    size_t vertices, edges;
-    g.addedge(1, 4);
+    std::cout << "Enter the number of vertices : ";
-    g.addedge(1, 3);
+    std::cin >> vertices;
-    // g.printgraph();
+    std::cout << "Enter the number of edges : ";
-    g.bfs(2);
+    std::cin >> edges;
+
+    /// creating a graph
+    std::vector<std::vector<int>> adj(vertices, std::vector<int>());
+
+    /// taking input for edges
+    std::cout << "Enter vertices in pair which have edges between them : "
+              << std::endl;
+    while (edges--) {
+        int u, v;
+        std::cin >> u >> v;
+        graph::addEdge(&adj, u, v);
+    }
+
+    /// running Breadth First Search Algorithm on the graph
+    graph::beadth_first_search(adj, 0);
     return 0;
 }

graph/bridge_finding_with_tarjan_algorithm.cpp

@@ -7,9 +7,11 @@
 #include <algorithm>  //  for min & max
 #include <iostream>   //  for cout
 #include <vector>     //  for std::vector
+
 using std::cout;
 using std::min;
 using std::vector;
+
 class Solution {
     vector<vector<int>> graph;
     vector<int> in_time, out_time;

graph/connected_components.cpp

@@ -15,9 +15,9 @@
  * <pre>
  * Example - Here is graph with 3 connected components
  *
- *      3   9           6               8
+ *      1   4           5               8
  *     / \ /           / \             / \
- *    2---4           2   7           3   7
+ *    2---3           6   7           9   10
  *
  *    first          second           third
  *    component      component        component
@@ -26,97 +26,123 @@
  */
 
 #include <algorithm>
+#include <cassert>
 #include <iostream>
 #include <vector>
 
-using std::vector;
-
 /**
- * Class for representing graph as a adjacency list.
+ * @namespace graph
+ * @brief Graph Algorithms
  */
-class graph {
- private:
-    /** \brief adj stores adjacency list representation of graph */
-    vector<vector<int>> adj;
-
-    /** \brief keep track of connected components */
-    int connected_components;
-
-    void depth_first_search();
-    void explore(int, vector<bool> &);
-
- public:
-    /**
-     * \brief Constructor that intiliazes the graph on creation and set
-     * the connected components to 0
-     */
-    explicit graph(int n) : adj(n, vector<int>()) { connected_components = 0; }
-
-    void addEdge(int, int);
-
-    /**
-     * \brief Function the calculates the connected compoents in the graph
-     * by performing the depth first search on graph
-     *
-     * @return connected_components total connected components in graph
-     */
-    int getConnectedComponents() {
-        depth_first_search();
-        return connected_components;
-    }
-};
 
+namespace graph {
 /**
- * \brief Function that add edge between two nodes or vertices of graph
+ * @brief Function that add edge between two nodes or vertices of graph
  *
- * @param u any node or vertex of graph
+ * @param adj adjacency list of graph.
- * @param v any node or vertex of graph
+ * @param u any node or vertex of graph.
+ * @param v any node or vertex of graph.
  */
-void graph::addEdge(int u, int v) {
+void addEdge(std::vector<std::vector<int>> *adj, int u, int v) {
-    adj[u - 1].push_back(v - 1);
+    (*adj)[u - 1].push_back(v - 1);
-    adj[v - 1].push_back(u - 1);
+    (*adj)[v - 1].push_back(u - 1);
 }
 
 /**
- * \brief Function that perfoms depth first search algorithm on graph
+ * @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 graph::depth_first_search() {
+void explore(const std::vector<std::vector<int>> *adj, int u,
-    int n = adj.size();
+             std::vector<bool> *visited) {
-    vector<bool> visited(n, false);
+    (*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(i, visited);
+            explore(adj, i, &visited);
             connected_components++;
         }
     }
+    return connected_components;
 }
-/**
+}  // namespace graph
- * \brief Utility function for depth first seach algorithm
+
- * this function explores the vertex which is passed into.
+/** Function to test the algorithm */
- *
+void tests() {
- * @param u vertex or node to be explored
+    std::cout << "Running predefined tests..." << std::endl;
- * @param visited already visited vertex
+    std::cout << "Initiating Test 1..." << std::endl;
- */
+    std::vector<std::vector<int>> adj1(9, std::vector<int>());
-void graph::explore(int u, vector<bool> &visited) {
+    graph::addEdge(&adj1, 1, 2);
-    visited[u] = true;
+    graph::addEdge(&adj1, 1, 3);
-    for (auto v : adj[u]) {
+    graph::addEdge(&adj1, 3, 4);
-        if (!visited[v]) {
+    graph::addEdge(&adj1, 5, 7);
-            explore(v, visited);
+    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() {
-    /// creating a graph with 4 vertex
+    /// running predefined tests
-    graph g(4);
+    tests();
 
-    /// Adding edges between vertices
+    int vertices = int(), edges = int();
-    g.addEdge(1, 2);
+    std::cout << "Enter the number of vertices : ";
-    g.addEdge(3, 2);
+    std::cin >> vertices;
+    std::cout << "Enter the number of edges : ";
+    std::cin >> edges;
 
-    /// printing the connected components
+    std::vector<std::vector<int>> adj(vertices, std::vector<int>());
-    std::cout << g.getConnectedComponents();
+
+    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;
 }

graph/cycle_check_directed_graph.cpp

@@ -1,313 +1,57 @@
-/**
+#include <iostream>
- * @file cycle_check_directed graph.cpp
+#include <vector>
- *
+#include <stdlib.h>
- * @brief BFS and DFS algorithms to check for cycle in a directed graph.
+using std::vector;
- *
+using std::pair;
- * @author [Anmol3299](mailto:mittalanmol22@gmail.com)
- *
- */
 
-#include <iostream>     // for std::cout
+void explore(int i, vector<vector<int>> &adj, int *state)
-#include <map>          // for std::map
+{
-#include <queue>        // for std::queue
+  state[i] = 1;
-#include <stdexcept>    // for throwing errors
+  for(auto it2 : adj[i])
-#include <type_traits>  // for std::remove_reference
+  {
-#include <utility>      // for std::move
+    if (state[it2] == 0)
-#include <vector>       // for std::vector
+    {
-
+      explore(it2, adj,state);
-/**
+    }
- * Implementation of non-weighted directed edge of a graph.
+    if (state[it2] == 1)
- *
+    {
- * The source vertex of the edge is labelled "src" and destination vertex is
+      std::cout<<"1";
- * labelled "dest".
+      exit(0);
- */
+    }
-struct Edge {
+  }
-    unsigned int src;
+  state[i] = 2;
-    unsigned int dest;
-
-    Edge() = delete;
-    ~Edge() = default;
-    Edge(Edge&&) = default;
-    Edge& operator=(Edge&&) = default;
-    Edge(Edge const&) = default;
-    Edge& operator=(Edge const&) = default;
-
-    /** Set the source and destination of the vertex.
-     *
-     * @param source is the source vertex of the edge.
-     * @param destination is the destination vertex of the edge.
-     */
-    Edge(unsigned int source, unsigned int destination)
-        : src(source), dest(destination) {}
 };
+int acyclic(vector<vector<int> > &adj,size_t n) {
+  //write your code here
 
-using AdjList = std::map<unsigned int, std::vector<unsigned int>>;
+  int state[n]; // permitted states are 0 1 and 2 
 
-/**
+  // mark the states of all vertices initially to 0
- * Implementation of graph class.
+  for(int i=0;i<n;i++)
- *
+    state[i] = 0;
- * The graph will be represented using Adjacency List representation.
- * This class contains 2 data members "m_vertices" & "m_adjList" used to
- * represent the number of vertices and adjacency list of the graph
- * respectively. The vertices are labelled 0 - (m_vertices - 1).
- */
-class Graph {
- public:
-    Graph() : m_vertices(0), m_adjList({}) {}
-    ~Graph() = default;
-    Graph(Graph&&) = default;
-    Graph& operator=(Graph&&) = default;
-    Graph(Graph const&) = default;
-    Graph& operator=(Graph const&) = default;
 
-    /** Create a graph from vertices and adjacency list.
+  for(auto it1 = 0; it1 != adj.size(); it1++)
-     *
+  {
-     * @param vertices specify the number of vertices the graph would contain.
+    if (state[it1] == 0)
-     * @param adjList is the adjacency list representation of graph.
+      explore(it1,adj,state);
-     */
+    if (state[it1] == 1)
-    Graph(unsigned int vertices, AdjList const& adjList)
+    {
-        : m_vertices(vertices), m_adjList(adjList) {}
+      std::cout<<"1";
-
+      exit(0);
-    /** Create a graph from vertices and adjacency list.
-     *
-     * @param vertices specify the number of vertices the graph would contain.
-     * @param adjList is the adjacency list representation of graph.
-     */
-    Graph(unsigned int vertices, AdjList&& adjList)
-        : m_vertices(vertices), m_adjList(std::move(adjList)) {}
-
-    /** Create a graph from vertices and a set of edges.
-     *
-     * Adjacency list of the graph would be created from the set of edges. If
-     * the source or destination of any edge has a value greater or equal to
-     * number of vertices, then it would throw a range_error.
-     *
-     * @param vertices specify the number of vertices the graph would contain.
-     * @param edges is a vector of edges.
-     */
-    Graph(unsigned int vertices, std::vector<Edge> const& edges)
-        : m_vertices(vertices) {
-        for (auto const& edge : edges) {
-            if (edge.src >= vertices || edge.dest >= vertices) {
-                throw std::range_error(
-                    "Either src or dest of edge out of range");
-            }
-            m_adjList[edge.src].emplace_back(edge.dest);
     }
   }
-
+  std::cout<<"0";
-    /** Return a const reference of the adjacency list.
-     *
-     * @return const reference to the adjacency list
-     */
-    std::remove_reference<AdjList>::type const& getAdjList() const {
-        return m_adjList;
-    }
-
-    /**
-     * @return number of vertices in the graph.
-     */
-    unsigned int getVertices() const { return m_vertices; }
-
-    /** Add vertices in the graph.
-     *
-     * @param num is the number of vertices to be added. It adds 1 vertex by
-     * default.
-     *
-     */
-    void addVertices(unsigned int num = 1) { m_vertices += num; }
-
-    /** Add an edge in the graph.
-     *
-     * @param edge that needs to be added.
-     */
-    void addEdge(Edge const& edge) {
-        if (edge.src >= m_vertices || edge.dest >= m_vertices) {
-            throw std::range_error("Either src or dest of edge out of range");
-        }
-        m_adjList[edge.src].emplace_back(edge.dest);
-    }
-
-    /** Add an Edge in the graph
-     *
-     * @param source is source vertex of the edge.
-     * @param destination is the destination vertex of the edge.
-     */
-    void addEdge(unsigned int source, unsigned int destination) {
-        if (source >= m_vertices || destination >= m_vertices) {
-            throw std::range_error(
-                "Either source or destination of edge out of range");
-        }
-        m_adjList[source].emplace_back(destination);
-    }
-
- private:
-    unsigned int m_vertices;
-    AdjList m_adjList;
-};
-
-/**
- * Check if a directed graph has a cycle or not.
- *
- * This class provides 2 methods to check for cycle in a directed graph:
- * isCyclicDFS & isCyclicBFS.
- *
- * - isCyclicDFS uses DFS traversal method to check for cycle in a graph.
- * - isCyclidBFS used BFS traversal method to check for cycle in a graph.
- */
-class CycleCheck {
- private:
-    enum nodeStates : uint8_t { not_visited = 0, in_stack, visited };
-
-    /** Helper function of "isCyclicDFS".
-     *
-     * @param adjList is the adjacency list representation of some graph.
-     * @param state is the state of the nodes of the graph.
-     * @param node is the node being evaluated.
-     *
-     * @return true if graph has a cycle, else false.
-     */
-    static bool isCyclicDFSHelper(AdjList const& adjList,
-                                  std::vector<nodeStates>* state,
-                                  unsigned int node) {
-        // Add node "in_stack" state.
-        (*state)[node] = in_stack;
-
-        // If the node has children, then recursively visit all children of the
-        // node.
-        auto const it = adjList.find(node);
-        if (it != adjList.end()) {
-            for (auto child : it->second) {
-                // If state of child node is "not_visited", evaluate that child
-                // for presence of cycle.
-                auto state_of_child = (*state)[child];
-                if (state_of_child == not_visited) {
-                    if (isCyclicDFSHelper(adjList, state, child)) {
-                        return true;
-                    }
-                } else if (state_of_child == in_stack) {
-                    // If child node was "in_stack", then that means that there
-                    // is a cycle in the graph. Return true for presence of the
-                    // cycle.
-                    return true;
-                }
-            }
-        }
-
-        // Current node has been evaluated for the presence of cycle and had no
-        // cycle. Mark current node as "visited".
-        (*state)[node] = visited;
-        // Return that current node didn't result in any cycles.
-        return false;
-    }
-
- public:
-    /** Driver function to check if a graph has a cycle.
-     *
-     * This function uses DFS to check for cycle in the graph.
-     *
-     * @param graph which needs to be evaluated for the presence of cycle.
-     * @return true if a cycle is detected, else false.
-     */
-    static bool isCyclicDFS(Graph const& graph) {
-        auto vertices = graph.getVertices();
-
-        /** State of the node.
-         *
-         * It is a vector of "nodeStates" which represents the state node is in.
-         * It can take only 3 values: "not_visited", "in_stack", and "visited".
-         *
-         * Initially, all nodes are in "not_visited" state.
-         */
-        std::vector<nodeStates> state(vertices, not_visited);
-
-        // Start visiting each node.
-        for (unsigned int node = 0; node < vertices; node++) {
-            // If a node is not visited, only then check for presence of cycle.
-            // There is no need to check for presence of cycle for a visited
-            // node as it has already been checked for presence of cycle.
-            if (state[node] == not_visited) {
-                // Check for cycle.
-                if (isCyclicDFSHelper(graph.getAdjList(), &state, node)) {
-                    return true;
-                }
-            }
-        }
-
-        // All nodes have been safely traversed, that means there is no cycle in
-        // the graph. Return false.
-        return false;
-    }
-
-    /** Check if a graph has cycle or not.
-     *
-     * This function uses BFS to check if a graph is cyclic or not.
-     *
-     * @param graph which needs to be evaluated for the presence of cycle.
-     * @return true if a cycle is detected, else false.
-     */
-    static bool isCyclicBFS(Graph const& graph) {
-        auto graphAjdList = graph.getAdjList();
-        auto vertices = graph.getVertices();
-
-        std::vector<unsigned int> indegree(vertices, 0);
-        // Calculate the indegree i.e. the number of incident edges to the node.
-        for (auto const& list : graphAjdList) {
-            auto children = list.second;
-            for (auto const& child : children) {
-                indegree[child]++;
-            }
-        }
-
-        std::queue<unsigned int> can_be_solved;
-        for (unsigned int node = 0; node < vertices; node++) {
-            // If a node doesn't have any input edges, then that node will
-            // definately not result in a cycle and can be visited safely.
-            if (!indegree[node]) {
-                can_be_solved.emplace(node);
-            }
-        }
-
-        // Vertices that need to be traversed.
-        auto remain = vertices;
-        // While there are safe nodes that we can visit.
-        while (!can_be_solved.empty()) {
-            auto solved = can_be_solved.front();
-            // Visit the node.
-            can_be_solved.pop();
-            // Decrease number of nodes that need to be traversed.
-            remain--;
-
-            // Visit all the children of the visited node.
-            auto it = graphAjdList.find(solved);
-            if (it != graphAjdList.end()) {
-                for (auto child : it->second) {
-                    // Check if we can visited the node safely.
-                    if (--indegree[child] == 0) {
-                        // if node can be visited safely, then add that node to
-                        // the visit queue.
-                        can_be_solved.emplace(child);
-                    }
-                }
-            }
-        }
-
-        // If there are still nodes that we can't visit, then it means that
-        // there is a cycle and return true, else return false.
-        return !(remain == 0);
-    }
-};
-
-/**
- * Main function.
- */
-int main() {
-    // Instantiate the graph.
-    Graph g(7, std::vector<Edge>{{0, 1}, {1, 2}, {2, 0}, {2, 5}, {3, 5}});
-    // Check for cycle using BFS method.
-    std::cout << CycleCheck::isCyclicBFS(g) << '\n';
-
-    // Check for cycle using DFS method.
-    std::cout << CycleCheck::isCyclicDFS(g) << '\n';
   return 0;
 }
+
+int main() {
+  size_t n, m;
+  std::cin >> n >> m;
+  vector<vector<int> > adj(n, vector<int>());
+  for (size_t i = 0; i < m; i++) {
+    int x, y;
+    std::cin >> x >> y;
+    adj[x - 1].push_back(y - 1);
+  }
+  acyclic(adj,n);
+}

graph/dfs.cpp

@@ -1,26 +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>
-using namespace std;
+#include <vector>
-int v = 4;
+
-void DFSUtil_(int graph[4][4], bool visited[], int s) {
+/**
-    visited[s] = true;
+ *
-    cout << s << " ";
+ * \namespace graph
-    for (int i = 0; i < v; i++) {
+ * \brief Graph Algorithms
-        if (graph[s][i] == 1 && visited[i] == false) {
+ *
-            DFSUtil_(graph, visited, i);
+ */
+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);
         }
     }
 }
 
-void DFS_(int graph[4][4], int s) {
+/**
-    bool visited[v];
+ * \brief
-    memset(visited, 0, sizeof(visited));
+ * initiates depth first search algorithm.
-    DFSUtil_(graph, visited, s);
+ *
-}
+ * @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() {
-    int graph[4][4] = {{0, 1, 1, 0}, {0, 0, 1, 0}, {1, 0, 0, 1}, {0, 0, 0, 1}};
+    size_t vertices, edges;
-    cout << "DFS: ";
+    std::cout << "Enter the Vertices : ";
-    DFS_(graph, 2);
+    std::cin >> vertices;
-    cout << endl;
+    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, v;
+        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;
 }

graph/dijkstra.cpp

@@ -1,52 +1,180 @@
-#include <cstdio>
+/**
+ * @file
+ * @brief [Graph Dijkstras Shortest Path Algorithm
+ * (Dijkstra's Shortest Path)]
+ * (https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)
+ *
+ * @author [Ayaan Khan](http://github.com/ayaankhan98)
+ *
+ * @details
+ * Dijkstra's Algorithm is used to find the shortest path from a source
+ * vertex to all other reachable vertex in the graph.
+ * The algorithm initially assumes all the nodes are unreachable from the
+ * given source vertex so we mark the distances of all vertices as INF
+ * (infinity) from source vertex (INF / infinity denotes unable to reach).
+ *
+ * in similar fashion with BFS we assume the distance of source vertex as 0
+ * and pushes the vertex in a priority queue with it's distance.
+ * we maintain the priority queue as a min heap so that we can get the
+ * minimum element at the top of heap
+ *
+ * Basically what we do in this algorithm is that we try to minimize the
+ * distances of all the reachable vertices from the current vertex, look
+ * at the code below to understand in better way.
+ *
+ */
+#include <cassert>
 #include <iostream>
+#include <limits>
 #include <queue>
+#include <utility>
 #include <vector>
-using namespace std;
+#include <memory>
-#define INF 10000010
-vector<pair<int, int>> graph[5 * 100001];
-int dis[5 * 100001];
-int dij(vector<pair<int, int>> *v, int s, int *dis) {
-    priority_queue<pair<int, int>, vector<pair<int, int>>,
-                   greater<pair<int, int>>>
-        pq;
-    // source distance to zero.
-    pq.push(make_pair(0, s));
-    dis[s] = 0;
-    int u;
-    while (!pq.empty()) {
-        u = (pq.top()).second;
-        pq.pop();
-        for (vector<pair<int, int>>::iterator it = v[u].begin();
-             it != v[u].end(); it++) {
-            if (dis[u] + it->first < dis[it->second]) {
-                dis[it->second] = dis[u] + it->first;
-                pq.push(make_pair(dis[it->second], it->second));
-            }
-        }
-    }
-}
-int main() {
-    int m, n, l, x, y, s;
-    // n--> number of nodes , m --> number of edges
-    cin >> n >> m;
-    for (int i = 0; i < m; i++) {
-        // input edges.
-        scanf("%d%d%d", &x, &y, &l);
-        graph[x].push_back(make_pair(l, y));
-        graph[y].push_back(
-            make_pair(l, x));  // comment this line for directed graph
-    }
-    // start node.
-    scanf("%d", &s);
-    // intialise all distances to infinity.
-    for (int i = 1; i <= n; i++) dis[i] = INF;
-    dij(graph, s, dis);
 
-    for (int i = 1; i <= n; i++)
+constexpr int64_t INF = std::numeric_limits<int64_t>::max();
-        if (dis[i] == INF)
+
-            cout << "-1 ";
+/**
-        else
+ * @namespace graph
-            cout << dis[i] << " ";
+ * @brief Graph Algorithms
+ */
+
+namespace graph {
+  /**
+   * @brief Function that add edge between two nodes or vertices of graph
+   *
+   * @param u any node or vertex of graph
+   * @param v any node or vertex of graph
+   */
+  void addEdge(std::vector<std::vector<std::pair<int, int>>> *adj, int u, int v,
+      int w) {
+    (*adj)[u - 1].push_back(std::make_pair(v - 1, w));
+    // (*adj)[v - 1].push_back(std::make_pair(u - 1, w));
+  }
+
+  /**
+   * @brief Function runs the dijkstra algorithm for some source vertex and
+   * target vertex in the graph and returns the shortest distance of target
+   * from the source.
+   *
+   * @param adj input graph
+   * @param s source vertex
+   * @param t target vertex
+   *
+   * @return shortest distance if target is reachable from source else -1 in
+   * case if target is not reachable from source.
+   */
+  int dijkstra(std::vector<std::vector<std::pair<int, int>>> *adj, int s, int t) {
+    /// n denotes the number of vertices in graph
+    int n = adj->size();
+
+    /// setting all the distances initially to INF
+    std::vector<int64_t> dist(n, INF);
+
+    /// creating a min heap using priority queue
+    /// first element of pair contains the distance
+    /// second element of pair contains the vertex
+    std::priority_queue<std::pair<int, int>, std::vector<std::pair<int, int>>,
+      std::greater<std::pair<int, int>>>
+        pq;
+
+    /// pushing the source vertex 's' with 0 distance in min heap
+    pq.push(std::make_pair(0, s));
+
+    /// marking the distance of source as 0
+    dist[s] = 0;
+
+    while (!pq.empty()) {
+      /// second element of pair denotes the node / vertex
+      int currentNode = pq.top().second;
+
+      /// first element of pair denotes the distance
+      int currentDist = pq.top().first;
+
+      pq.pop();
+
+      /// for all the reachable vertex from the currently exploring vertex
+      /// we will try to minimize the distance
+      for (std::pair<int, int> edge : (*adj)[currentNode]) {
+        /// minimizing distances
+        if (currentDist + edge.second < dist[edge.first]) {
+          dist[edge.first] = currentDist + edge.second;
+          pq.push(std::make_pair(dist[edge.first], edge.first));
+        }
+      }
+    }
+    if (dist[t] != INF) {
+      return dist[t];
+    }
+    return -1;
+  }
+}  // namespace graph
+
+/** Function to test the Algorithm */
+void tests() {
+  std::cout << "Initiatinig Predefined Tests..." << std::endl;
+  std::cout << "Initiating Test 1..." << std::endl;
+  std::vector<std::vector<std::pair<int, int>>> adj1(
+      4, std::vector<std::pair<int, int>>());
+  graph::addEdge(&adj1, 1, 2, 1);
+  graph::addEdge(&adj1, 4, 1, 2);
+  graph::addEdge(&adj1, 2, 3, 2);
+  graph::addEdge(&adj1, 1, 3, 5);
+
+  int s = 1, t = 3;
+  assert(graph::dijkstra(&adj1, s - 1, t - 1) == 3);
+  std::cout << "Test 1 Passed..." << std::endl;
+
+  s = 4, t = 3;
+  std::cout << "Initiating Test 2..." << std::endl;
+  assert(graph::dijkstra(&adj1, s - 1, t - 1) == 5);
+  std::cout << "Test 2 Passed..." << std::endl;
+
+  std::vector<std::vector<std::pair<int, int>>> adj2(
+      5, std::vector<std::pair<int, int>>());
+  graph::addEdge(&adj2, 1, 2, 4);
+  graph::addEdge(&adj2, 1, 3, 2);
+  graph::addEdge(&adj2, 2, 3, 2);
+  graph::addEdge(&adj2, 3, 2, 1);
+  graph::addEdge(&adj2, 2, 4, 2);
+  graph::addEdge(&adj2, 3, 5, 4);
+  graph::addEdge(&adj2, 5, 4, 1);
+  graph::addEdge(&adj2, 2, 5, 3);
+  graph::addEdge(&adj2, 3, 4, 4);
+
+  s = 1, t = 5;
+  std::cout << "Initiating Test 3..." << std::endl;
+  assert(graph::dijkstra(&adj2, s - 1, t - 1) == 6);
+  std::cout << "Test 3 Passed..." << std::endl;
+  std::cout << "All Test Passed..." << std::endl << 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<std::pair<int, int>>> adj(
+      vertices, std::vector<std::pair<int, int>>());
+
+  int u = int(), v = int(), w = int();
+  while (edges--) {
+    std::cin >> u >> v >> w;
+    graph::addEdge(&adj, u, v, w);
+  }
+
+  int s = int(), t = int();
+  std::cin >> s >> t;
+  int dist = graph::dijkstra(&adj, s - 1, t - 1);
+  if (dist == -1) {
+    std::cout << "Target not reachable from source" << std::endl;
+  } else {
+    std::cout << "Shortest Path Distance : " << dist << std::endl;
+  }
   return 0;
 }

graph/kosaraju.cpp

@@ -4,8 +4,8 @@
 
 #include <iostream>
 #include <vector>
+#include <stack>
 
-using namespace std;
 
 /**
  * Iterative function/method to print graph:
@@ -13,13 +13,13 @@ using namespace std;
  * @param V : vertices
  * @return void
  **/
-void print(vector<int> a[], int V) {
+void print(std::vector<int> a[], int V) {
     for (int i = 0; i < V; i++) {
         if (!a[i].empty())
-            cout << "i=" << i << "-->";
+            std::cout << "i=" << i << "-->";
-        for (int j = 0; j < a[i].size(); j++) cout << a[i][j] << " ";
+        for (int j = 0; j < a[i].size(); j++) std::cout << a[i][j] << " ";
         if (!a[i].empty())
-            cout << endl;
+            std::cout << std::endl;
     }
 }
 
@@ -31,7 +31,7 @@ void print(vector<int> a[], int V) {
  * @param adj[] : array of vectors to represent graph
  * @return void
  **/
-void push_vertex(int v, stack<int> &st, bool vis[], vector<int> adj[]) {
+void push_vertex(int v, std::stack<int> &st, bool vis[], std::vector<int> adj[]) {
     vis[v] = true;
     for (auto i = adj[v].begin(); i != adj[v].end(); i++) {
         if (vis[*i] == false)
@@ -47,7 +47,7 @@ void push_vertex(int v, stack<int> &st, bool vis[], vector<int> adj[]) {
  * @param grev[] : graph with reversed edges
  * @return void
  **/
-void dfs(int v, bool vis[], vector<int> grev[]) {
+void dfs(int v, bool vis[], std::vector<int> grev[]) {
     vis[v] = true;
     // cout<<v<<" ";
     for (auto i = grev[v].begin(); i != grev[v].end(); i++) {
@@ -66,15 +66,15 @@ no SCCs i.e. none(0) or there will be x no. of SCCs (x>0)) i.e. it returns the
 count of (number of) strongly connected components (SCCs) in the graph.
 (variable 'count_scc' within function)
 **/
-int kosaraju(int V, vector<int> adj[]) {
+int kosaraju(int V, std::vector<int> adj[]) {
     bool vis[V] = {};
-    stack<int> st;
+    std::stack<int> st;
     for (int v = 0; v < V; v++) {
         if (vis[v] == false)
             push_vertex(v, st, vis, adj);
     }
     // making new graph (grev) with reverse edges as in adj[]:
-    vector<int> grev[V];
+    std::vector<int> grev[V];
     for (int i = 0; i < V + 1; i++) {
         for (auto j = adj[i].begin(); j != adj[i].end(); j++) {
             grev[*j].push_back(i);
@@ -102,20 +102,20 @@ int kosaraju(int V, vector<int> adj[]) {
 // Input your required values: (not hardcoded)
 int main() {
     int t;
-    cin >> t;
+    std::cin >> t;
     while (t--) {
         int a, b;  // a->number of nodes, b->directed edges.
-        cin >> a >> b;
+        std::cin >> a >> b;
         int m, n;
-        vector<int> adj[a + 1];
+        std::vector<int> adj[a + 1];
         for (int i = 0; i < b; i++)  // take total b inputs of 2 vertices each
                                      // required to form an edge.
         {
-            cin >> m >> n;  // take input m,n denoting edge from m->n.
+            std::cin >> m >> n;  // take input m,n denoting edge from m->n.
             adj[m].push_back(n);
         }
         // pass number of nodes and adjacency array as parameters to function:
-        cout << kosaraju(a, adj) << endl;
+        std::cout << kosaraju(a, adj) << std::endl;
     }
     return 0;
 }

graph/kruskal.cpp

@@ -1,4 +1,6 @@
 #include <iostream>
+#include <vector>
+#include <algorithm>
 //#include <boost/multiprecision/cpp_int.hpp>
 // using namespace boost::multiprecision;
 const int mx = 1e6 + 5;

graph/lca.cpp

@@ -1,7 +1,9 @@
 //#include<bits/stdc++.h>
 #include <iostream>
-
+#include <vector>
-using namespace std;
+#include <cmath>
+#include <cassert>
+#include <cstring>
 // Find the lowest common ancestor using binary lifting in O(nlogn)
 // Zero based indexing
 // Resource : https://cp-algorithms.com/graph/lca_binary_lifting.html
@@ -9,7 +11,7 @@ const int N = 1005;
 const int LG = log2(N) + 1;
 struct lca {
     int n;
-    vector<int> adj[N];  // Graph
+    std::vector<int> adj[N];  // Graph
     int up[LG][N];       // build this table
     int level[N];        // get the levels of all of them
 
@@ -18,7 +20,7 @@ struct lca {
         memset(level, 0, sizeof(level));
         for (int i = 0; i < n - 1; ++i) {
             int a, b;
-            cin >> a >> b;
+            std::cin >> a >> b;
             a--;
             b--;
             adj[a].push_back(b);
@@ -30,15 +32,15 @@ struct lca {
     }
     void verify() {
         for (int i = 0; i < n; ++i) {
-            cout << i << " : level: " << level[i] << endl;
+            std::cout << i << " : level: " << level[i] << std::endl;
         }
-        cout << endl;
+        std::cout << std::endl;
         for (int i = 0; i < LG; ++i) {
-            cout << "Power:" << i << ": ";
+            std::cout << "Power:" << i << ": ";
             for (int j = 0; j < n; ++j) {
-                cout << up[i][j] << " ";
+                std::cout << up[i][j] << " ";
             }
-            cout << endl;
+            std::cout << std::endl;
         }
     }
 
@@ -65,7 +67,7 @@ struct lca {
         u--;
         v--;
         if (level[v] > level[u]) {
-            swap(u, v);
+            std::swap(u, v);
         }
         // u is at the bottom.
         int dist = level[u] - level[v];

graph/topological_sort.cpp

@@ -1,12 +1,11 @@
 #include <algorithm>
 #include <iostream>
 #include <vector>
-using namespace std;
 
 int n, m;  // For number of Vertices (V) and number of edges (E)
-vector<vector<int>> G;
+std::vector<std::vector<int>> G;
-vector<bool> visited;
+std::vector<bool> visited;
-vector<int> ans;
+std::vector<int> ans;
 
 void dfs(int v) {
     visited[v] = true;
@@ -27,21 +26,21 @@ void topological_sort() {
     reverse(ans.begin(), ans.end());
 }
 int main() {
-    cout << "Enter the number of vertices and the number of directed edges\n";
+    std::cout << "Enter the number of vertices and the number of directed edges\n";
-    cin >> n >> m;
+    std::cin >> n >> m;
     int x, y;
-    G.resize(n, vector<int>());
+    G.resize(n, std::vector<int>());
     for (int i = 0; i < n; ++i) {
-        cin >> x >> y;
+        std::cin >> x >> y;
         x--, y--;  // to convert 1-indexed to 0-indexed
         G[x].push_back(y);
     }
     topological_sort();
-    cout << "Topological Order : \n";
+    std::cout << "Topological Order : \n";
     for (int v : ans) {
-        cout << v + 1
+        std::cout << v + 1
              << ' ';  // converting zero based indexing back to one based.
     }
-    cout << '\n';
+    std::cout << '\n';
     return 0;
 }