/**
 * @brief Check whether a given graph is bipartite or not
 * @details
 * A bipartite graph is the one whose nodes can be divided into two
 * disjoint sets in such a way that the nodes in a set are not
 * connected to each other at all, i.e. no intra-set connections.
 * The only connections that exist are that of inter-set,
 * i.e. the nodes from one set are connected to a subset of nodes
 * in the other set.
 * In this implementation, using a graph in the form of adjacency
 * list, check whether the given graph is a bipartite or not.
 *
 * References used:
 * [GeeksForGeeks](https://www.geeksforgeeks.org/bipartite-graph/)
 * @author [tushar2407](https://github.com/tushar2407)
 */
#include <cassert>   /// for assert
#include <iostream>  /// for IO operations
#include <queue>     /// for queue data structure
#include <vector>    /// for vector data structure

/**
 * @namespace graph
 * @brief Graphical algorithms
 */
namespace graph {
/**
 * @brief function to check whether the passed graph is bipartite or not
 * @param graph is a 2D matrix whose rows or the first index signify the node
 * and values in that row signify the nodes it is connected to
 * @param index is the valus of the node currently under observation
 * @param visited is the vector which stores whether a given node has been
 * traversed or not yet
 * @returns boolean
 */
bool checkBipartite(const std::vector<std::vector<int64_t>> &graph,
                    int64_t index, std::vector<int64_t> *visited) {
    std::queue<int64_t> q;  ///< stores the neighbouring node indexes in squence
                            /// of being reached
    q.push(index);          /// insert the current node into the queue
    (*visited)[index] = 1;  /// mark the current node as travelled
    while (q.size()) {
        int64_t u = q.front();
        q.pop();
        for (uint64_t i = 0; i < graph[u].size(); i++) {
            int64_t v =
                graph[u][i];     ///< stores the neighbour of the current node
            if (!(*visited)[v])  /// check whether the neighbour node is
                                 /// travelled already or not
            {
                (*visited)[v] =
                    ((*visited)[u] == 1)
                        ? -1
                        : 1;  /// colour the neighbouring node with
                              /// different colour than the current node
                q.push(v);    /// insert the neighbouring node into the queue
            } else if ((*visited)[v] ==
                       (*visited)[u])  /// if both the current node and its
                                       /// neighbour has the same state then it
                                       /// is not a bipartite graph
            {
                return false;
            }
        }
    }
    return true;  /// return true when all the connected nodes of the current
                  /// nodes are travelled and satisify all the above conditions
}
/**
 * @brief returns true if the given graph is bipartite else returns false
 * @param graph is a 2D matrix whose rows or the first index signify the node
 * and values in that row signify the nodes it is connected to
 * @returns booleans
 */
bool isBipartite(const std::vector<std::vector<int64_t>> &graph) {
    std::vector<int64_t> visited(
        graph.size());  ///< stores boolean values
                        /// which signify whether that node had been visited or
                        /// not

    for (uint64_t i = 0; i < graph.size(); i++) {
        if (!visited[i])  /// if the current node is not visited then check
                          /// whether the sub-graph of that node is a bipartite
                          /// or not
        {
            if (!checkBipartite(graph, i, &visited)) {
                return false;
            }
        }
    }
    return true;
}
}  // namespace graph

/**
 * @brief Self-test implementations
 * @returns void
 */
static void test() {
    std::vector<std::vector<int64_t>> graph = {{1, 3}, {0, 2}, {1, 3}, {0, 2}};

    assert(graph::isBipartite(graph) ==
           true);  /// check whether the above
                   /// defined graph is indeed bipartite

    std::vector<std::vector<int64_t>> graph_not_bipartite = {
        {1, 2, 3}, {0, 2}, {0, 1, 3}, {0, 2}};

    assert(graph::isBipartite(graph_not_bipartite) ==
           false);  /// check whether
                    /// the above defined graph is indeed bipartite
    std::cout << "All tests have successfully passed!\n";
}
/**
 * @brief Main function
 * Instantitates a dummy graph of a small size with
 * a few edges between random nodes.
 * On applying the algorithm, it checks if the instantiated
 * graph is bipartite or not.
 * @returns 0 on exit
 */
int main() {
    test();  // run self-test implementations
    return 0;
}