diff --git a/DIRECTORY.md b/DIRECTORY.md index dcf0a6568..5a8c7fa04 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -79,6 +79,7 @@ * [Line Segment Intersection](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/geometry/line_segment_intersection.cpp) ## Graph + * [Bidirectional Dijkstra](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/bidirectional_dijkstra.cpp) * [Breadth First Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/breadth_first_search.cpp) * [Bridge Finding With Tarjan Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/bridge_finding_with_tarjan_algorithm.cpp) * [Connected Components](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/connected_components.cpp) diff --git a/graph/bidirectional_dijkstra.cpp b/graph/bidirectional_dijkstra.cpp new file mode 100644 index 000000000..deef66227 --- /dev/null +++ b/graph/bidirectional_dijkstra.cpp @@ -0,0 +1,293 @@ +/** + * @file + * @brief [Bidirectional Dijkstra Shortest Path Algorithm] + * (https://www.coursera.org/learn/algorithms-on-graphs/lecture/7ml18/bidirectional-dijkstra) + * + * @author [Marinovksy](http://github.com/Marinovsky) + * + * @details + * This is basically the same Dijkstra Algorithm but faster because it goes from + * the source to the target and from target to the source and stops when + * finding a vertex visited already by the direct search or the reverse one. + * Here some simulations of it: + * https://www.youtube.com/watch?v=DINCL5cd_w0&t=24s + */ + +#include /// for assert +#include /// for io operations +#include /// for variable INF +#include /// for the priority_queue of distances +#include /// for make_pair function +#include /// for store the graph, the distances, and the path + +constexpr int64_t INF = std::numeric_limits::max(); + +/** + * @namespace graph + * @brief Graph Algorithms + */ +namespace graph { +/** + * @namespace bidirectional_dijkstra + * @brief Functions for [Bidirectional Dijkstra Shortest Path] + * (https://www.coursera.org/learn/algorithms-on-graphs/lecture/7ml18/bidirectional-dijkstra) + * algorithm + */ +namespace bidirectional_dijkstra { +/** + * @brief Function that add edge between two nodes or vertices of graph + * + * @param adj1 adjacency list for the direct search + * @param adj2 adjacency list for the reverse search + * @param u any node or vertex of graph + * @param v any node or vertex of graph + */ +void addEdge(std::vector>> *adj1, + std::vector>> *adj2, + uint64_t u, uint64_t v, uint64_t w) { + (*adj1)[u - 1].push_back(std::make_pair(v - 1, w)); + (*adj2)[v - 1].push_back(std::make_pair(u - 1, w)); + // (*adj)[v - 1].push_back(std::make_pair(u - 1, w)); +} +/** + * @brief This function returns the shortest distance from the source + * to the target if there is path between vertices 's' and 't'. + * + * @param workset_ vertices visited in the search + * @param distance_ vector of distances from the source to the target and + * from the target to the source + * + */ +uint64_t Shortest_Path_Distance( + const std::vector &workset_, + const std::vector> &distance_) { + int64_t distance = INF; + for (uint64_t i : workset_) { + if (distance_[0][i] + distance_[1][i] < distance) { + distance = distance_[0][i] + distance_[1][i]; + } + } + return distance; +} + +/** + * @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 adj1 input graph + * @param adj2 input graph reversed + * @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 Bidijkstra(std::vector>> *adj1, + std::vector>> *adj2, + uint64_t s, uint64_t t) { + /// n denotes the number of vertices in graph + uint64_t n = adj1->size(); + + /// setting all the distances initially to INF + std::vector> dist(2, std::vector(n, INF)); + + /// creating a a vector of min heap using priority queue + /// pq[0] contains the min heap for the direct search + /// pq[1] contains the min heap for the reverse search + + /// first element of pair contains the distance + /// second element of pair contains the vertex + std::vector< + std::priority_queue, + std::vector>, + std::greater>>> + pq(2); + /// vector for store the nodes or vertices in the shortest path + std::vector workset(n); + /// vector for store the nodes or vertices visited + std::vector visited(n); + + /// pushing the source vertex 's' with 0 distance in pq[0] min heap + pq[0].push(std::make_pair(0, s)); + + /// marking the distance of source as 0 + dist[0][s] = 0; + + /// pushing the target vertex 't' with 0 distance in pq[1] min heap + pq[1].push(std::make_pair(0, t)); + + /// marking the distance of target as 0 + dist[1][t] = 0; + + while (true) { + /// direct search + + // If pq[0].size() is equal to zero then the node/ vertex is not + // reachable from s + if (pq[0].size() == 0) { + break; + } + /// second element of pair denotes the node / vertex + uint64_t currentNode = pq[0].top().second; + + /// first element of pair denotes the distance + uint64_t currentDist = pq[0].top().first; + + pq[0].pop(); + + /// for all the reachable vertex from the currently exploring vertex + /// we will try to minimize the distance + for (std::pair edge : (*adj1)[currentNode]) { + /// minimizing distances + if (currentDist + edge.second < dist[0][edge.first]) { + dist[0][edge.first] = currentDist + edge.second; + pq[0].push(std::make_pair(dist[0][edge.first], edge.first)); + } + } + // store the processed node/ vertex + workset.push_back(currentNode); + + /// check if currentNode has already been visited + if (visited[currentNode] == 1) { + return Shortest_Path_Distance(workset, dist); + } + visited[currentNode] = true; + /// reversed search + + // If pq[1].size() is equal to zero then the node/ vertex is not + // reachable from t + if (pq[1].size() == 0) { + break; + } + /// second element of pair denotes the node / vertex + currentNode = pq[1].top().second; + + /// first element of pair denotes the distance + currentDist = pq[1].top().first; + + pq[1].pop(); + + /// for all the reachable vertex from the currently exploring vertex + /// we will try to minimize the distance + for (std::pair edge : (*adj2)[currentNode]) { + /// minimizing distances + if (currentDist + edge.second < dist[1][edge.first]) { + dist[1][edge.first] = currentDist + edge.second; + pq[1].push(std::make_pair(dist[1][edge.first], edge.first)); + } + } + // store the processed node/ vertex + workset.push_back(currentNode); + + /// check if currentNode has already been visited + if (visited[currentNode] == 1) { + return Shortest_Path_Distance(workset, dist); + } + visited[currentNode] = true; + } + return -1; +} +} // namespace bidirectional_dijkstra +} // namespace graph + +/** + * @brief Function to test the + * provided algorithm above + * @returns void + */ +static void tests() { + std::cout << "Initiatinig Predefined Tests..." << std::endl; + std::cout << "Initiating Test 1..." << std::endl; + std::vector>> adj1_1( + 4, std::vector>()); + std::vector>> adj1_2( + 4, std::vector>()); + graph::bidirectional_dijkstra::addEdge(&adj1_1, &adj1_2, 1, 2, 1); + graph::bidirectional_dijkstra::addEdge(&adj1_1, &adj1_2, 4, 1, 2); + graph::bidirectional_dijkstra::addEdge(&adj1_1, &adj1_2, 2, 3, 2); + graph::bidirectional_dijkstra::addEdge(&adj1_1, &adj1_2, 1, 3, 5); + + uint64_t s = 1, t = 3; + assert(graph::bidirectional_dijkstra::Bidijkstra(&adj1_1, &adj1_2, 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::bidirectional_dijkstra::Bidijkstra(&adj1_1, &adj1_2, s - 1, + t - 1) == 5); + std::cout << "Test 2 Passed..." << std::endl; + + std::vector>> adj2_1( + 5, std::vector>()); + std::vector>> adj2_2( + 5, std::vector>()); + graph::bidirectional_dijkstra::addEdge(&adj2_1, &adj2_2, 1, 2, 4); + graph::bidirectional_dijkstra::addEdge(&adj2_1, &adj2_2, 1, 3, 2); + graph::bidirectional_dijkstra::addEdge(&adj2_1, &adj2_2, 2, 3, 2); + graph::bidirectional_dijkstra::addEdge(&adj2_1, &adj2_2, 3, 2, 1); + graph::bidirectional_dijkstra::addEdge(&adj2_1, &adj2_2, 2, 4, 2); + graph::bidirectional_dijkstra::addEdge(&adj2_1, &adj2_2, 3, 5, 4); + graph::bidirectional_dijkstra::addEdge(&adj2_1, &adj2_2, 5, 4, 1); + graph::bidirectional_dijkstra::addEdge(&adj2_1, &adj2_2, 2, 5, 3); + graph::bidirectional_dijkstra::addEdge(&adj2_1, &adj2_2, 3, 4, 4); + + s = 1, t = 5; + std::cout << "Initiating Test 3..." << std::endl; + assert(graph::bidirectional_dijkstra::Bidijkstra(&adj2_1, &adj2_2, s - 1, + t - 1) == 6); + std::cout << "Test 3 Passed..." << std::endl; + std::cout << "All Test Passed..." << std::endl << std::endl; +} + +/** + * @brief Main function + * @returns 0 on exit + */ +int main() { + tests(); // running predefined tests + uint64_t vertices = uint64_t(); + uint64_t edges = uint64_t(); + std::cout << "Enter the number of vertices : "; + std::cin >> vertices; + std::cout << "Enter the number of edges : "; + std::cin >> edges; + + std::vector>> adj1( + vertices, std::vector>()); + std::vector>> adj2( + vertices, std::vector>()); + + uint64_t u = uint64_t(), v = uint64_t(), w = uint64_t(); + std::cout << "Enter the edges by three integers in this form: u v w " + << std::endl; + std::cout << "Example: if there is and edge between node 1 and node 4 with " + "weight 7 enter: 1 4 7, and then press enter" + << std::endl; + while (edges--) { + std::cin >> u >> v >> w; + graph::bidirectional_dijkstra::addEdge(&adj1, &adj2, u, v, w); + if (edges != 0) { + std::cout << "Enter the next edge" << std::endl; + } + } + + uint64_t s = uint64_t(), t = uint64_t(); + std::cout + << "Enter the source node and the target node separated by a space" + << std::endl; + std::cout << "Example: If the source node is 5 and the target node is 6 " + "enter: 5 6 and press enter" + << std::endl; + std::cin >> s >> t; + int dist = + graph::bidirectional_dijkstra::Bidijkstra(&adj1, &adj2, 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; +}