feat: Create Bidirectional Dijkstra Algorithm (#1410)

* Create Bidirectional Dijkstra

Modified Dijkstra Algorithm with euclidean distance.

* Update Bidirectional Dijkstra

* Delete Bidirectional Dijkstra

* Create bidirectional_dijkstra.cpp

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* updating DIRECTORY.md

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update bidirectional_dijkstra.cpp

Headers description added

* Fixed error in bidirectional_dijkstra.cpp

The third test cases didn't pass because there was an error in the Shortest_Path_Distance function in the indexes. The error has been fixed.

* Update bidirectional_dijkstra.cpp

Change of int into uint64_t

* Update bidirectional_dijkstra.cpp

* Update bidirectional_dijkstra.cpp

Int variables changed to uint64_t type

* Update bidirectional_dijkstra.cpp

Added description of input parameters

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/bidirectional_dijkstra.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

Co-authored-by: David Leal <halfpacho@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

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)

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 <cassert>   /// for assert
+#include <iostream>  /// for io operations
+#include <limits>    /// for variable INF
+#include <queue>     /// for the priority_queue of distances
+#include <utility>   /// for make_pair function
+#include <vector>    /// for store the graph, the distances, and the path
+
+constexpr int64_t INF = std::numeric_limits<int64_t>::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<std::vector<std::pair<uint64_t, uint64_t>>> *adj1,
+             std::vector<std::vector<std::pair<uint64_t, uint64_t>>> *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<uint64_t> &workset_,
+    const std::vector<std::vector<uint64_t>> &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<std::vector<std::pair<uint64_t, uint64_t>>> *adj1,
+               std::vector<std::vector<std::pair<uint64_t, uint64_t>>> *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<std::vector<uint64_t>> dist(2, std::vector<uint64_t>(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::pair<uint64_t, uint64_t>,
+                            std::vector<std::pair<uint64_t, uint64_t>>,
+                            std::greater<std::pair<uint64_t, uint64_t>>>>
+        pq(2);
+    /// vector for store the nodes or vertices in the shortest path
+    std::vector<uint64_t> workset(n);
+    /// vector for store the nodes or vertices visited
+    std::vector<bool> 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<int, int> 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<int, int> 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<std::vector<std::pair<uint64_t, uint64_t>>> adj1_1(
+        4, std::vector<std::pair<uint64_t, uint64_t>>());
+    std::vector<std::vector<std::pair<uint64_t, uint64_t>>> adj1_2(
+        4, std::vector<std::pair<uint64_t, uint64_t>>());
+    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<std::vector<std::pair<uint64_t, uint64_t>>> adj2_1(
+        5, std::vector<std::pair<uint64_t, uint64_t>>());
+    std::vector<std::vector<std::pair<uint64_t, uint64_t>>> adj2_2(
+        5, std::vector<std::pair<uint64_t, uint64_t>>());
+    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<std::vector<std::pair<uint64_t, uint64_t>>> adj1(
+        vertices, std::vector<std::pair<uint64_t, uint64_t>>());
+    std::vector<std::vector<std::pair<uint64_t, uint64_t>>> adj2(
+        vertices, std::vector<std::pair<uint64_t, uint64_t>>());
+
+    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;
+}