Create Dijkstras_MinHeap.cpp

Add Dijkstra's algorithm implementation in C++, using a min-heap.

Author: OzPol

src/cpp/Dijkstras_MinHeap.cpp

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+/**
+ * Dijkstras_MinHeap.cpp
+ *
+ * This file implements Dijkstra's algorithm using a min-heap (priority queue).
+ * The algorithm finds the shortest paths from the source vertex to all other vertices in a weighted graph.
+ *
+ * Functions:
+ * - void dijkstra(const unordered_map<int, unordered_map<int, int>>& graph, int start_vertex)
+ *      - graph: An adjacency list representation of the graph.
+ *          - key: vertex
+ *          - value: unordered_map of connected vertices and their edge weights
+ *      - start_vertex: The starting vertex for Dijkstra's algorithm.
+ *
+ * Example Usage:
+ * Uncomment the main function to run a sample test case.
+ * The sample graph used in the main function is represented as an adjacency list.
+ */
+
+#include <iostream>
+#include <vector>
+#include <queue>
+#include <unordered_map>
+#include <limits>
+
+using namespace std;
+
+// A structure to represent a node in the priority queue
+struct Node {
+    int vertex;
+    int distance;
+    bool operator>(const Node& other) const {
+        return distance > other.distance;
+    }
+};
+
+void dijkstra(const unordered_map<int, unordered_map<int, int>>& graph, int start_vertex) {
+    // Initialize distances and predecessors
+    unordered_map<int, int> dist;
+    unordered_map<int, int> pred;
+    for (const auto& pair : graph) {
+        dist[pair.first] = numeric_limits<int>::max();
+        pred[pair.first] = -1;
+    }
+    dist[start_vertex] = 0;
+
+    // Priority queue to store vertices and their distances
+    priority_queue<Node, vector<Node>, greater<Node>> priority_queue;
+    priority_queue.push({ start_vertex, 0 });
+
+    while (!priority_queue.empty()) {
+        Node current = priority_queue.top();
+        priority_queue.pop();
+
+        // If this distance is not updated, continue
+        if (current.distance > dist[current.vertex]) {
+            continue;
+        }
+
+        // Visit each neighbor of the current vertex
+        for (const auto& neighbor_pair : graph.at(current.vertex)) {
+            int neighbor = neighbor_pair.first;
+            int weight = neighbor_pair.second;
+            int distance = current.distance + weight;
+
+            // If a shorter path to the neighbor is found
+            if (distance < dist[neighbor]) {
+                dist[neighbor] = distance;
+                pred[neighbor] = current.vertex;
+                priority_queue.push({ neighbor, distance });
+            }
+        }
+    }
+
+    // Print distances and predecessors
+    cout << "Distances: \n";
+    for (const auto& pair : dist) {
+        cout << "Vertex " << pair.first << ": " << pair.second << endl;
+    }
+    cout << "\nPredecessors: \n";
+    for (const auto& pair : pred) {
+        cout << "Vertex " << pair.first << ": " << pair.second << endl;
+    }
+}
+
+// Uncomment the following main function to run a sample test case
+/*
+int main() {
+    // Example graph represented as an adjacency list
+    unordered_map<int, unordered_map<int, int>> graph = {
+        {0, {{1, 1}, {2, 4}}},
+        {1, {{0, 1}, {2, 2}, {3, 5}}},
+        {2, {{0, 4}, {1, 2}, {3, 1}}},
+        {3, {{1, 5}, {2, 1}}}
+    };
+
+    // Running Dijkstra's algorithm from vertex 0
+    dijkstra(graph, 0);
+
+    return 0;
+}
+*/