What is the Dijkstra algorithm in C++?

Can you explain the Dijkstra algorithm and how to implement it in C++?

Sure! The Dijkstra algorithm finds the shortest path from a source node to all other nodes in a graph. In C++, you can implement it using a priority queue.

What data structures do I need for this implementation?

You'll need a graph representation, typically an adjacency list, and a priority queue to efficiently get the next node with the smallest distance.

Can you provide a simple code example?

Absolutely! Here's a basic implementation:

#include <iostream>
#include <vector>
#include <queue>
#include <limits>
using namespace std;

void dijkstra(int src, vector<vector<pair<int, int>>>& graph) {
    vector<int> dist(graph.size(), numeric_limits<int>::max());
    priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
    dist[src] = 0;
    pq.push({0, src});

    while (!pq.empty()) {
        int u = pq.top().second;
        pq.pop();

        for (auto& edge : graph[u]) {
            int v = edge.first;
            int weight = edge.second;
            if (dist[u] + weight < dist[v]) {
                dist[v] = dist[u] + weight;
                pq.push({dist[v], v});
            }
        }
    }
}

This code initializes distances and uses a priority queue to find the shortest paths.

What is the time complexity of Dijkstra's algorithm?

The time complexity of Dijkstra's algorithm is O((V + E) log V) when using a priority queue, where V is the number of vertices and E is the number of edges.