Dijkstra's Algorithm (for shortest path in weighted graphs):

• Finds the shortest path from a source to all other vertices in a weighted graph.
• Time complexity: \(O(V \log V + E)\) using priority queue.

void dijkstra(int source, vector<vector<pair<int, int>>> &adj, int V) {
    vector<int> dist(V, INT_MAX);
    priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
    dist[source] = 0;
    pq.push({0, source});

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

        for (auto &neighbor : adj[u]) {
            int v = neighbor.first;
            int weight = neighbor.second;

            if (dist[u] + weight < dist[v]) {
                dist[v] = dist[u] + weight;
                pq.push({dist[v], v});
            }
        }
    }
}