Complexity of Dijkstra

You process every edge once. For every edge, you might push to the priority queue. Pushing takes $O(\log V)$. Total time: $O(E \log V)$ with a binary heap. Space: $O(V + E)$ for adjacency list and distance array, plus $O(V)$ for the priority queue.

With Fibonacci heap, you can get $O(V \log V + E)$, but binary heap is simpler and fast enough for competitive programming.