Step 1 — Initialization: Set the distance to the source node to 0 and all other distances to infinity. Mark all nodes as unvisited. Insert the source into a min-priority queue (keyed by distance).

Step 2 — Extract minimum: Repeatedly extract the node u with the smallest distance from the priority queue. When we extract a node, its distance is finalized (we have found the shortest path to u) because non-negative weights ensure no later path can be shorter.

Step 3 — Relax neighbors: For each neighbor v of u, compute candidate = dist[u] + weight(u, v). If candidate is less than the current dist[v], update dist[v] = candidate, set (or update) the predecessor of v to u, and insert v into the priority queue (or decrease its key if already present).

Step 4 — Termination: When the priority queue is empty, we have computed the shortest distance from the source to every reachable node. The predecessor pointers form shortest-path trees. Time is O((V + E) log V) with a binary heap; space O(V).