The Relaxation Step

While the priority queue is not empty:

$1.$ Pop the top element {$d$, $u$}. This is the closest unprocessed node.

$2.$ If you have already processed $u$ (found shorter path earlier), skip it.

$3.$ Mark $u$ as processed.

$4.$ For each neighbor $v$ of $u$, try to relax the edge: if going through $u$ is shorter, update dist[v] and push to the queue. The "skip if processed" check handles duplicates in the priority queue.