Dijkstra's algorithm computes the single-source shortest paths to all reachable vertices in a weighted graph bearing non-negative edge costs. Maintaining a priority queue of tentative vertex distances initialized from the source, the algorithm greedily extracts the unvisited node with minimal cumulative weight, progressively relaxing adjacent incident edges. By expanding monotonically along the minimum-cost frontier, it builds minimum-distance spanning trees in O((|V| + |E|) log |V|) time.