Which algorithm is used for finding the shortest path in weighted graphs?

Dijkstra's algorithm is a well-known algorithm specifically designed to find the shortest path in weighted graphs. It systematically explores the graph by maintaining a priority queue, allowing it to efficiently select the next closest vertex based on the cumulative weights of the paths explored so far. The algorithm starts at a source vertex and expands outward, updating the shortest known distances to neighboring vertices until the shortest path to the target vertex is discovered.

Dijkstra's algorithm embodies crucial principles of graph theory and optimization, making it versatile for various applications, such as navigation systems and network routing protocols. It is particularly effective in graphs where all the edge weights are non-negative, ensuring that once it visits a vertex, the shortest path to that vertex has been found.

In contrast to Dijkstra's algorithm, the other options present different functionalities: quick sort and selection sort are sorting algorithms that organize data rather than finding paths in graphs, and depth-first search is a graph traversal technique that explores nodes as far down a branch as possible before backtracking, lacking the capacity to determine the shortest path in a weighted format due to its unstructured exploration approach.