The pseudocode initializes distances to infinity and predecessors to nil, sets the source distance to 0, and uses a priority queue H. It repeatedly extracts the vertex u with the minimum distance, relaxes all outgoing edges (u,v), updating dist(v) and prev(v) if a shorter path is found, and decreases the key of v in H.
Conditions: Input: Graph G=(V,E), directed or undirected.; Positive edge lengths {le : e∈E}.; Source vertex s∈V.; Output: dist(u) is the shortest distance from s to u for all reachable u.
The pseudocode initializes distances to infinity and predecessors to nil, sets the source distance to 0, and uses a priority queue H. It repeatedly extracts the vertex u with the minimum distance, relaxes all outgoing edges (u,v), updating dist(v) and prev(v) if a shorter path is found, and decreases the key of v in H.
Conditions: Input: Graph G=(V,E), directed or undirected.; Positive edge lengths {le : e∈E}.; Source vertex s∈V.; Output: dist(u) is the shortest distance from s to u for all reachable u.
Dijkstra's algorithm is a method for finding the shortest path from a single starting node to all other nodes in a weighted directed graph. It is distinct from minimum spanning tree algorithms like Prim's and Kruskal's, which connect all nodes with the minimum total edge weight rather than finding paths from a specific source.
Conditions: The graph must be weighted.; The graph can be directed or undirected, though the video primarily demonstrates it on a directed graph.
Dijkstra's algorithm is a method for finding the shortest path from a single starting node to all other nodes in a weighted directed graph. It is distinct from minimum spanning tree algorithms like Prim's and Kruskal's, which connect all nodes with the minimum total edge weight rather than finding paths from a specific source.
Conditions: The graph must be weighted.; The graph can be directed or undirected, though the video primarily demonstrates it on a directed graph.