Dijkstra's algorithm updates distances by iteratively selecting the unvisited node with the smallest known distance, marking it as visited, and relaxing its outgoing edges. Relaxation involves checking if the path to a neighbor through the current node is shorter than the previously known path.
Conditions: Requires a priority queue or list to track unvisited nodes and their current shortest distances.; The graph must have non-negative edge weights (positive in the pseudocode).
Dijkstra's algorithm updates distances by iteratively selecting the unvisited node with the smallest known distance, marking it as visited, and relaxing its outgoing edges. Relaxation involves checking if the path to a neighbor through the current node is shorter than the previously known path.
Conditions: Requires a priority queue or list to track unvisited nodes and their current shortest distances.; The graph must have non-negative edge weights (positive in the pseudocode).
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.