Dijkstraalgoritmi

Dijkstra's algorithm is a greedy algorithm that solves the single-source shortest path problem for a graph with non-negative edge weights. Developed by computer scientist Edsger W. Dijkstra in 1956, it finds the shortest path from a designated starting node to all other nodes in a weighted graph.

The algorithm works by maintaining a set of visited nodes and a set of unvisited nodes. It starts by initializing the distance to the starting node as zero and the distances to all other nodes as infinity. At each step, the algorithm selects the unvisited node with the smallest known distance from the start node. This node is then marked as visited, and its neighbors' distances are updated. If the path to a neighbor through the current node is shorter than the neighbor's current known distance, the neighbor's distance is updated. This process continues until all nodes have been visited or the destination node has been reached.

Dijkstra's algorithm is widely used in various applications, including network routing protocols (like OSPF), GPS navigation systems, and finding the shortest path in game development. Its efficiency depends on the data structure used to store the distances to unvisited nodes. Using a priority queue, its time complexity is typically O(E + V log V) or O(E log V), where V is the number of vertices and E is the number of edges in the graph. It's crucial to remember that Dijkstra's algorithm only works correctly for graphs where edge weights are non-negative. For graphs with negative edge weights, other algorithms like the Bellman-Ford algorithm are required.