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Dijkstra's algorithm

Find Shortest Paths from Source to all Vertices using ...

DSA Dijkstra's Algorithm

Dijkstra's Shortest Path Algorithm

• Dijkstra's algorithm, developed by Edsger Dijkstra in 1959, identifies the shortest path from a starting node to a target node in a weighted graph, creating a tree of shortest paths.
• The algorithm is applicable to both directed and undirected graphs, as long as all edge weights are nonnegative.
• In real-world applications, such as navigating congested roads, Dijkstra's algorithm focuses on lower-weight paths to determine the shortest route.
• Key components of the algorithm include an array of distances from the source node, a queue of all nodes, and a set of visited nodes.
• The algorithm works by selecting the unvisited node with the smallest distance, updating the distances of its adjacent nodes, and marking it as visited until all nodes are processed.
• The output of Dijkstra's algorithm is a shortest path tree, which shows the minimum distances from the source to all other nodes in the graph.
• Pseudocode for Dijkstra's algorithm is available for implementation in various programming languages, resembling Python syntax.
• The algorithm can be illustrated through examples, where distances are calculated step-by-step to arrive at the final shortest-path tree.
• In practical scenarios, such as navigating an ice rink, the algorithm can determine the least number of moves needed to reach a specific position while avoiding obstacles.
• The effectiveness of the algorithm can be evaluated across multiple scenarios, including calculating the sum of shortest paths in various ice rinks of defined dimensions.

Dijkstra's Shortest Path Algorithm - A Detailed and Visual ...

Dijkstra's Algorithm for Adjacency List Representation

• The code implements a graph data structure using an adjacency list, where each node includes a destination vertex, weight, and a pointer to the next node.
• A `Graph` structure is defined to store the number of vertices and an array of adjacency lists for each vertex.
• The `newAdjListNode` function allocates memory for a new adjacency list node and initializes its destination vertex and weight.
• The `createGraph` function initializes a graph with a specified number of vertices, setting all adjacency list heads to NULL.
• The `addEdge` function creates an undirected edge between two vertices with a specified weight by adding two adjacency list nodes.
• A min-heap data structure is defined to support Dijkstra's algorithm, including functions for creating the heap, extracting the minimum node, and decreasing a node's key.
• The `minHeapify` function ensures the min-heap property is maintained after node extraction or key decrease operations.
• The `dijkstra` function implements Dijkstra's algorithm to find the shortest paths from a source vertex to all other vertices in the graph.
• The algorithm initializes all vertex distances to infinity, sets the source vertex distance to zero, and uses the min-heap for efficient graph exploration.
• The results of the shortest paths are printed in a formatted manner, displaying each vertex and its distance from the source.
• The `main` function creates a graph with 9 vertices, adds edges with specified weights, and invokes the Dijkstra function starting from vertex 0.