Table of contents
DSA enthusiasts must be familiar with these two names, these are two of the most popular used algorithms on graphs. Let’s explore the purpose they serve, similarity and dissimilarity.
Similarity
Both algorithms use breadth first method to explore their neighbors.
Both are used to find minimum cost or shortest path between a single source and a destination node in a graph.
Both can work for directed and non-directed graphs.
Dissimilarity
Dijkstra’s algo. works on graphs, having no negative wight edges BUT Bellman-Ford’s algo. works on both type of graphs (with or without negative edge weights).
Dijkstra’s method uses Greedy approach BUT Billman-Ford’s method uses Dynamic approach.
If V denotes Vertices and E as Edges, then time complexity of Dijkstra’s algo will be -
O((E + V)logV)BUT for Bellman-Ford it’ll beO(VE).
Conclusion
In summary, while Dijkstra’s algorithm is faster and more efficient for non-negative weighted graphs, Bellman-Ford provides essential capabilities for handling negative weights and cycles. The choice between these algorithms should be guided by the specific requirements of the graph being analyzed and its edge weight characteristics.