What is difference between BFS and Dijkstra's algorithms when looking for shortest path?

The primary difference between Breadth-First Search (BFS) and Dijkstra's algorithm when looking for the shortest path lies in how they handle edge weights and their respective data structures.

Breadth-First Search (BFS)

• Usage: BFS is used for finding the shortest path in unweighted graphs or graphs where all edges have the same weight.
• Mechanism: BFS explores the graph level by level, starting from the source node and visiting all its neighbors before moving on to the next level of nodes.
• Data Structure: BFS uses a simple queue to keep track of nodes to be explored.
• Time Complexity: The time complexity of BFS is $$O(V + E)$$, where $$V$$ is the number of vertices and $$E$$ is the number of edges[2][4][7].

Dijkstra's Algorithm

• Usage: Dijkstra's algorithm is used for finding the shortest path in weighted graphs where edge weights can vary.
• Mechanism: Dijkstra's algorithm uses a priority queue to always expand the least costly node first. It updates the shortest known distance to each node and ensures that each node is processed in order of increasing distance from the source.
• Data Structure: Dijkstra's algorithm uses a priority queue (often implemented as a min-heap) to efficiently retrieve the next node with the smallest tentative distance.
• Time Complexity: The time complexity of Dijkstra's algorithm is $$O(V + E \log V)$$ when using a priority queue, where $$V$$ is the number of vertices and $$E$$ is the number of edges[2][3][5].

Key Differences

1. Edge Weights:

   • BFS assumes all edge weights are equal (or unweighted).
   • Dijkstra's algorithm handles varying edge weights.

2. Data Structures:

   • BFS uses a simple queue.
   • Dijkstra's algorithm uses a priority queue to manage the nodes based on their current shortest distance.

3. Applications:

   • BFS is suitable for unweighted graphs or scenarios where the shortest path is defined by the number of edges.
   • Dijkstra's algorithm is suitable for weighted graphs where the shortest path is defined by the sum of edge weights.

4. Complexity:

   • BFS has a time complexity of $$O(V + E)$$.
   • Dijkstra's algorithm has a time complexity of $$O(V + E \log V)$$ due to the use of a priority queue[2][5][17].

Example

Consider a graph where you need to find the shorte...