Exploring Dijkstra's Algorithm

To find the shortest path between two nodes in a graph

To sort elements in a list

To multiply matrices

To solve linear equations

Stack

Queue

Priority Queue

Linked List

Adjacency Matrix

Adjacency List

Both A and B

Incidence Matrix

$$O(V^2)$$

$$O(V + E \log V)$$

$$O(E \log V)$$

$$O(V \log V)$$

It cannot handle graphs with negative weight edges

It is not efficient for dense graphs

It cannot find the shortest path in unweighted graphs

It requires a directed graph

Sorting a list of numbers

Finding the shortest driving route on a map

Encrypting data

Balancing a chemical equation

Dijkstra's is faster but cannot handle negative weights

Bellman-Ford is faster and can handle negative weights

Both have the same time complexity

Dijkstra's can handle negative weights, Bellman-Ford cannot

Set all node distances to infinity except the start node

Set all node distances to zero

Randomly select a node as the start

Sort all nodes by their weights

Greedy approach

Dynamic programming

Uses a priority queue

Backtracking

A* uses heuristics to improve performance

Dijkstra's is used for sorting

A* cannot handle weighted graphs

Dijkstra's is used for unweighted graphs only