Which of the following is the most commonly used data structure for implementing Dijkstra's Algorithm?

Question

Accepted Answer

The correct option is (4):
The **Min priority queue** is the most essential data structure for an efficient implementation of Dijkstra's algorithm. Dijkstra's is a greedy algorithm whose core principle is to repeatedly select the unvisited vertex that has the **smallest current tentative distance** from the source node. This distance value is treated as the node's priority, where the minimum value has the highest priority, aligning perfectly with the functionality of a Min priority queue. This data structure allows the algorithm to perform the crucial "extract-min" operation quickly, typically in O(log V) time, where V is the number of vertices. This fast selection and the ability to update a key (distance) in the queue are what enable the algorithm to achieve an optimal time complexity for finding the shortest path in graphs with non-negative edge weights.

The incorrect option is (1):
A Max priority queue is not suitable because it is designed to prioritize the element with the **largest** value. If used in Dijkstra's algorithm, it would continuously select the unvisited vertex with the longest known distance from the source. This would cause the algorithm to explore paths in a non-optimal, descending order of cost, directly contradicting the greedy, shortest-path nature of Dijkstra's, and thus would not produce the correct shortest path solution.

The incorrect option is (2):
A **Stack** follows the Last-In, First-Out (LIFO) principle, which governs the order of operations in data structures like a call stack or algorithms like Depth-First Search (DFS). Since a stack processes nodes based purely on their insertion order rather than their shortest accumulated path distance, it does not possess the necessary mechanism for distance-based prioritization. Therefore, implementing Dijkstra's with a stack would result in an incorrect traversal order and would fail to guarantee the discovery of the true shortest paths.

The incorrect option is (3):
A **Circular queue** is a First-In, First-Out (FIFO) data structure, typically used to manage buffers or implement algorithms like Breadth-First Search (BFS). While BFS uses a standard queue to find the shortest path in *unweighted* graphs (by number of edges), it is incapable of handling the variable edge weights required by Dijkstra's algorithm. A circular queue lacks the capability to continuously identify and extract the minimum-distance node from the set, a function mandatory for Dijkstra's to correctly relax edges and find the shortest paths in a weighted graph.