Introduction

Dijkstra's Algorithm: Dijkstra's Algorithm is a graph search algorithm that finds the shortest path between nodes in a weighted graph. It is widely used in network routing and mapping applications.
This algorithm ensures the shortest path from the source node to all other nodes in the graph.

Efficiently find the shortest path in weighted graphs.

How does it work?

Start with a source node and assign it a tentative distance of 0, while all other nodes are assigned infinity.

Mark the source node as visited and explore its unvisited neighbors.

For each neighbor, calculate the tentative distance through the current node and update it if it's smaller than the previously recorded distance.

Choose the unvisited node with the smallest tentative distance as the next node to process.

Repeat the process until all nodes are visited or the shortest path to the target node is determined.

Important Observations

The graph must have non-negative weights for the algorithm to work correctly.
The algorithm guarantees the shortest path in weighted graphs.
It uses a priority queue to efficiently select the next node to process.

Key Characteristics:

Greedy algorithm for shortest path calculation.
Efficient for graphs with non-negative weights.
Can handle both directed and undirected graphs.

Advantages:

Accurate and reliable for shortest path calculations.
Works well for sparse graphs.
Time complexity is manageable for medium-sized graphs.

Disadvantages:

Not suitable for graphs with negative weight edges.
Can be slow for very large graphs.

Time Complexity:

Using a simple array: O(V²), where V is the number of vertices.
Using a priority queue: O((V + E) log V), where E is the number of edges.

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