### Dijkstra's Algorithm

**Dijkstra’s Algorithm** is a method used to find the shortest path between nodes in a graph, particularly in weighted graphs where each edge has a numerical weight assigned to it. The algorithm operates by iteratively selecting the vertex with the lowest tentative distance from a source node and updating the distances of its neighboring vertices. Through this process, it gradually constructs the shortest path tree from the source node to all other nodes in the graph.

In the below **PDF** we discuss about **Dijkstra’s Algorithm** in detail in simple language, Hope this will help in better understanding.

#### Components of **Dijkstra's Algorithm**:

**Priority Queue:**Dijkstra’s Algorithm relies heavily on a priority queue data structure to efficiently select the next vertex with the smallest tentative distance. This data structure ensures that vertices are explored in order of increasing distance from the source node.**Distance Array:**A crucial aspect of the algorithm is maintaining an array to keep track of the tentative distances from the source node to each vertex. This array is updated iteratively as shorter paths are discovered.**Visited Set:**To prevent revisiting vertices unnecessarily, Dijkstra’s Algorithm utilizes a set to keep track of visited vertices.

**Algorithm Steps:**

- Initialize the distance array, setting the distance of the source node to 0 and all other nodes to infinity.
- Add all vertices to the priority queue with their respective tentative distances.
- While the priority queue is not empty, select the vertex with the smallest tentative distance.
- For each neighboring vertex of the selected vertex, update its tentative distance if a shorter path is found.
- Mark the selected vertex as visited.
- Repeat steps 3-5 until all vertices have been visited.

#### Application of **Dijkstra's Algorithm:**

**Network Routing:**It forms the basis for determining the shortest paths in computer networks, guiding data packets efficiently from source to destination.**Transportation Networks:**In transportation planning, Dijkstra’s Algorithm assists in optimizing routes for vehicles, minimizing travel time and fuel consumption.

Geographic Information Systems**(GIS):**GIS applications utilize Dijkstra’s Algorithm to compute optimal routes for navigation and logistics.**Telecommunications:**Telecom networks utilize the algorithm for call routing and network optimization.

**Conclusion:**

In Conclusion, Dijkstra’s Algorithm stands as a testament to the power of elegant problem-solving in computer science. Its simplicity and efficiency have made it a cornerstone in various fields where the optimization of routes and paths is paramount. As technology continues to advance, the principles underlying Dijkstra’s Algorithm will undoubtedly remain relevant, guiding us through the complex networked landscapes of the digital age.

#### Related Question

Dijkstra’s Algorithm is a graph search algorithm that finds the shortest path between nodes in a weighted graph.

Dijkstra’s Algorithm works by iteratively exploring the closest unvisited node to the source node until the destination node is reached, updating the shortest distances from the source node to each node along the way.

The key feature of Dijkstra’s Algorithm is that it guarantees the shortest path from the source node to all other nodes in the graph.

Dijkstra’s Algorithm works on graphs with non-negative edge weights. Negative weights may cause the algorithm to produce incorrect results.

Dijkstra’s Algorithm doesn’t handle negative weights well. If negative weights are present, it may produce incorrect results. For such cases, other algorithms like Bellman-Ford Algorithm should be used.

#### Relevant

String Matching Algorithms String Matching

Algorithm Design Techniques Algorithm design

Introduction to Sorting Networks A

Introduction to Flow Networks A

Floyd Warshall Algorithm The Floyd

Bellman Ford Algorithm The Bellman

Minimum Spanning Tree (MST) A