Dijkstra’s Algorithm

What is Dijkstra’s Algorithm?

What if you were shown a graph of nodes in which each node is connected to a number of other nodes at different distances? What is the shortest path to every other node in the graph if you start from one of the nodes in the graph?

Well, Dijkstra’s Algorithm is a simple algorithm that is used to find the shortest distance, or path, from a starting node to a target node in a weighted graph.

The shortest path from the starting node, the source, to all other nodes (points) in the graph is created by this algorithm.

Dijkstra’s algorithm makes use of weights of the edges for finding the path that minimizes the total distance (weight) among the source node and all other nodes. This algorithm is also known as the single-source shortest path algorithm.

Dijkstra’s algorithm is an iterative algorithm that finds the shortest path from a single starting node to all other nodes in a graph. It differs from the minimum spanning tree in that the shortest distance between two vertices may not include all of the graph’s vertices.

It’s important to note that Dijkstra’s algorithm works only when all of the weights are positive since the weights of the edges are added to find the shortest path during execution.

Dijkstra’s algorithm, in general, works on the principle of relaxation, in which an approximation of the exact distance is gradually displaced by more appropriate values until the shortest distance is reached.

Furthermore, the estimated distance to each node is always an overestimate of the true distance, and it is usually replaced with the distance of a recently determined path.

Example

For instance, suppose a person needs to calculate the shortest distance between a source and a destination, A and D, as well as a subpath that is also the shortest path between the source and destination. Let’s take a look at Dijkstra’s algorithm in action.

It is based on the fact that any subpath of the shortest path between vertices A and D, such as subpath B to D, is also the shortest path between vertices B and D, i.e., each subpath is the shortest path.

Dijkstra’s algorithm reverses this property, which means that when calculating distance, we overestimate each vertex’s distance from the starting vertex, then inspect each node and its neighbors for the shortest subpath to those neighbors.

In this way, the algorithm uses a greedy approach to find the next plausible solution, with the expectation that the end result will be the best solution for the whole problem.

How to Implement the Dijkstra Algorithm?

Let us consider some key features of Dijkstra’s algorithm before moving on to the step-by-step process of implementing it.

Essentially, the Dijkstra’s algorithm starts with the source node, evaluates the entire graph, and finds the shortest path between that node and all the other nodes in the graph.

The algorithm keeps track of the currently known shortest path between each node and the source code and updates these values if another shortest path is discovered.

The node is marked as “visited” and can be added to the path once the algorithm has determined the shortest path between the source code and another node.

This procedure is repeated until all of the nodes in the graph have been added to the path, resulting in a path that connects the source node to all of the other nodes while following the shortest plausible path to each node.

Now, I’ll walk you through the algorithm implementation process step by step.

The first step is to designate all nodes as unvisited.

Set the current distance of the chosen starting node to 0 and the rest of the nodes to infinity.

Choose the beginning node as the current node now.

Analyze all of the current node’s unvisited neighbours and measure their distances by multiplying the current node’s current distance by the weight of the edge that connects the neighbour node and the current node.

Compare the recently measured distance to the current distance assigned to the neighbouring node, and use the new distance as the new current distance of the neighbouring node.

After that, consider all of the current node’s unvisited neighbours and mark the current node as visited.

The algorithm will end, if the destination node has been marked visited.

Otherwise, select the unvisited node with the shortest distance and set it as the new current node, then repeat the procedure from step 4.

Applications of Dijkstra’s Algorithm

Before learning any algorithm, it’s important to understand what it’s for and how it can help us in real-world applications. For example, we are attempting to solve the least path-based problems using Dijkstra’s algorithm.

For instance, suppose a person wishes to travel from city A to city B, both of which are connected by different routes. What is the most common path he/ she can take?

Without a doubt, we would choose the path that would allow us to arrive at our destination in the shortest amount of time, distance, and even money.

Furthermore, the debate has a variety of real-world applications, including the following:

It’s widely used in map applications for things like Google Maps, finding map sites pointing to the vertices of a graph, calculating traffic and delay-timing, and so on.

This is also widely used in data transmission in networking and telecommunication domains to reduce the obstacles encountered.

This algorithm is used in robotics, transportation, embedded systems, laboratory or production plants, and other areas where shortest path explications are required.

Advantages and Disadvantages of Dijkstra’s Algorithm

Its low complexity, which is almost linear, is one of its major advantages.

It can be used to find the shortest path between a single node and all other nodes, as well as the shortest path between a single source node and a single destination node, by stopping the algorithm once the shortest distance is found for the destination node.

Only directed, weighted graphs are supported, and all edges must have non-negative values.

Conclusion

We have seen :

The main components of graphs are nodes and edges, which are used to show connections between objects, entities, or individuals.

The shortest path between one chosen node and each other node in a graph can be determined using Dijkstra’s algorithm.

Finally, the steps involved in putting Dijkstra’s algorithm into action.

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