Practice Problems on Dijkstra’s Algorithm

Dijkstra’s Algorithm:

Dijkstra’s algorithm is a popular algorithms for solving many single-source shortest path problems having non-negative edge weight in the graphs i.e., it is to find the shortest distance between two vertices on a graph. It was conceived by Dutch computer scientist Edsger W. Dijkstra in 1956....

Need for Dijkstra’s Algorithm (Purpose and Use-Cases)

The need for Dijkstra’s algorithm arises in many applications where finding the shortest path between two points is crucial....

Can Dijkstra’s Algorithm work on both Directed and Undirected graphs?

Yes, Dijkstra’s algorithm can work on both directed graphs and undirected graphs as this algorithm is designed to work on any type of graph as long as it meets the requirements of having non-negative edge weights and being connected....

Algorithm for Dijkstra’s Algorithm:

Mark the source node with a current distance of 0 and the rest with infinity.Set the non-visited node with the smallest current distance as the current node.For each neighbor, N of the current node adds the current distance of the adjacent node with the weight of the edge connecting 0->1. If it is smaller than the current distance of Node, set it as the new current distance of N.Mark the current node 1 as visited.Go to step 2 if there are any nodes are unvisited....

How does Dijkstra’s Algorithm works?

Let’s see how Dijkstra’s Algorithm works with an example given below:...

Pseudo Code for Dijkstra’s Algorithm

function Dijkstra(Graph, source):   // Initialize distances to all nodes as infinity, and to the source node as 0. distances = map(all nodes -> infinity) distances = 0    // Initialize an empty set of visited nodes and a priority queue to keep track of the nodes to visit.   visited = empty set   queue = new PriorityQueue()   queue.enqueue(source, 0)    // Loop until all nodes have been visited.   while queue is not empty:       // Dequeue the node with the smallest distance from the priority queue.       current = queue.dequeue()        // If the node has already been visited, skip it.       if current in visited:           continue        // Mark the node as visited.       visited.add(current)        // Check all neighboring nodes to see if their distances need to be updated.       for neighbor in Graph.neighbors(current):           // Calculate the tentative distance to the neighbor through the current node.           tentative_distance = distances[current] + Graph.distance(current, neighbor)            // If the tentative distance is smaller than the current distance to the neighbor, update the distance.           if tentative_distance < distances[neighbor]:               distances[neighbor] = tentative_distance                // Enqueue the neighbor with its new distance to be considered for visitation in the future.               queue.enqueue(neighbor, distances[neighbor])    // Return the calculated distances from the source to all other nodes in the graph.   return distances...

Implemention of Dijkstra’s Algorithm:

There are several ways to Implement Dijkstra’s algorithm, but the most common ones are:...

Dijkstra’s Algorithms vs Bellman-Ford Algorithm

Dijkstra’s algorithm and Bellman-Ford algorithm are both used to find the shortest path in a weighted graph, but they have some key differences. Here are the main differences between Dijkstra’s algorithm and Bellman-Ford algorithm:...

Dijkstra’s Algorithm vs Floyd-Warshall Algorithm

Dijkstra’s algorithm and Floyd-Warshall algorithm are both used to find the shortest path in a weighted graph, but they have some key differences. Here are the main differences between Dijkstra’s algorithm and Floyd-Warshall algorithm:...

Dijkstra’s Algorithm vs A* Algorithm

Dijkstra’s algorithm and A* algorithm are both used to find the shortest path in a weighted graph, but they have some key differences. Here are the main differences between Dijkstra’s algorithm and A* algorithm:...

Practice Problems on Dijkstra’s Algorithm:

Dijkstra’s shortest path algorithm | Greedy Algo-7Dijkstra’s Algorithm for Adjacency List Representation | Greedy Algo-8Dijkstra’s Algorithm – Priority Queue and Array ImplementationDijkstra’s shortest path algorithm using set in STLDijkstra’s shortest path algorithm using STL in C++Dijkstra’s Shortest Path Algorithm using priority_queue of STLDijkstra’s shortest path algorithm using matrix in C++Dijkstra’s Algorithm for Single Source Shortest Path in a DAGDijkstra’s Algorithm using Fibonacci HeapDijkstra’s shortest path algorithm for directed graph with negative weightsPrinting Paths in Dijkstra’s Shortest Path AlgorithmDijkstra’s shortest path algorithm with priority queue in JavaDijkstra’s shortest path algorithm with adjacency list in JavaDijkstra’s shortest path algorithm using adjacency matrix in JavaDijkstra’s Algorithm using Adjacency List in PythonDijkstra’s Algorithm using PriorityQueue in PythonDijkstra’s Algorithm using heapq module in PythonDijkstra’s Algorithm using dictionary and priority queue in Python...

Conclusion:

Overall, Dijkstra’s Algorithm is a simple and efficient way to find the shortest path in a graph with non-negative edge weights. However, it may not work well with graphs that have negative edge weights or cycles. In such cases, more advanced algorithms such as the Bellman-Ford algorithm or the Floyd-Warshall algorithm may be used....