Greedy
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1. Dijkstra's algorithm is a greedy algorithm that finds the shortest path between nodes in a graph. It maintains a priority queue of all nodes and iteratively selects the node with the smallest distance. 2. It initializes all distances as infinity except the source node which is 0. On each iteration, it selects the node with the smallest distance and updates neighboring nodes' distances if a shorter path is found. 3. The example shows running Dijkstra's on a graph from node A. It iteratively selects the closest node and updates distances until all nodes are visited and the shortest paths from A are found.
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Dijkstra's algorithm allows finding the shortest path between any two vertices in a graph. It works by overestimating the distance of each vertex from the starting point and then visiting neighbors to find shorter paths. The algorithm uses a greedy approach, finding the next best solution at each step. It maintains path distances in an array and maps each vertex to its predecessor in the shortest path. A priority queue is used to efficiently retrieve the closest vertex. The time complexity is O(E Log V) and space is O(V). Applications include social networks, maps, and telephone networks.
Analysis of Pathfinding Algorithms
An overview of the most simple algorithms used in data structures for path finding. Dijkstra, Breadth First Search, Depth First Search, Best First Search and A-star
Naturally feel free to copy for assignments and all
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This document describes finding the longest path between two nodes in a graph using a modified Dijkstra's algorithm. It provides an example graph and walks through the steps of the algorithm to calculate the longest path from node A to B. Pseudocode is provided for the longest path Dijkstra's algorithm. Programming code in C is shown to implement the algorithm on the example graph. The output of running the program on the input graph is the longest path A B C F E D.Dijkstra's algorithm
Dijkstra's algorithm finds the shortest paths from a source node to all other nodes in a graph. It works by maintaining two sets - one for nodes whose shortest paths are determined, and one for remaining nodes. It iteratively selects the node with the smallest distance from the source, calculates the distances to its neighbors, and moves them to the determined set until all nodes are processed. Some applications include finding fastest routes in transportation networks like road maps or flight schedules.
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Greedy
- 1. Presented By: Minhaz Uddin ID: 151001612
- 2. Greedy algorithm Definition: A greedy algorithm always makes the choice that seems to be the best at that moment. So it makes a locally optimal choice in the hope that this choice will lead to a globally optimal solution. GreedyAlgorithm : Dijkstra's Algorithm Step: 1.Set all vertices distances equal to infinity without for the source vertex, set the source distance equal zero. 2.Push the source vertex in a min-priority queue in the form as the comparison in the min-priority queue will be according to vertices distances.
- 3. 3.Pop the vertex with the minimum distance from the priority queue . 4.Update the distances of the connected vertices to the popped vertex in case of "current vertex distance + edge weight < next vertex distance", then push the vertex with the new distance to the priority queue. 5.If the popped vertex is visited before, just continue without using it. 6.Apply the same algorithm again until the priority queue is empty.
- 4. Dijkstra's Example: 2 B C 5 1 3 A D 8
- 5. Dijkstra's Example: 2 ∞ B C ∞ 5 1 3 0 A D ∞ 8
- 6. Dijkstra's Example: Start from A because A distance equal zero. 2 5 B C ∞ 5 3 0 A D 8 8 Now A to B (0+5)< ∞ So B distance =5 Now A to D (0+8)< ∞ So D distance = 8 Output : A
- 7. Dijkstra's Example: New start point B because B distance (5) < D distance (8) 5 B 2 C 7 5 1 3 0 A D 8 8 Now B to A is not needed because A already visited Now B to C (5+2)< ∞ So C distance = 7 Output : A B
- 8. Dijkstra's Example: New start point C 5 B 2 C 7 5 3 0 A D 10 8 Now C to B is not needed because B already visited Now C to D (7+3)< ∞ So D distance = 10 Output : A B C
- 9. Dijkstra's Example: New start point D 5 B 2 C 7 5 3 0 A D 10 8 No unvisited edges are present. So the work is done. Output : A B C D