The document discusses Dijkstra's algorithm, which is a greedy algorithm that finds the shortest path between nodes in a weighted graph. It finds the shortest path tree from a source node to every other node by tracking the shortest distance at each step. The example shows applying the steps of Dijkstra's algorithm to find the shortest path from node A to node Z in a sample graph.

1. 19IS303 – DATA STRUCTURES
AND ALGORITHMS
UNIT 4

2. RECAP
• Introduction to graphs
• Types of graphs
• Graph Traversals
– BFT
– DFT
• Topological sorting

3. Dijkstra Algorithm
• Dijkstra algorithm is a greedy algorithm.
• It finds a shortest path tree for a given weighted graph.
• This means it finds a shortest paths between nodes in a graph,
which may represent, for example, road networks
• For a given source node in the graph, the algorithm finds the
shortest path between source node and every other node.
• This algorithm also used for finding the shortest paths from a
single node to a single destination node by stopping the
algorithm once the shortest path to the destination node has
been determined.

4. Example
• Find the shortest path from A to Z:

5. Step 1

6. Step 2

7. Step 3

8. Step 4

9. Step 5

10. Step 6

11. Step 7

12. Step 8

13. Step 9

14. Apply the steps of the Dijkstra’s Algorithm to
find the shortest path from A to Z using the
following graph:

15. Apply the steps of the Dijkstra’s Algorithm to
find the shortest path from A to Z using the
following graph:

16. • Visualization Link:
https://www.101computing.net/dijkstras-
shortest-path-algorithm/