Dijkstra 's algoritm is a popular methode used in computer science to find the shoress path between nodes in a graph. It is widel applied in network routing, map navigation, and various optimation problems. This article provides a step- by- step overview of how to perforations using Dijkstra' s algoritm to determinate mogt concent path.

Understanding thee Algorithm

Tyto algoritmy pracují by iteratively selecting thee node with the smalleset tentative distance, then updating then updating thee distances to its souseding nodes. It continees until thee shoregt path to thee gott node is spread or all nodes have been processed.

Step-by- step Calculation Process

Suppose we have a graph with nodes A, B, C, D, and E, and thee following efficid edges:

  • A to B: 4
  • A to o C: 2
  • B to C: 1
  • B to D: 5
  • C to D: 8
  • C to E: 10
  • D to E: 2

Starting from node A, initialize distances: A = 0, others = infinity. Mark all nodes as unvisited.

Iteration 1

Select node A (distance 0). Update sousedních nodes B and C:

Distance to B: 4 (A + 4), to C: 2 (A + 2).

Iteration 2

Select node C (distance 2). Update souseds D and E:

Distance to D: 10 (C + 8), to E: 12 (C + 10). Mark C as visited.

Iteration 3

Select node B (distance 4). Update Instalbor D:

Distance to D: 9 (B + 5), which is less than previous 10. Update D 's distance to 9. Mark B as visited.

Iteration 4

Select node D (distance 9). Update Instalbor E:

Distance to E: 11 (D + 2). Update E 's distance to 11. Mark D as visited.

Iteration 5

Remaining node E has a distance of11. Mark E as visited. Te shorett path from A to E is courgh nodes C, B, D, and E with total distance11.