Dijkstra’s Algorithm

Transcript

1. Dijkstra’s Algorithm Do Dijkstra’s on this graph, starting from A. Best distance to A: 0 All other nodes: 1 (so far, unreachable) 52 / 71
2. Dijkstra’s Algorithm A is done. Choose shortest total distance (B at distance 3) From B, find a better path to C (3+3=6) Path to A is worse (3+3, worse than 0) 53 / 71
3. Dijkstra’s Algorithm B is done. Choose shortest total distance (F at distance 4) Better path to E (4+5=9) Worse paths to A (4+4 vs 0) and D (4+2=6 vs 5) 54 / 71
4. Dijkstra’s Algorithm F is done. Choose shortest total distance (D at distance 5) Better path for E (5+3 = 8 vs 9) Worse paths for other nodes 55 / 71
5. Dijkstra’s Algorithm D is done. Choose shortest total distance (C at distance 6) Better path to E (6+1 = 7 vs 8) Worse paths to B and D 56 / 71
6. Dijkstra’s Algorithm C is done. Choose shortest total distance (E at distance 7) Worse paths everywhere 57 / 71
7. Dijkstra’s Algorithm All nodes are done. Note we could have recorded paths in table Also could stop early if we only wanted a single destination. 58 / 71