Dijkstra for longest path in a DAG

Question

I am trying to find out if it is possible to use Dijkstra\'s algorithm to find the longest path in a directed acyclic path. I know that it is not possible to find the longes

Answer 1

Not enough reputation to comment on @punkyduck's answer, but I'd like to mention that replacing min with max in the DAG

a ——2——→ b ——2——→ c
│                 ↑
│                 │
1                 4
│                 │
└——————→ d ———————┘

actually works, as the algorithm will

• first examine a ⇨ ab=2, ad=1 ⇨ l(b)=(ab,2), l(d)=(ad,1)
• then examine b since we use max ⇨ abc=2 ⇨ l(c)=(abc,2)
• then examine c since abc>ad ⇨ Nothing happens
• at last examine d ⇨ adc=5 ⇨ update l(c)=(adc,5)

So at the last step the correct longest path adc is found. Just to point out the mistake.