A longest path maximizes path length, either the number of edges or the sum of specified edge weights, under the stated endpoints and simple-path convention. In a general graph, imposing vertex simplicity makes the optimization computationally difficult; a Directed acyclic graph admits a direct dynamic programming solution. Allowing arbitrary walks instead requires care with reachable positive cycles. The convention permitting a zero-edge path gives a possible value zero even when all nonempty paths have negative weight.
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