GATE CS 2026 Set 2 — Question 37
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Algorithms → Graph Algorithms → Topological Sort
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Question
Let be a weighted directed acyclic graph with edges and vertices. Given and a source vertex in , which one of the following options gives the worst case time complexity of the fastest algorithm to find the lengths of shortest paths from to all vertices that are reachable from in ?
Correct answer
(A) Θ(m + n)
Solution
For a general weighted graph, Dijkstra's algorithm (for non-negative weights) takes and Bellman-Ford (for general weights) takes .However, the problem specifies that is a Directed Acyclic Graph (DAG). For DAGs, the shortest path problem from a single source can be solved more efficiently using topological sorting, regardless of whether edge weights are positive or negative.The algorithm is as follows:
1.Perform a topological sort of the vertices. This takes time.
2.Initialize distances to all vertices as infinity and distance to source as 0.
3.Process vertices in topological order. For each vertex , relax all outgoing edges . Since each edge is processed exactly once, this step takes time.
The total time complexity is .Continue learning with Success Tracker
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