DAG Optimization

Shortest Path (DAG)

Find the shortest paths from a source in a Directed Acyclic Graph in O(V + E). By relaxing edges in topological order, we guarantee that each node's shortest path is finalized in a single pass.

Time ComplexityO(V + E)

Space ComplexityO(V)

Try Interactive Simulator

Topological Order

Processing nodes in topological order ensures that when we relax edges from node u, its own shortest path distance is already finalized.

Linear Efficiency

Unlike Dijkstra's, this algorithm doesn't need a priority queue. It simply visits each node and its outgoing edges once, making it optimal for DAGs.

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DAG Optimization

Shortest Path (DAG)

Time ComplexityO(V + E)

Space ComplexityO(V)

Try Interactive Simulator

Topological Order

Processing nodes in topological order ensures that when we relax edges from node u, its own shortest path distance is already finalized.

Linear Efficiency

Unlike Dijkstra's, this algorithm doesn't need a priority queue. It simply visits each node and its outgoing edges once, making it optimal for DAGs.

🖱️ Click to Add • ↔️ Drag to Move • ⌨️ Shift+Drag to Join

Shortest Path Dag

Shortest Path Dag

Shortest Path (DAG)

Topological Order

Linear Efficiency

Shortest Path (DAG)

Topological Order

Linear Efficiency