Graph Algorithms • Ordering

Topological Sort (DFS)

A linear ordering of vertices in a Directed Acyclic Graph (DAG). The DFS approach works by visiting nodes and adding them to the result list in reverse order of their completion.

Try Interactive Simulator

Post-Order

We perform DFS and wait for a node to "finish" all its neighbors before adding it to our topological sort.

The Stack

A recursion stack tracks the currently active nodes. This helps detect if the graph is truly acyclic.

Cycle Check

If we revisit a node that is already on the recursion stack, we've found a cycle! Topological sort is impossible.

Reverse Prep

Because we add nodes as they finish, the result is in reverse topological order. We prepend them to get the final list.

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Graph Algorithms • Ordering

Topological Sort (DFS)

A linear ordering of vertices in a Directed Acyclic Graph (DAG). The DFS approach works by visiting nodes and adding them to the result list in reverse order of their completion.

Try Interactive Simulator

Post-Order

We perform DFS and wait for a node to "finish" all its neighbors before adding it to our topological sort.

The Stack

A recursion stack tracks the currently active nodes. This helps detect if the graph is truly acyclic.

Cycle Check

If we revisit a node that is already on the recursion stack, we've found a cycle! Topological sort is impossible.

Reverse Prep

Because we add nodes as they finish, the result is in reverse topological order. We prepend them to get the final list.

Topological Sort Dfs

Topological Sort Dfs

Topological Sort (DFS)

Post-Order

The Stack

Cycle Check

Reverse Prep

Topological Sort (DFS)

Post-Order

The Stack

Cycle Check

Reverse Prep