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AiTechWorlds
AiTechWorlds
Animate Kahn's topological sort removing in-degree-0 nodes from a DAG, with live order, in-degrees, and synced code.
from collections import deque
def topo_sort(adj, n):
indeg = [0] * n
for u in range(n):
for v in adj[u]: indeg[v] += 1
q = deque(i for i in range(n) if indeg[i] == 0)
order = []
while q:
u = q.popleft(); order.append(u)
for v in adj[u]:
indeg[v] -= 1
if indeg[v] == 0: q.append(v)
return orderTopological Sort orders the nodes of a directed acyclic graph so that every edge points from an earlier to a later node. Kahn's algorithm repeatedly removes in-degree-0 nodes.
| Time | O(V + E) |
| Space | O(V) |
| Graph | Directed, unweighted |
The Topological Sort Visualizer animates how topological sorting works on a directed acyclic graph (DAG): Kahn's algorithm repeatedly removes nodes with in-degree 0 and outputs them, decrementing the in-degrees of their neighbors. It produces an ordering where every edge points from an earlier to a later node. The algorithm runs in O(V + E) time and O(V) space.
Generate a DAG
Click New Graph or set the node-count slider to create a random directed acyclic graph.
Play the animation
Press Play to watch in-degree-0 nodes output and in-degrees decrement.
Step and scrub
Use Step Forward/Back or the timeline to inspect each removal.
Read the synced code
The highlighted pseudocode line tracks Kahn's algorithm; switch tabs for C++, Java, Python, or JavaScript.
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Last reviewed on June 14, 2026 by the AiTechWorlds Tools Team. All processing runs locally in your browser.