DAG Validation Algorithm Visualization

Three-color DFS algorithm for cycle detection in learning graphs

DFS Stack

Loops
Recursion
Traversal Order:
  1. Variables
  2. Functions
  3. Loops
  4. Recursion
  5. Data Structures
  6. Algorithms
⚠️ CYCLE DETECTED: Loops ← Recursion ← Loops (Back edge shown in RED)
White: Unvisited nodes
Gray: In progress (on stack)
Black: Completed
Black arrow: Valid edge
Red arrow: Back edge (cycle)

How the Algorithm Works

Three-Color DFS Algorithm:

Cycle Detection: If we encounter an edge pointing to a gray node, we've found a cycle! Gray nodes are ancestors in the current DFS path, so pointing back to them creates a loop.

In this example: When exploring "Recursion", we find it points back to "Loops" which is still gray (on the stack), creating the cycle: Loops → Recursion → Loops.