graph Pattern
Pattern hubs are for building transferable solving frames. Learn the recognition signals first, then drill state definition, update rules, and edge explanation until the pattern feels stable.
Pattern brief
Recognize first
Look for nodes with no incoming edges as a hint for mandatory inclusion.
Solve rhythm
State the active state and invariant first, explain how each update preserves them, then pressure-test with counterexamples.
Most common miss
Assuming any node can be included without checking in-degree may lead to non-minimal sets.
Recognition signals
- Look for nodes with no incoming edges as a hint for mandatory inclusion.
- Consider in-degree counting to avoid full traversal of the DAG.
- The hint about thinking in reverse is a strong signal to identify which color could have been printed last.
Solve flow
- 1. Define the active state/window.
- 2. Update state while preserving invariants.
- 3. Validate with edge-heavy examples.
Common misses
- Assuming any node can be included without checking in-degree may lead to non-minimal sets.
- Adding dependencies in the wrong direction is the most common bug; if color d appears inside color c's rectangle, then c must come before d.
- Double-counting a road that connects both cities when calculating network rank.
Recommended Ladder
Problem bank
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