Roadmap › Stage 9: Greedy & Dynamic Programming › Pattern 49 of 53
DSA pattern guide

DP — Trees & DAGs

Optimal choices on trees (rob or skip a node).

Stage 9 · Greedy & Dynamic Programming2 problems2 Medium

Use it when

Optimal choices on trees (rob or skip a node).

Key idea

Post-order DFS returns a small tuple per node, such as (take, skip).

Practice problems, in order

  1. House Robber IIIMedium
  2. Path Sum IIIMedium

How to practise this pattern

  1. Read the problem and look for the signal above before writing any code.
  2. Say the brute force out loud, with its time complexity, then ask what work it repeats.
  3. Apply the key idea and write the optimised version yourself.
  4. If you're stuck for more than 10 minutes, take one small hint, not the full solution.
  5. Move to the next problem only when you can explain why this pattern fits.

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