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DP Foundations Ladder

This ladder is about learning to design states deliberately, not just filling tables by pattern matching.

Who This Is For

Use this ladder if:

  • DP still feels like memorizing recurrences
  • you struggle to explain what dp[i] or dp[i][j] actually means
  • greedy ideas fail, but you are not yet sure what the state should be

Warm-Up

  • prefix DP
  • one-dimensional maximize / minimize
  • counting ways on prefixes

Target skill:

  • write the state meaning before writing code

Core

  • reconstruction
  • top-down vs bottom-up reformulation
  • two-dimensional state design

Target skill:

  • treat state, transition, and answer location as one coherent contract

Stretch

  • convert a statement into state meaning before coding
  • compare a DP solution against a tempting greedy idea and explain why greedy fails

Target skill:

  • reason about DP design instead of only recognizing familiar formulas

Exit Criteria

You are ready to move on when:

  • you can count states and transitions before implementation
  • you know where the final answer lives
  • you can compress memory only when dependencies allow it

External Practice

Representative Solved Note

  • VMSCALE: a minimax decision-tree DP where the transition cost comes from balanced ternary rather than a uniform comparison price