Skill

role-algorithms:dynamic-programming

Solves optimization problems using dynamic programming — top-down memoization, bottom-up tabulation, state space design, dimension reduction, bitmask DP, interval DP, tree DP (with rerooting), DP on DAGs, and convex hull trick / divide-and-conquer optimizations. Use when solving optimization problems with overlapping subproblems, implementing memoized solutions, or converting recursive solutions to iterative DP.

Install

npx claudepluginhub rnavarych/alpha-engineer --plugin role-algorithms

Tool Access

This skill is limited to using the following tools:

ReadGrepGlobBash

Preview

- Recognizing whether a problem has overlapping subproblems and optimal substructure

Supporting Assets

references/advanced-techniques.mdreferences/classic-patterns.mdreferences/identification-and-approach.md

SKILL.md

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Parent Repo Stars9

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Last CommitMar 3, 2026

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role-algorithms:dynamic-programming

When to use

Recognizing whether a problem has overlapping subproblems and optimal substructure

Choosing between top-down memoization and bottom-up tabulation

Designing state variables and minimizing state space dimensions

Implementing knapsack, sequence (LCS, LIS, edit distance), interval, or grid DP patterns

Applying bitmask DP for small subset enumeration (n ≤ 20)

Optimizing O(n²) DP transitions with convex hull trick or D&C optimization

Core principles

State captures everything — if future decisions need more information, the state is incomplete

Bottom-up for production — no stack overflow, easier space optimization, predictable memory access

Rolling array before adding a dimension — space optimization is almost always possible

Bitmask DP is exact exponential, not a hack — O(2^n × n) is acceptable for n ≤ 20

Identify the DAG — every DP is a shortest/longest path on a state DAG; if you can draw it, you can implement it

Reference Files

references/identification-and-approach.md — DP recognition heuristics, top-down vs bottom-up trade-offs, state variable design, state compression, redundant state elimination

references/classic-patterns.md — knapsack variants (0/1, unbounded, bounded, multi-dimensional), sequence DP (LCS, LIS, edit distance), interval DP, grid/path DP

references/advanced-techniques.md — bitmask DP (TSP, assignment), tree DP with rerooting, DP on DAGs, convex hull trick, D&C optimization, rolling arrays, dimension reduction, implementation checklist

Dynamic Programming

When to use

Recognizing whether a problem has overlapping subproblems and optimal substructure
Choosing between top-down memoization and bottom-up tabulation
Designing state variables and minimizing state space dimensions
Implementing knapsack, sequence (LCS, LIS, edit distance), interval, or grid DP patterns
Applying bitmask DP for small subset enumeration (n ≤ 20)
Optimizing O(n²) DP transitions with convex hull trick or D&C optimization

Core principles

State captures everything — if future decisions need more information, the state is incomplete
Bottom-up for production — no stack overflow, easier space optimization, predictable memory access
Rolling array before adding a dimension — space optimization is almost always possible
Bitmask DP is exact exponential, not a hack — O(2^n × n) is acceptable for n ≤ 20
Identify the DAG — every DP is a shortest/longest path on a state DAG; if you can draw it, you can implement it

Reference Files

references/identification-and-approach.md — DP recognition heuristics, top-down vs bottom-up trade-offs, state variable design, state compression, redundant state elimination
references/classic-patterns.md — knapsack variants (0/1, unbounded, bounded, multi-dimensional), sequence DP (LCS, LIS, edit distance), interval DP, grid/path DP
references/advanced-techniques.md — bitmask DP (TSP, assignment), tree DP with rerooting, DP on DAGs, convex hull trick, D&C optimization, rolling arrays, dimension reduction, implementation checklist