dp-state-designer

# DP State Designer Skill ## Purpose Assist in designing optimal dynamic programming states, transitions, and optimizations for complex DP problems. ## Capabilities - Identify subproblem structure from problem description - Suggest state representations (dimensions, parameters) - Derive transition formulas - Identify optimization opportunities (rolling array, bitmask compression) - Generate state space complexity estimates - Detect overlapping subproblems ## Target Processes - dp-pattern-matching - dp-state-optimization - dp-transition-derivation - advanced-dp-techniques ## DP Design Framework 1. **Subproblem Identification**: What smaller problems compose the solution? 2. **State Definition**: What parameters uniquely identify a subproblem? 3. **Transition Formula**: How do we combine subproblem solutions? 4. **Base Cases**: What are the trivial subproblems? 5. **Computation Order**: In what order should we solve subproblems? 6. **Space Optimization**: Can we reduce memory usage? ## Input Schema ```json { "type": "object", "properties": { "problemDescription": { "type": "string" }, "constraints": { "type": "object" }, "examples": { "type": "array" }, "requestType": { "type": "string", "enum": ["fullDesign", "stateOnly", "transitions", "optimize"] } }, "required": ["problemDescription", "requestType"] } ``` ## Output Schema ```json { "type": "object", "properties": { "success": { "type": "boolean" }, "state": { ...