Dynamic Programming Analysis

Breaks any complex problem into DP-style sub-problems: optimal substructure (solution depends on smaller solutions) + overlapping sub-problems (recurring parts, solve once, reuse). Applies to business, personal decisions, architecture, research, learning, projects.

Protocol

#	Step	Action	Gate
1	Define main problem	Restate precisely, final state, explicit/implicit constraints	—
2	Decompose	Break into smaller parts; recurse until base cases (directly solvable)	tree structure, see references/response-template.md
3	Identify overlaps	Which sub-problems recur across branches? Which partial solutions reuse?	mark explicitly — biggest efficiency win
4	Resolution order	Base cases first, then by dependency (prereq before dependent)	execution sequence
5	Solve each	Smallest → largest; compare options if multiple; note which parent problem it feeds	—
6	Compose	Combine sub-solutions into original problem; validate fit	—
7	Verify	Edge cases, external dependencies, optimal vs. good-enough	—

Respond using the template in references/response-template.md.

Adaptations by problem type

Type	Sub-problem	Base case	Overlap	Composition
Decision	each criterion	verifiable facts, not opinions	criteria affecting multiple options	decision table/matrix
Planning/Project	each deliverable/milestone	atomic task (1 person, 1 day)	shared deps between phases	schedule/roadmap
Technical/Architecture	each component/module	primitive functions/services	reusable utilities/patterns	integration diagram
Learning	each prerequisite concept	needs-no-prerequisite knowledge	fundamentals unlocking multiple topics	ordered learning path
Business/Strategy	each strategic lever	observable metrics, concrete actions	capabilities supporting multiple strategies	integrated strategic plan

Quality principles

• Granular: each sub-problem has a clear, direct answer.
• No pseudo-decomposition: genuinely break down, don't just rename the problem.
• Name dependencies explicitly (what depends on what).
• Bottom-up only — solving big before small causes rework.
• State reuse explicitly when one solution supports another.

Reference files

• references/response-template.md — verbatim markdown response template + sub-problem tree text format.
• references/example.md — worked example (career transition into AI).