---
id:"kb-2026-00134"
title:"Dynamic Programming"
schema_type:"TechArticle"
category:"computer-science"
language:"en"
confidence:"high"
last_verified:"2026-05-22"
generation_method: "human_only"
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completeness: 0.88
ai_citations:
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    url: "https://dl.acm.org/"
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secondary_sources:
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---

## TL;DR

DP solves problems by breaking them into overlapping subproblems, solving each once (memoization/tabulation). Converts exponential to polynomial time. Requires optimal substructure. Classic: Fibonacci, knapsack, LCS, edit distance.

## Core Explanation

Top-down: recursion + cache (memoization). Bottom-up: iterative table filling (tabulation). 0/1 Knapsack: max value from n items with weight limit — O(nW) pseudo-polynomial. Longest Common Subsequence: O(mn). DP vs. greedy: greedy makes locally optimal choice (may fail globally); DP explores all possibilities via subproblem decomposition.

## Further Reading

- [Introduction to Algorithms (CLRS)](undefined)