title: "Dynamic Programming in Practice" description: "Learn Dynamic Programming with Vibe Coding! From knapsack problems to LCS and edit distance, let AI help you derive recurrence relations and solve optimal substructure problems!" duration: "120 minutes" difficulty: "Intermediate"
Dynamic Programming in Practice
Dynamic Programming (DP) is one of the most important and elegant algorithm design methods in computer science.
"Engineers who do not know DP can only write O(2^n) brute force solutions to complex problems; engineers who know DP solve them elegantly with O(n^2)."
The core idea of DP is simple: break big problems into smaller subproblems, remember the answers to subproblems, and avoid repeated calculations.
Vibe Coding Core Prompt
[DP Problem Prompt Example] "Please help me solve the 0/1 Knapsack problem:" "1. There are N items, each with weight w[i] and value v[i]." "2. Knapsack capacity is W." "3. Build a 2D DP array dp[i][w] representing max value with first i items and capacity w." "4. Derive the recurrence: dp[i][w] = max(dp[i-1][w], dp[i-1][w-w[i]] + v[i])." "5. Output the max value and selected items." "6. Explain why this recurrence is correct in Vibe Coding style."
Course Outline
- DP Core: Recursion + Memoization
- 0/1 Knapsack & Complete Knapsack
- Longest Common Subsequence (LCS)
- Edit Distance
- Hands-On: Auto Spell Check & Recommendation
Course Overview
Dynamic Programming is one of the most important and frequently tested algorithm design techniques. Core concept: break big problems into smaller subproblems, record answers, avoid repeated calculations.
Chapter 1: DP Core
Recursion + Memoization. Starting from Fibonacci, understand overlapping subproblems and optimal substructure.
Chapter 2: 0/1 Knapsack Problem
Classic NP-hard problem - but solvable optimally with DP under constraints. Understand state definition and state transition.
Chapter 3: Longest Common Subsequence (LCS)
Foundation of string comparison. LCS DP table is a prototype for many advanced algorithms.
Chapter 4: Edit Distance (Levenshtein Distance)
Core of spell checking - minimum operations to transform one string to another.
Chapter 5: Spell Check API
Wrap edit distance into a FastAPI service - input a misspelled word, return correct suggestions.