Competitive Coding
Unit 4: Basic Dynamic Programming
From recursive brute force to elegant optimal solutions — master the art of dynamic programming, solve classic problems, and ace coding interviews at top Indian tech companies.
⏱️ 8 hrs theory + 6 hrs practice | 💰 Earning Potential: ₹10,000–₹40,000/month | 📝 30 MCQs (Bloom's Mapped)
💼 Jobs this unlocks: Competitive Programmer | SDE at FAANG/Product Cos (₹12–40 LPA) | Algorithm Engineer
Opening Hook — The Hidden Algorithm Behind Billions
🏢 How Paytm, Amazon & Google Use Dynamic Programming Every Second
Every time Paytm shows you a cashback offer, a dynamic programming algorithm is running behind the scenes. It evaluates thousands of possible offer combinations and picks the one that maximises your engagement while keeping Paytm's costs optimal. This isn't a simple if-else — it's a variant of the classic Knapsack problem, one of the foundational DP problems you'll learn in this chapter.
Amazon's pricing engine uses DP to dynamically set prices across 10 crore+ products. When you see "₹499" instead of "₹599," a DP-based optimisation decided that price point maximises revenue across the entire product catalog. Google Maps finds the shortest route from your location to any destination using Dijkstra's algorithm — which relies on the optimal substructure property, a core concept of DP.
What if YOU could solve these problems? What if you could look at a complex optimisation problem and say, "I know how to break this down"? That's exactly what this chapter teaches you — the systematic art of Dynamic Programming.
Learning Outcomes — Bloom's Taxonomy Mapped
| Bloom's Level | Learning Outcome |
|---|---|
| 🔵 Remember | Define dynamic programming and list its two key properties: overlapping subproblems and optimal substructure |
| 🔵 Remember | State the recurrence relations for Fibonacci, tiling, climbing stairs, and coin change problems |
| 🔵 Understand | Explain the difference between memoization (top-down) and tabulation (bottom-up) using Fibonacci as an example |
| 🔵 Understand | Illustrate why naive recursion for Fibonacci is O(2ⁿ) while DP reduces it to O(n) |
| 🟢 Apply | Implement DP solutions for climbing stairs, coin change, and house robber problems in C/C++ |
| 🟢 Apply | Trace and fill DP tables for given inputs step-by-step |
| 🟢 Analyze | Compare time and space complexity of recursive vs memoized vs tabulated approaches |
| 🟢 Analyze | Identify whether a given problem exhibits optimal substructure and overlapping subproblems |
| 🟠 Evaluate | Judge which DP technique (memoization vs tabulation) is better suited for a given problem scenario |
| 🟠 Evaluate | Evaluate space optimisation opportunities in DP solutions (e.g., O(n) → O(1)) |
| 🟠 Create | Design DP solutions for unseen problems by identifying states, transitions, and base cases |
| 🟠 Create | Formulate optimised DP solutions with reduced space complexity for classic problems |