Competitive Coding
Unit 5: Dynamic Programming Problems
Master the seven classic DP problems — from Binomial Coefficients to Balanced Partitions — with complete recurrences, table traces, C++/Python code, and optimization techniques used at top tech companies.
⏱️ 10 hrs theory + 8 hrs practice | 💰 Earning Potential: ₹15K–₹50K/month | 📝 30 MCQs (Bloom's Mapped)
💼 Jobs this unlocks: SDE at FAANG (₹25–60 LPA) | Competitive Programmer (₹15–40 LPA) | Algorithm Engineer (₹20–50 LPA)
Opening Hook — DP Powers the Products You Use Daily
📦 How Flipkart's Warehouse Optimizer Packs Maximum Items
Every time you order from Flipkart during the Big Billion Days sale, a warehouse robot needs to decide how to stack boxes of different sizes into delivery trucks to maximise the number of items shipped per trip. This isn't trial-and-error — it's the Box Stacking Problem, a classic Dynamic Programming challenge. Flipkart's logistics engine uses a variant of DP-based stacking to reduce shipping costs by 18% — saving ₹200+ crores annually.
Meanwhile, when Netflix recommends your next binge-watch, it computes the Longest Common Subsequence (LCS) between your watch history and millions of other users. If you watched Breaking Bad → Narcos → Money Heist, and another user watched Breaking Bad → Peaky Blinders → Narcos → Money Heist → Ozark, the LCS is [Breaking Bad, Narcos, Money Heist] — and Netflix recommends Peaky Blinders and Ozark to you. That's DP in production at scale.
What if YOU could build these algorithms? In this unit, you'll master 7 classic DP problems that appear in 60%+ of FAANG interviews. These same algorithms power spell-checkers (Edit Distance), DNA analysis (LCS), investment portfolios (Knapsack), and compiler optimizers (LIS).
Learning Outcomes — Bloom's Taxonomy Mapped (12 Outcomes)
| Bloom's Level | Learning Outcome |
|---|---|
| 🔵 Remember | LO1: State the recurrence relations for Binomial Coefficient, 0/1 Knapsack, LIS, LCS, and Edit Distance |
| 🔵 Remember | LO2: List the base cases and boundary conditions for each of the 7 DP problems |
| 🟢 Understand | LO3: Explain the principle of optimal substructure and overlapping subproblems using the Knapsack problem as an example |
| 🟢 Understand | LO4: Describe how the Box Stacking problem reduces to a variant of Longest Increasing Subsequence |
| 🟡 Apply | LO5: Trace and fill complete DP tables for Edit Distance, LCS, and Knapsack given specific inputs |
| 🟡 Apply | LO6: Implement all 7 DP problems in C++ and Python with correct time and space complexity |
| 🟠 Analyze | LO7: Compare the O(n²) and O(n log n) approaches for LIS and determine when each is appropriate |
| 🟠 Analyze | LO8: Analyze how space optimization reduces 2D DP tables to 1D arrays in Knapsack and Binomial Coefficient |
| 🔴 Evaluate | LO9: Evaluate whether a given problem has DP structure (optimal substructure + overlapping subproblems) vs. greedy structure |
| 🔴 Evaluate | LO10: Assess the trade-offs between top-down memoization and bottom-up tabulation approaches |
| 🟣 Create | LO11: Design a DP solution for a novel problem by identifying states, transitions, and base cases |
| 🟣 Create | LO12: Construct backtracking logic to reconstruct the actual solution (not just optimal value) for LCS and Edit Distance |