DP Fundamentals

Dynamic Programming (DP) is one of the most powerful problem-solving techniques in computer science. It optimizes problems by breaking them into simpler subproblems and storing solutions to avoid redundant calculations. The key insight is simple: instead of recalculating the same thing repeatedly, calculate it once and remember the answer.

DP can feel intimidating at first, but it follows a systematic approach. This unit teaches you to recognize DP problems by their characteristics (optimal substructure and overlapping subproblems), understand the two approaches (top-down memoization and bottom-up tabulation), and follow a step-by-step process for solving any DP problem.

What You'll Learn

• Introduction to Dynamic Programming: What DP is, when to use it, and the two approaches. You'll learn the six-step problem-solving process: identify if it's DP, define the state, find the recurrence relation, identify base cases, determine computation order, and implement. Includes detailed examples with Fibonacci, climbing stairs, and time/space complexity analysis.

• Common DP Patterns: The essential patterns that cover most interview problems, including linear DP (house robber), grid paths, knapsack variations, longest common subsequence, and state machine patterns for buy/sell stock problems. Recognition guides help you map problems to patterns quickly.

Why It Matters

DP problems are extremely common in coding interviews at top companies. They test your ability to identify patterns, define state, and build solutions systematically. The good news: most interview DP problems follow one of a handful of patterns. Learn these patterns and you'll handle most DP questions confidently.