aloalgoDynamic Programming Summary
Dynamic Programming (DP) is one of those topics that feels foggy… until it suddenly snaps into focus. This guide is designed to get you from vague intuition to confident execution, especially for coding interviews and real-world problem solving.Chapters
Work through these chapters in order to build a solid foundation in dynamic programming:1. Recursion to Memoization
Learn what dynamic programming is and how to transform recursive solutions into efficient memoized solutions. Covers overlapping subproblems, optimal substructure, and the FAST strategy for solving DP problems.2. 1D Dynamic Programming
Master one-dimensional DP with tabulation. Learn the bottom-up approach, compare memoization vs tabulation, and solve classic problems like Fibonacci, House Robber, and Coin Change.3. 2D Dynamic Programming
Tackle two-dimensional DP for grid problems, string comparisons, and knapsack variants. Includes Unique Paths, Edit Distance, and Longest Common Subsequence.4. Space Optimization for DP
Learn how to reduce memory usage in your DP solutions. Compress 1D DP to O(1) space and 2D DP to O(n) space without changing time complexity.Quick Reference: The FAST Strategy
A simple mental checklist for DP problems. Whenever you suspect a problem can be solved with dynamic programming, walk through these four steps in order. They will guide you from understanding the problem to writing a complete solution.F – Define the Function
What does
dp(state) represent? Write a clear English sentence describing what the function returns for a given state. For example, "dp(i) returns the maximum profit using items 0 through i." Getting this definition right is the most important step.A – Arguments (State)
What variables uniquely define a subproblem? These become the parameters of your function or the dimensions of your table. Common states include the current index, remaining capacity, or a pair of indices for two sequences.
S – State Transition
How do you move from one state to smaller states? This is your recurrence relation. For each state, you make a choice and combine the results of smaller subproblems. For example, dp(i) = max(dp(i-1), dp(i-2) + value[i]).
T – Termination
What are the base cases? These are the smallest subproblems that you can solve directly without further recursion. For example, dp(0) = 0 or dp(1) = value[1].
If you can answer these four questions, you can write a DP solution.
Memoization vs Tabulation
There are two main approaches to implementing a DP solution. Memoization (top-down) starts from the original problem and recursively breaks it into subproblems, caching results as it goes. Tabulation (bottom-up) starts from the base cases and builds up to the answer iteratively using a table.Memoization is often easier to write because it follows the natural recursive structure of the problem. Tabulation avoids recursion overhead and stack overflow issues, and it makes space optimization more straightforward since you can see exactly which previous states are needed. In interviews, either approach is acceptable. Choose the one that feels more natural for the specific problem.Practice Problems by Difficulty
BeginnerIntermediateAdvancedFinal Thoughts
Dynamic Programming is less about memorizing patterns and more about state definition discipline. Once you master that, DP stops being scary and starts feeling mechanical, almost relaxing.Start with Chapter 1: Recursion to MemoizationWas this helpful?
Company
Practice
© 2026 aloalgo. All rights reserved.