Dynamic Programming (DP) is one of the most challenging yet rewarding topics in technical interviews. Master the art of breaking problems into overlapping subproblems and building optimal solutions from the bottom up.
Core Concepts:
Memoization: Top-down recursive approach with caching
Tabulation: Bottom-up iterative approach
State definition: Identifying what to store in DP table
Recurrence relation: Mathematical formula for subproblems
Common Patterns:
0/1 Knapsack and variations
Longest Common Subsequence (LCS)
Edit distance and string matching
Matrix chain multiplication
Subset sum and partition problems
When to Use DP:
Problem has optimal substructure
Overlapping subproblems exist
Need to find optimal value (min/max)
Counting possibilities or combinations
Difficulty: Medium to Hard. Practice 20-30 problems to build pattern recognition.
Stock trading dynamic programming problems are a classic interview cluster. Every variant – one transaction, unlimited, at most k, cooldown, […]
What is Interval DP? Interval DP is a dynamic programming pattern where you optimize over all sub-intervals of a range.
2D DP Pattern Overview 2D dynamic programming problems use a 2D table where dp[i][j] represents the optimal value considering only
Dynamic Programming on Strings Interview Patterns String DP problems share a common structure: a 2D table where one dimension indexes
Core Pattern Tree DP follows a single structural pattern: post-order DFS. You recurse into children first, then compute the answer
Longest Common Subsequence (LCS) is a fundamental string DP problem that appears in interviews at Google, Microsoft, and Amazon —
Edit Distance (Levenshtein Distance) is a classic string DP problem that appears in interviews at Google, Microsoft, and Dropbox. It’s
Word Break (LeetCode 139) is a string DP problem that tests whether you can partition a string using a given
The 0/1 Knapsack problem is one of the most important DP patterns. Unlike coin change (unbounded knapsack), each item can
Coin Change (LeetCode 322) is the canonical dynamic programming problem. It tests your ability to identify optimal substructure, choose between
Write a function to find the longest palindrome in a string. 2026 Update: Longest Palindrome — Character Frequency Approach There
Prime Numbers: Sieve of Eratosthenes, Trial Division, and the Miller-Rabin Test Prime number problems appear at FAANG interviews, fintech screens,
The Fruit Jar Labeling Puzzle: Three Mislabeled Jars, One Fruit Picked The fruit jar labeling puzzle is a famous lateral-thinking
Longest Palindromic Substring: Expand Around Center, DP, and Manacher’s Algorithm Finding the longest palindromic substring of a string is one
Question: You have two identical eggs. Standing in front of a 100 floor building, you wonder what is the maximum
