How do you identify a dynamic programming problem?

DP problems have two key properties: optimal substructure (the optimal solution contains optimal solutions to subproblems) and overlapping subproblems (the same subproblems are solved repeatedly). If a recursive solution has exponential time due to repeated computation, it is likely a DP problem. Ask: 'Can I make a choice at each step and cache the result?'

What are the most common DP patterns in coding interviews?

The six most common DP patterns: 0/1 Knapsack (include or exclude), Unbounded Knapsack (multiple uses), Longest Common Subsequence (2D string DP), Fibonacci-style (1D sequence DP), Interval DP (operate on subarrays), and Tree DP (bottom-up on trees). Most DP interview questions are variants of these six.

Is dynamic programming asked at FAANG?

Yes. DP questions appear at all FAANG companies. Google and Meta ask DP more frequently than Amazon. Common problems: Longest Common Subsequence, Edit Distance, Coin Change, Word Break, Regular Expression Matching, and Burst Balloons. Expect 1-2 DP problems in a standard 4-5 round loop at Google or Meta.

What is the difference between top-down and bottom-up DP?

Top-down DP (memoization) starts from the full problem and recursively breaks it down, caching results. Bottom-up DP (tabulation) starts from base cases and builds up to the answer. Both have the same time complexity. Top-down is easier to reason about; bottom-up avoids recursion overhead and is easier to optimize space.

Dynamic Programming Interview Questions 2026

DP patterns, how to recognize them in the first 3 minutes, the most frequently asked DP questions at FAANG, and the approach that turns "I don't know where to start" into systematic problem solving.

Quick Answer

Dynamic programming applies when a problem has optimal substructure and overlapping subproblems. The six core DP patterns to master: 0/1 Knapsack, Unbounded Knapsack, LCS/2D string DP, Fibonacci-style 1D DP, Interval DP, and Tree DP. Most FAANG DP questions are variants of these patterns. Recognize DP by asking: 'Does a recursive solution recompute the same subproblems?'

Why DP is High Signal

Dynamic programming appears in roughly 15% of coding interview questions based on LeakCode's database, but accounts for a disproportionate share of hiring decisions at senior levels. A correct DP solution signals mastery of problem decomposition, state definition, and optimization thinking. An incorrect DP attempt with sound reasoning often scores higher than a correct brute-force solution.

DP is also one of the most learnable interview topics. Unlike system design (which requires broad experience) or graph theory (which requires intuition), DP has recognizable patterns. Knowing 5-6 core patterns covers the majority of interview DP questions.

How to Recognize a DP Problem

A problem likely requires DP if it asks for: maximum or minimum of something, count of ways to do something, whether something is possible, or the optimal value given some constraints. The presence of overlapping subproblems is the key signal: if solving a problem requires solving the same smaller problem multiple times, memoize it.

The 3-question test: Can I solve a smaller version of this problem? Does solving larger versions require solving smaller versions repeatedly? Can I define the answer to the large problem in terms of answers to smaller problems? If all three are yes, it is a DP problem.

The Core DP Patterns

1D DP (linear)

Climbing stairs, house robber, maximum subarray, jump game, coin change

2D DP (grid)

Unique paths, minimum path sum, edit distance, longest common subsequence

Knapsack (0/1 and unbounded)

Partition equal subset sum, coin change, target sum, perfect squares

Interval DP

Burst balloons, merge stones, matrix chain multiplication

Tree DP

House robber III, diameter of binary tree, maximum path sum in tree

State machine DP

Best time to buy and sell stock (with cooldown/fee/k transactions)

Top-Down vs Bottom-Up

Top-down (memoization): write the recursive solution first, add a cache. Easier to reason about, closer to how you think about the problem. Better for interviews where explaining the recurrence relation matters.

Bottom-up (tabulation): fill a DP table starting from base cases. More space-efficient (can often reduce to O(n) space), no recursion stack overhead. Better for problems where space optimization is part of the question.

In interviews: start with top-down if you're not immediately sure of the table layout. Top-down makes the subproblem structure explicit and easier to explain. After getting to a working solution, discuss how you'd convert to bottom-up and whether you could optimize space.

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See actual dynamic programming questions from verified FAANG and top tech company interviews.

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