Dynamic Programming Questions at Turing: What to Expect

Dynamic Programming (DP) is a core algorithmic technique that separates strong candidates from the rest at Turing. With 10 out of 40 total questions dedicated to DP, it’s clear the company prioritizes your ability to break down complex problems, identify overlapping subproblems, and build efficient solutions from the ground up. Mastering DP demonstrates you can think recursively, optimize for performance, and handle the kind of scalable system design challenges Turing engineers face daily. If you neglect this topic, you’re leaving a significant portion of your interview score on the table.

What to Expect — Types of Problems

Turing’s DP questions typically fall into a few classic categories. You won’t see overly obscure problems; instead, expect well-known patterns applied with a twist. The most common types are:

• 1D/2D Dynamic Programming: These involve sequences or grids. Classic examples include the "Climbing Stairs" variant (1D) or problems involving paths on a grid (2D).
• Knapsack Problems: Questions about selecting items with weights and values to maximize a total within a constraint. This tests your understanding of optimal substructure.
• String/Subsequence Problems: Problems like Longest Common Subsequence (LCS) or Edit Distance, which require comparing two sequences.
• Interval or Partition Problems: These involve making decisions over ranges, such as matrix chain multiplication or palindrome partitioning. The key is recognizing the underlying pattern. A problem about maximizing points from a sequence of tasks with cooldowns might be a disguised 1D DP, while a task scheduling problem could be a variant of the knapsack pattern.

How to Prepare — Study Tips with One Code Example

Start by understanding the core principle: DP is "careful brute force" with memoization or tabulation. For any problem, ask: 1) What is the state? (What parameters define a subproblem?) 2) What is the recurrence relation? (How does a solution to a larger problem depend on smaller ones?) 3) What is the base case? Practice deriving the recurrence relation before writing code. Use a top-down (recursive with memoization) approach first for clarity, then convert it to a bottom-up (iterative tabulation) solution for optimal space complexity. Always analyze time and space complexity.

Let’s look at the foundational "Climbing Stairs" pattern, where you count distinct ways to reach the top given you can take 1 or 2 steps at a time. The recurrence is dp[i] = dp[i-1] + dp[i-2].

def climbStairs(n: int) -> int:
    if n <= 2:
        return n
    # dp[i] = ways to reach step i
    dp = [0] * (n + 1)
    dp[1], dp[2] = 1, 2
    for i in range(3, n + 1):
        dp[i] = dp[i-1] + dp[i-2]
    return dp[n]
    # Space-optimized version uses two variables

Recommended Practice Order

Don’t jump into hard problems. Build your intuition systematically:

1. Foundation: Start with 1D problems like Fibonacci, Climbing Stairs, and House Robber. Master the state definition and recurrence.
2. 2D & Strings: Move to 2D grid problems (Unique Paths) and classic string problems like Longest Common Subsequence.
3. Knapsack: Learn the 0/1 Knapsack pattern thoroughly. This is a major category at Turing.
4. Variations & Hard Problems: Finally, tackle interval problems and harder variations that combine concepts, like "Coin Change" (knapsack variant) or "Decode Ways" (1D with constraints).

Focus on quality over quantity. Solve each problem, then immediately attempt a variation. Can you solve it with space optimization? What if the constraints change? This deep practice is what builds the pattern recognition you need for the interview.

Practice Dynamic Programming at Turing