Dynamic Programming Questions at Intuit: What to Expect

Dynamic Programming (DP) is a core algorithmic technique for optimizing solutions to complex problems by breaking them into overlapping subproblems. At Intuit, where engineers build financial and tax software like TurboTax and QuickBooks, DP is not an academic exercise. It’s a practical tool for solving real-world optimization challenges. These could involve minimizing computational cost in tax calculations, optimizing resource allocation for data processing, or finding the most efficient path in a system workflow. Mastering DP demonstrates you can think recursively about a problem, optimize for performance, and handle the kind of scalable, state-dependent logic that underpins large-scale financial systems.

What to Expect — Types of Problems

Intuit’s DP questions tend to focus on practical applications of classic patterns rather than obscure puzzles. You can expect a strong emphasis on:

• 1D/2D Dynamic Programming: These are the most common. Problems often involve sequences or grids, like finding maximum profit, counting ways to reach a position, or making optimal decisions over time (a key concept in finance).
• Knapsack and Subset Problems: Given Intuit’s domain, problems about selecting optimal subsets (e.g., allocating budget, choosing transactions) are highly relevant. The 0/1 Knapsack pattern is fundamental here.
• String/Sequence Alignment: Problems involving comparing or transforming strings (like edit distance) test your ability to handle state transitions in two dimensions, a skill useful in data matching and validation.
• State Machine DP: Some problems may involve systems that move between different states (like buy/sell/hold in a trading context), requiring a DP table to track the best outcome for each state at each step.

The problems are designed to assess your ability to identify the optimal substructure and overlapping subproblems—the two hallmarks of a DP solution.

How to Prepare — Study Tips with One Code Example

Start by internalizing the core DP patterns, not just memorizing solutions. For each pattern, learn to:

1. Define the dp array/table and what dp[i] represents.
2. Establish the base case(s).
3. Derive the recurrence relation (the state transition).
4. Determine the order of iteration.

A fundamental pattern is the Fibonacci-style 1D DP, which extends to problems like "Climbing Stairs" or "Min Cost Climbing Stairs." Here’s the "Min Cost Climbing Stairs" solution, where you start from step 0 or 1 and pay cost[i] to step from i, aiming to reach the top with minimum cost.

def minCostClimbingStairs(cost):
    n = len(cost)
    # dp[i] = min cost to reach step i
    dp = [0] * (n + 1)

    # Base cases: starting at step 0 or 1 costs nothing initially
    dp[0] = 0
    dp[1] = 0

    for i in range(2, n + 1):
        # Recurrence: reach step i from i-1 or i-2, paying the cost of that starting step.
        dp[i] = min(dp[i-1] + cost[i-1], dp[i-2] + cost[i-2])
    return dp[n]

Recommended Practice Order

Tackle problems in this logical progression to build a solid foundation:

1. Foundations: Start with 1D DP (Fibonacci, Climbing Stairs, Min Cost Climbing Stairs).
2. Classic Patterns: Move to 0/1 Knapsack and Unbounded Knapsack problems.
3. 2D DP: Practice sequence problems (Longest Common Subsequence) and grid-based problems (Unique Paths).
4. String DP: Tackle Edit Distance and related string transformation challenges.
5. State Machine & Advanced: Finally, explore problems with buy/sell states or more complex dependencies.

Focus on understanding the recurrence relation for each problem type. Draw out the DP table for small examples to visualize the state transitions.

Practice Dynamic Programming at Intuit