Dynamic Programming Questions at Infosys: What to Expect

Dynamic Programming (DP) is a core algorithmic technique tested in Infosys coding assessments and technical interviews. With 38 DP problems in their question bank—representing nearly a quarter of their total technical problems—mastering this topic is non-negotiable for serious candidates. Infosys uses these problems to evaluate a candidate's ability to break down complex problems, optimize inefficient solutions, and write clean, efficient code. Success here demonstrates strong analytical skills and preparedness for real-world software development challenges where optimization is key.

What to Expect — Types of Problems

Infosys DP questions typically fall into classic categories, focusing on fundamental patterns rather than obscure variations. Expect to encounter:

• 1D/2D DP Problems: These form the bulk of questions. Classic examples include the Fibonacci sequence, climbing stairs, or minimum path sum in a grid.
• Knapsack Variants: Problems involving optimal selection given a constraint, such as subset sum or unbounded knapsack for resource allocation scenarios.
• String DP: Common problems include longest common subsequence (LCS) and edit distance, which test your ability to handle two-dimensional state based on string indices.
• DP on Intervals or Sequences: Problems like matrix chain multiplication, which require building solutions for all subarrays or subsequences.

The difficulty often lies in recognizing the underlying DP pattern within a slightly disguised problem statement. The focus is on applying a known pattern correctly and implementing it efficiently.

How to Prepare — Study Tips with One Code Example

Start by understanding the core principle: DP is "optimized recursion" that avoids redundant calculations by storing results of subproblems. Follow this method:

1. Identify the Subproblem: What smaller instance of the problem must you solve repeatedly?
2. Define the DP State: Usually an array (dp[] or dp[][]) where each entry represents the solution to a subproblem.
3. Formulate the Recurrence Relation: The rule that builds a solution from smaller subproblem solutions.
4. Set Base Cases: The smallest, trivial subproblems you can solve directly.
5. Determine the Order of Computation: Iterate in an order that ensures needed subproblems are solved first.
6. Extract the Final Answer: It will typically be stored in a specific cell of your DP table, like dp[n] or dp[m][n].

Example: Solving "Climbing Stairs" (Count ways to reach the n-th step using 1 or 2 steps at a time)

This is a foundational 1D DP problem. The recurrence is dp[i] = dp[i-1] + dp[i-2].

def climbStairs(n: int) -> int:
    if n <= 2:
        return n
    dp = [0] * (n + 1)
    dp[1] = 1  # 1 way for 1 step
    dp[2] = 2  # 2 ways for 2 steps: (1,1) or (2)
    for i in range(3, n + 1):
        dp[i] = dp[i - 1] + dp[i - 2]
    return dp[n]

Recommended Practice Order

Do not attempt random problems. Build competence systematically:

1. Foundation: Start with 1D DP: Fibonacci, Climbing Stairs, Min Cost Climbing Stairs.
2. Core Patterns: Move to 2D DP: Unique Paths, Minimum Path Sum. Then learn the 0/1 Knapsack pattern.
3. String Problems: Practice Longest Common Subsequence and Edit Distance.
4. Infosys-Specific Practice: Finally, tackle the curated set of DP problems from the Infosys question bank to familiarize yourself with their phrasing and difficulty.

Consistent, pattern-focused practice is more effective than memorizing solutions. For targeted preparation, work through the full set of problems Infosys uses.

Practice Dynamic Programming at Infosys