Recursion Interview Questions & Tips

By Jai Pandya | Last updated: July 24, 2023

What is Recursion?

Recursion is a strategy used in computer science where a function invokes itself to solve a problem. This self-referential nature of recursion helps to solve problems that can be broken down into simpler, similar problems. In other words, recursion is a strategy where the solution to a problem depends on solutions to smaller instances of the same problem.

Recursion is a potent tool when dealing with problems related to data structures, such as traversing trees or graphs, sorting arrays, or exploring permutations and combinations. Functional languages like Haskell, Scala, and Erlang tend to favor recursion for control flow since they lack traditional looping constructs present in imperative languages.

How Recursion Works

Let's understand recursion with an analogy. Suppose you're standing at the bottom of a staircase and want to reach the top. The staircase has many steps, and your task is to climb them all. A non-recursive way of thinking would be to count each step as you climb, one after the other, until you reach the top.

However, a recursive approach would be different. Instead of thinking about all the steps you need to climb, in a recursive way, you wouldn't consider each step separately. Instead, you would break down the problem. How do you reach the top? You climb one step, and then you are left with a staircase that is shorter by one step.

This is your recursive step: climbing to the top of a staircase is the same as climbing one step and then climbing to the top of a smaller staircase.

But we're missing an important part - what if there's only one step? Or what if there are no steps at all? This brings us to the concept of a base case. In recursion, a base case acts as a stopping signal, telling the function when to stop calling itself and start returning.

In our analogy, the base case is when there are no more steps to climb. If there's only one step, you climb it, and you're done. If there are no steps, you're already at the top!

Pseudo Code

function climb_steps(n):
    # Base case: if there are no more steps, stop recursion
    if n == 0:
        print("You're at the top! All steps climbed.")
        return

# Recursive step: climb one step
    print("Climb one step. Remaining steps: ", n-1)
    # Recursive call: continue climbing the remaining steps
    climb_steps(n - 1)

Output Example when calling climb_steps(3):

Climb one step. Remaining steps: 2
Climb one step. Remaining steps: 1
Climb one step. Remaining steps: 0
You're at the top! All steps climbed.

This might seem like a mind-bender, but that's the nature of recursion!

Call Stack

Before we move on, let's take a moment to understand how recursion works under the hood.

Think of each recursive call to climb_steps as sending a climber to ascend the staircase. When the function calls itself, it's like it's sending another climber to ascend a slightly smaller staircase. The original climber waits at his step until the climber he sent finishes his climb.

In terms of a call stack, each climber represents a function call placed on the stack. The call at the top of the stack is the current step being climbed, and the calls below it are the steps waiting to be completed.

Tail Call Optimization

While we did tell you that recursion takes space on the call stack, some modern compilers can use a cheeky trick called tail call optimization (TCO) to reduce the space used by recursion.

Companies That Ask Recursion Questions

• Meta

When to Use Recursion in Interviews

The beauty of recursion lies in its ability to express complex problems in a few lines of code. While iterating with loops can achieve the same results, the ability to decompose a problem into smaller instances of itself makes recursion a favorite technique in problem-solving. In interviews, you may use recursion when the problem fits into one of the following patterns.

Divide and Conquer

In the divide and conquer approach, we break down a problem into smaller subproblems, solve each subproblem independently, and combine the solutions to answer the main problem.

Backtracking

Problems requiring exploring all possible configurations to find a solution can be tackled using recursion. Backtracking often involves a sequence of choices, where each choice leads you down a path, and if that path does not lead to a solution, you backtrack and explore another path.

Dynamic Programming

Dynamic programming (DP) is a strategic approach employed for efficient problem-solving. It decomposes the main problem into simpler, smaller subproblems, which are solved only once. Their solutions are stored for future use.

Recursion vs Dynamic Programming

When using dynamic programming with recursion, we introduce a memory function or a lookup table, known as memoization.

Common Mistakes in Interviews Featuring Recursion

Misunderstanding Recursion Flow

Understanding recursion flow is fundamental to writing and debugging recursive algorithms effectively. A crucial part of recursion is how it involves a function calling itself with a modified argument, progressing toward the base case.

Not Setting Base/Stop Conditions Correctly

Base cases form the foundation of any recursive algorithm. They determine the conditions under which the recursion should terminate, preventing the program from entering an infinite loop.

Overlooking Space Complexity

One of the often overlooked aspects of recursion is its space complexity. Each recursive call adds a new layer to the system's call stack, which can lead to high space complexity for deeply recursive algorithms.

What to Say in Interviews to Show Mastery Over Recursion

Demonstrating mastery of recursion in interviews requires more than just solving the problem. You must also articulate your thought process, explain your problem-solving approach, and showcase your understanding of recursion.

Common Recursion Interview Questions

EASY

Reverse String\ Write a program to reverse the given string.

MEDIUM

Decode String\ Return the decoded string.

Find Leaves of a Binary Tree\ Given a binary tree, extract all the leaves.

HARD

Longest Increasing Path in a Matrix\ Return the length of the longest increasing path.

Jai Pandya

Jai is a software engineer and a technical leader. He is also a founder of a SaaS product used by over 10K companies across the globe. He loves teaching and mentoring software engineers.

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