Implement Factorial and Squares
Company: Morgan Stanley
Role: Data Scientist
Category: Coding & Algorithms
Difficulty: medium
Interview Round: HR Screen
##### Question
In a live coding interview, write two Python functions and be ready to discuss their behavior.
1. `factorial(n)`: Given a non-negative integer `n`, return `n!`. Implement it **iteratively**, and be prepared to explain how a **recursive** version would differ. State the time and space complexity of each approach.
2. `squares(n)`: Given a non-negative integer `n`, return a list containing the squares of the first `n` integers, in order. Clearly state your convention—either `[0^2, 1^2, ..., (n-1)^2]` or `[1^2, 2^2, ..., n^2]`. For example, with the 0-based convention, `n = 5` should return `[0, 1, 4, 9, 16]`.
For both functions, discuss input validation and edge cases such as `n = 0` and invalid negative input.
Quick Answer: A Morgan Stanley data scientist HR-screen live-coding warm-up: implement Python `factorial(n)` (iteratively, then explain the recursive version) and `squares(n)` returning the squares of the first n integers. Evaluates clean Python, the iteration-vs-recursion trade-off, time and space complexity analysis, input validation, and edge cases like n = 0 and negative input.
Iterative Factorial
Implement solution(n) that returns n! for a non-negative integer n. Return None for negative input.
Constraints
- n is an integer
Examples
Input: (0,)
Expected Output: 1
Input: (1,)
Expected Output: 1
Hints
- Start with 1 and multiply values from 2 through n.
Squares of the First n Integers
Implement solution(n) using the 0-based convention: return [0^2, 1^2, ..., (n-1)^2]. Return None for negative input.
Constraints
- n is an integer
Examples
Input: (0,)
Expected Output: []
Input: (1,)
Expected Output: [0]
Hints
- Use a loop or list comprehension over range(n).