Citadel Interview Questions

Reverse a linked list in place.

Implement a balanced binary search tree from scratch, explain its time complexity, and optimize it to efficiently handle duplicate values.

Given an array representing user events, find the length of the longest contiguous subarray where the most frequent user in that subarray has the same number of events as the least frequent user in the entire event log. Write an efficient function to solve this problem.

How can a deadlock occur?

Given an array representing heights of points on a mountain and a starting position, what is the highest point that is visible from that position?

Given a set of numbers [a, b, c, d, e] and a target t, find the number of triplets from the set whose sum is less than or equal to t.

Given a sentence containing three types of brackets—parentheses (), square brackets [], and curly braces {}—determine if the brackets are properly matched and ordered.

Given a sorted array of integers, can you find two numbers such that their sum equals a target integer?

Implement a hashtable data structure that handles hash collisions using probing.

In Python, use object-oriented design to implement a defaultdict from scratch.

Given a matrix and the coordinates of the top-left and bottom-right corners, calculate the sum of the elements within the specified submatrix in (1) linear time and (2) constant time. You are allowed to preprocess the matrix.

Write the code for a multi-reader/single-writer lock.

Write a program to schedule a stream of pizza delivery orders.

Calculate the Sharpe ratio of a 60/40 coin toss where each toss results in a gain of $1 or a loss of $1, respectively.

What is a probability density function?

Explain how to use a binomial tree to determine the price of a European call option.

How do you reverse a string using Python?

How can you generate a probability of 1/4, 1/3, or 1/π using only coin flips?

Suppose you have three random variables. The correlation between A and B is 0.6, and the correlation between A and C is 0.8. What is the possible range of the correlation between B and C?

You are given an array of integers, which may include both negative and positive values, and another integer S. Find three different integers in the array whose sum is closest to S. If multiple solutions exist, any is acceptable. Is there an algorithm to find the three integers in O(n^2) time?

If you have a dataset with many features, what methods can you use to reduce its dimensionality?

How do you derive the Black-Scholes formula for pricing European options?

1. Describe your past research experience related to reinforcement learning and model explainability. 2. Explain the bias-variance trade-off in random forests. 3. What is the closed-form solution to linear regression, with and without L2 regularization?

Analyze the variance of a momentum trading strategy.

Sample points randomly from a unit sphere. If you generate independent standard normal variables X1, X2, X3 for the three coordinates and normalize by dividing by sqrt(X1^2 + X2^2 + X3^2), then (X1, X2, X3) / sqrt(X1^2 + X2^2 + X3^2) is a uniform random point on the sphere. What is the variance of each coordinate of the resulting uniform distribution on the sphere?

Given the numbers 1 to 1000 arranged around a circle in order, start at 1 and delete every alternate number (i.e., remove 1, then 3, then 5, and so on). Continue this process of deleting every other remaining number, wrapping around the circle as necessary, until only one number remains. Determine this final remaining number.

How do you generate a uniform distribution over a disk given access to two independent uniform random variables?

What is the expected value of the cube of a fair six-sided die roll?

Given a matrix of size N by T, where the entry at the i-th row and j-th column represents the price of buying i shares of a stock at time j, determine the minimum total cost of purchasing N shares by the end of time T.

You are given two ropes that, when lit, each burn for exactly one hour, but not necessarily at a constant rate. Which one of the following times CANNOT be measured using these ropes? a) 50 minutes b) 30 minutes c) 25 minutes d) 35 minutes.