Citadel Interview Questions

Given a series of real numbers, what is the optimal point on the real line that minimizes the sum of the distances to all these numbers? Follow-up: What is the best algorithm to calculate the median of a sequence of numbers? Follow-up 2: Design an algorithm that can update the median of a sequence as new numbers are added.

Given an array of numbers: 1, 5, 3, 2, 4, 2, 3, 1, 2, 3, 2, 4, return another array where duplicate numbers are grouped in consecutive positions, maintaining the order of their first appearance. For example, the result should be: 1, 1, 5, 3, 3, 3, 2, 2, 2, 2, 4, 4.

Given an array of numbers, find three numbers such that their product is the maximum possible.

Write a program to output all the prime numbers smaller than a given integer N.

Find the minimum value of the function f(x) = x^x for real x > 0.

You have two eggs and a 100-story building. If an egg is dropped from a floor below floor X, it will not break; if dropped from floor X or higher, it will always break. What strategy would you use to determine the exact value of X with the minimum number of drops in the worst-case scenario?

How will the probability of an option ending up in the money change if the volatility of the underlying stock increases?

What is the difference between Gaussian Naive Bayes (GNB) and logistic regression? Under what circumstances would you choose one over the other?

Given that log X is normally distributed with mean 0 and variance 1, compute the expected value of X.

How do you estimate the square root of 5?

You have two strings, each of which takes exactly one hour to burn completely when lit at one end. The rate of burning is non-uniform and differs between the strings. Using only these two strings and a way to light them, how can you measure 45 minutes?

There are three random variables, X, Y, and Z. The three correlations between the variables are equal, i.e., ρ = Corr(X, Y) = Corr(Y, Z) = Corr(Z, X). What is the tightest possible bound you can give for ρ? How about the general case for n random variables?

What is the difference between LASSO and ridge regression?

Describe linear regression in detail.

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?