Jump Trading Interview Questions

Given an array of characters, implement the 'malloc' function as in C. Ensure you write 'malloc' in a way that allows you to implement the 'free' function later. (The second part of the question is to implement 'free').

Compute the expected value of the maximum of n dice rolls.

There are four balls, two black and two white. You randomly pick two balls and flip their color (black to white or white to black). You repeat this process. How many times, on average, must you repeat this to ensure all four balls are the same color?

How can two devices synchronize their clock times over a network?

What are the different states a Verilog register can have?

Explain the difference between blocking and non-blocking assignments.

Let U₁, U₂, ... be independent uniform (0,1) random variables. Define N = min{ n : sum_{i=1}^n Uᵢ > 1 }. What is E[N]?

How many zeros are there in 100 factorial (100!)?

You have 8 balls that are identical in appearance, but one of them is heavier and the rest all have the same weight. Using a balance scale, what is the minimum number of weighings required to guarantee finding the heaviest ball, and how would you do it?

Write a function that prints 'fizz' if the parameter is divisible by 3 and prints 'buzz' if it is divisible by 5. You may use any programming language.

What is the Global Interpreter Lock (GIL) in Python, and how does it affect multi-threaded programs?

Implement a vector in C++ that stores its elements on the stack when the number of elements N is less than 10, but uses the heap to store any exceeding elements when N is 10 or greater.

Describe an efficient way to implement a lazily initialized singleton pattern in C++.

Design a linked list class.

Swap two variables without using a temporary variable.

What is a virtual destructor?

Task 1: You are given a string containing only numbers and the mathematical operators '+' and '*'. Read the string character by character. If it is a digit, push it onto a stack. If it is an operator, pop two elements from the stack, apply the operator, and push the result onto the stack. If there are not enough elements on the stack or no operator to apply, return -1. For example, for '12+4*7*', the result should be 84. Task 2: You have three ticket options: a 1-day ticket for $2, a 7-day ticket for $7 (valid for 7 consecutive days), and a 30-day ticket for $25. Given a list of days (integers in increasing order) on which you plan to travel, return the minimum possible amount of money you need to spend on tickets. For example, given [1,2,3,4,5,11,12,25], the minimum possible cost is 13.

Suppose a collection of n random variables have all pairwise correlations equal to c. Find, with proof, the range of possible values of c.

You have 5 unknown numbers. When selecting any two out of these five, there are 10 possible pairs. You are given the sums of all these 10 pairs. Using this information, find the original 5 numbers.

There are four balls: two black and two white. You randomly pick two balls and flip their colors (from black to white or vice versa), and repeat this process. How many times must you repeat this process to be certain that all four balls end up the same color?