IMC Trading Interview Questions

1) What is the minimum number of moves required for a knight, when a bishop is also available, to reach a target square on a chessboard? 2) Implement a stack data structure that supports push, pop, and peek operations, as well as additional functions to return the sum of all elements and increment all elements by a given value.

Describe the data structures and algorithms needed for a program that keeps track of checked out books for a library. The program should: 1. Check out books for a member with a library card, 2. Return books, 3. Find all books that are overdue and who has them checked out, 4. Find all books that are due tomorrow. Note: New releases and popular books have shorter checkout periods than normal books.

Implement a tic-tac-toe game.

Is an immutable object always thread safe? Explain your reasoning.

Is searching through a sorted binary tree (binary search tree) always more efficient in terms of complexity than binary search?

What is the Big O notation for common operations performed on a heap? What about operations on a hashmap?

How would you implement a trade matching engine? The API for it should support: (1) adding Buy/Sell orders (these methods should return a Trade if an existing order matches the new one), (2) deleting pending orders, and (3) getting market depth or demand (i.e., range of buy/sell prices and total volume of pending orders at each price).

Given a string, find the longest possible valid password, where a valid password is defined by specific rules (such as containing at least one uppercase letter, one lowercase letter, and one digit).

What is the difference between a set and a list?

Given a binary tree, return all nodes whose value is greater than that of all their ancestors (i.e., nodes that are visible from the root along any path).

Determine whether two given words are anagrams of each other.

Given a telephone keypad display with the numbers arranged as: 1 2 3 4 5 6 7 8 9 You press a random number, then move to a random adjacent number (no diagonals), then move again to a random adjacent number (again, no diagonals). You record the three numbers in order to form a three-digit number (e.g., 569). What is the probability that the resulting number is divisible by 2?

Given six distinct weights labeled 101, 102, 103, 104, 105, and 106, three weights are placed on each side of a balance scale. What is the probability that the weight labeled 106 is on the heavier side of the scale?

How many integers less than 100000 contain two consecutive '1's in their decimal representation?

Draw the payoff diagrams for buying and selling a call option and a put option.

Brainteaser: If there are 27 clinks (glasses clinking) in a room, how many people are there?

What is the expected number of coin flips required for two players, who take turns flipping, to get two tails in a row?

Can you perform binary search on a linked list? Explain why or why not.

What is a race condition?

What does amortized runtime mean?

Explain the central limit theorem in a way that non-STEM students can understand.

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

Derive the Central Limit Theorem for a sequence of independent coin tosses.

What is a pointer and a shared pointer? How do you manage object ownership using these in programming?

Five people are sitting at a circular table. What is the probability that they are seated in the order of their birthdays?

What makes a good hash function? Describe the key characteristics and properties that define an effective hash function.

1) Given a chessboard size, a knight's starting position, an end position, and a bishop's position, find the minimum number of moves required for the knight to reach the end position. The knight cannot move to any square that the bishop is attacking, unless it captures the bishop on that square. 2) Implement a stack with the following functions: pop, push, inc, isEmpty, and peek. The inc function should increase the first n elements of the stack by a value i.

What is the minimum number of moves required for a knight to reach a target position on a chessboard, given that there is a bishop present which threatens certain squares? The knight cannot move to squares attacked by the bishop.

Implement a stack data structure with an additional method increment(k, v), which increments the bottom k elements of the stack by the value v.

Describe a stack and a queue to someone who does not have a background in data structures.