30+ Tower Research Capital LLC Interview Questions and Answers

Find the maximum profit by buying and selling a stock once based on given prices.

• Iterate through the prices array and keep track of the minimum price seen so far and the maximum profit achievable.

• Calculate the profit by subtracting the current price from the minimum price and update the maximum profit if needed.

• Return the maximum profit, ensuring it is not negative.

• Example: prices = [2, 100, 150, 120], Buy at 2, sell at 150, profit = 150 - 2 = 148.

Given a binary tree, a target node, and an integer K, find all nodes at distance K from the target node.

• Traverse the binary tree to find the target node.

• Use BFS to traverse the tree from the target node to nodes at distance K.

• Keep track of the distance while traversing the tree.

• Return the values of nodes at distance K in any order.

The challenge involves forming dance pairs from available boys and girls based on potential pairings to maximize the number of pairs.

• Parse the input to get the number of test cases, boys, girls, and potential pairings.

• Iterate through the potential pairings and form pairs based on the given indexes.

• Output '1' if a set of maximum possible pairs is returned, else output '0'.

• There can be multiple valid configurations of pairs.

• Example: For input '2 2 2' and pairings '1 1' and '2 2...read more

In a group of people with a symmetric relation of knowing each other, there will always be at least two people who know the same number of people.

• Consider the person who knows the maximum number of people in the group.

• If there is no one who knows the same number of people, then everyone else must know a different number of people.

• But this would mean that the total number of people known by everyone else is different from the total number of people known by the person who know...read more

Find the shortest path between two houses in a city represented as an unweighted graph.

• Use breadth-first search (BFS) algorithm to find the shortest path in an unweighted graph.

• Start BFS from the source house and keep track of the path taken to reach each house.

• Once the destination house is reached, backtrack from destination to source to find the shortest path.

• Consider using a queue data structure to implement BFS efficiently.

• Handle cases where multiple shortest paths exist ...read more

Calculate the minimum number of steps Ninja needs to cut down all trees in a forest grid.

• Iterate through the grid to find the shortest path to cut down all trees in order.

• Use a priority queue to keep track of the shortest trees to cut next.

• If it's impossible to cut all trees, return -1.

• Consider all four cardinal directions for movement in the grid.

For any subset of size n+1 of the set S of the first 2n numbers, there exists 2 numbers u and v such that u divides v.

• Divide the set S into two subsets of n numbers each.

• By the pigeonhole principle, at least one of the subsets contains two numbers whose ratio is an integer.

• If the subset contains n+1 numbers, then one of the numbers must be in the subset with the two numbers whose ratio is an integer.

• Therefore, there exists 2 numbers u and v such that u divides v.

At a party with 7 guests and a host, each guest shakes hands with a certain number of people. How many people did the host shake hands with?

• The first guest shakes hands with 1 person, the second with 2 people, and so on.

• The kth guest shakes hands with k people.

• The host shakes hands with all 7 guests, so the number of people the host shakes hands with is the sum of 1 to 7.

• The sum of 1 to n is n(n+1)/2, so the host shakes hands with 28 people.

Return all distinct palindromic substrings of a given string in alphabetical order.

• Iterate through all possible substrings of the given string.

• Check if each substring is a palindrome by comparing it with its reverse.

• Store all palindromic substrings in a set to ensure uniqueness.

• Return the sorted list of palindromic substrings.

Rearrange array numbers to form the largest possible numerical value by combining digits of each number in the array.

• Convert integers in the array to strings for easier manipulation.

• Sort the array of strings in non-increasing order based on custom comparison function.

• Join the sorted strings to form the largest possible number.

Algorithm to determine visible buildings in a 2D plane with given positions and heights

• Sort the buildings by their x-coordinates

• Traverse the sorted buildings from left to right

• For each building, check if it is visible by comparing its height with the maximum height of previously visited buildings

• If visible, add it to the list of visible buildings

• Return the list of visible buildings

Find the minimum cost to reduce an array to one element by merging adjacent elements.

• Iterate through the array and merge adjacent elements with the smallest sum each time.

• Keep track of the total cost as you merge elements.

• Repeat the merging process until only one element remains in the array.

Check if two nodes in a binary tree are cousins by comparing their levels and parents.

• Traverse the tree to find the levels and parents of the given nodes.

• Compare the levels and parents of the two nodes to determine if they are cousins.

• If the levels are the same and the parents are different, the nodes are cousins.

Count the total number of nodes in a complete binary tree given its root.

• Traverse the tree in level order and count the nodes

• Use a queue to keep track of nodes at each level

• Check for null nodes represented by -1 in the input

• The total number of nodes in the example tree is 7

Find the length of the largest subarray with equal number of 0s and 1s in a given array.

• Iterate through the array and maintain a count of 0s and 1s encountered so far.

• Store the count difference in a hashmap with the index as the key.

• If the same count difference is encountered again, the subarray between the two indices has equal 0s and 1s.

• Return the length of the longest subarray found.

The Word Ladder problem involves finding the shortest transformation sequence from one word to another by changing one letter at a time.

• Use breadth-first search to find the shortest transformation sequence.

• Create a graph where each word is a node and edges connect words that differ by one letter.

• Keep track of visited words to avoid revisiting them.

• Return -1 if no transformation sequence is possible.

Count the number of islands in a 2D matrix of 1s and 0s.

• Use Depth First Search (DFS) or Breadth First Search (BFS) to traverse the matrix and identify connected groups of 1s.

• Maintain a visited array to keep track of visited cells to avoid redundant traversal.

• Increment the island count whenever a new island is encountered.

• Consider all eight possible directions for connectivity between cells.

• Handle edge cases like out of bounds indices and already visited cells.

If dist(u,v)>n/2 in an undirected graph, there exists a vertex x such that removing x makes u and v go to different connected components.

• Find the shortest path between u and v

• If the path length is greater than n/2, then there must be a vertex x on the path

• Removing x will separate u and v into different connected components

Find the largest substring formed from repetition of a smaller string.

• Identify all possible substrings of the given string.

• Check if each substring can be formed by repeating a smaller string.

• Return the largest substring that can be formed from repetition of a smaller string.

Calculate the perimeter of an island represented by a binary grid.

• Iterate through the grid and count the perimeter based on land cells and their adjacent cells.

• Each land cell contributes 4 units to the perimeter, subtract 2 units for each adjacent land cell.

• Handle edge cases where land cells are at the boundaries of the grid.

• Return the total perimeter for each test case.

Find the minimum time required to rot all fresh oranges in a grid.

• Use Breadth First Search (BFS) to simulate the rotting process

• Track the time taken to rot all oranges and return it

• If any fresh oranges remain after simulation, return -1

• Handle edge cases like empty grid or no fresh oranges

For an odd-sized grid, there cannot be a Hamiltonian cycle in the graph.

• A Hamiltonian cycle is a path that visits every vertex exactly once and ends at the starting vertex.

• In an n*n grid, there are n^2 vertices and each vertex has degree 4.

• For an odd n, the total degree of all vertices is odd, which means there cannot be a Hamiltonian cycle.

Prove that F_nk is divisible by F_n where F_i is the ith Fibonacci number. with f_0 = 0

• Use mathematical induction to prove the statement

• Base case: F_n0 = 0, F_n is also 0, so 0 is divisible by 0

• Inductive step: Assume F_nk is divisible by F_n, prove F_n(k+1) is divisible by F_n

• F_n(k+1) = F_nk + F_n(k-1), use the assumption to show that F_nk is divisible by F_n

• Therefore, F_n(k+1) is also divisible by F_n

• Hence, the statement is true for all k

Prove that there exists a rectangle with all corners of the same color in a 2D plane with blue and red points.

• Divide the plane into a grid of squares.

• By the pigeonhole principle, there must be at least one row or column with four points of the same color.

• Consider the pairs of points in that row or column and check if any of them form a rectangle.

Solution to Red-Blue Hat Prisoners puzzle that saves n - log(n) prisoners.

• Red-Blue Hat Prisoners puzzle involves prisoners guessing the color of their own hat to save their lives.

• The actual solution saves n-1 prisoners, but there are alternative solutions that can save more prisoners.

• One such solution involves using binary encoding to communicate the color of the hats, which can save n - log(n) prisoners.

• This solution works by having each prisoner encode the color of their ha...read more

Expected length of segment containing (1,0) on a unit circle with three random points.

• Use law of cosines to find length of each segment.

• Calculate expected value using probability density function.

• Answer is (4/pi) + (2/3).

The question asks to construct a k-ary tree using the given k and DFS traversal string.

• Iterate through the DFS traversal string

• If the current character is 'P', create a parent node

• If the current character is 'L', create a leaf node

• Link the nodes according to the DFS traversal order

Splitwise is a system for managing shared expenses among groups of people.

• Classes: User, Expense, Group

• Functions: addExpense(), settleUp(), calculateBalance()

ACID properties ensure database transactions are processed reliably. Rollback mechanism undoes changes if transaction fails.

• ACID properties: Atomicity, Consistency, Isolation, Durability

• Atomicity ensures all operations in a transaction are completed successfully or none at all

• Consistency ensures database remains in a valid state before and after transaction

• Isolation ensures transactions are independent and do not interfere with each other

• Durability ensures changes made by com...read more

Output the person with the maximum earnings from each department

• Join the employee and department tables on department ID

• Group by department ID and find the max earnings for each department

• Join the result with the employee table to get the person with max earnings

To determine if a graph has a node with n degree, iterate through all nodes and count their edges.

• Iterate through each node in the graph

• Count the number of edges connected to each node

• If any node has n edges, then the graph has a node with n degree

To find and correct a bug in code, analyze problem statement, review code, use debugging tools, and test different scenarios.

• Understand the problem statement and expected output.

• Review the code for syntax errors, logical errors, and potential bugs.

• Use debugging tools like breakpoints, print statements, and IDE debuggers.

• Test the code with different inputs to identify the bug.

• Make necessary corrections based on the identified bug.

• Re-test the code to ensure the bug is fixed.

Multiprocessing involves multiple processes running concurrently, while multithreading involves multiple threads within a single process.

• Multiprocessing utilizes multiple processes to execute tasks simultaneously.

• Multithreading involves multiple threads within a single process sharing the same memory space.

• Multiprocessing is typically used for CPU-bound tasks, while multithreading is more suitable for I/O-bound tasks.

• Example: Running multiple instances of a web server on diff...read more

Splitwise is a system for managing shared expenses among groups of people.

• 1. Allow users to create groups and add members to track shared expenses.

• 2. Implement features for adding expenses, specifying who paid and who owes.

• 3. Calculate balances for each member and settle debts efficiently.

• 4. Provide notifications and reminders for pending payments.

• 5. Ensure security and privacy of user data.

• 6. Implement features like expense categorization, comments, and attachments.

• 7. Allow ...read more

I would prefer to develop mathematical models.

• I enjoy the process of creating and testing mathematical models.

• Developing trading infrastructure is important, but not my primary interest.

• Mathematical models can be applied to various industries, not just trading.

• Examples of mathematical models I have developed include predictive models for customer behavior and financial forecasting models.

Check if a string containing parenthesis is balanced

• Use a stack to keep track of opening parenthesis

• Iterate through the string and push opening parenthesis onto the stack

• If a closing parenthesis is encountered, check if the stack is empty or if the top of the stack is the corresponding opening parenthesis

• If the stack is empty or the top of the stack doesn't match, the string is not balanced

• After iterating through the string, if the stack is empty, the string is balanced

A graph has a unique topological sort if and only if it is a directed acyclic graph (DAG).

• A topological sort is a linear ordering of the vertices of a graph such that for every directed edge (u, v), vertex u comes before vertex v in the ordering.

• To check if a graph has a unique topological sort, we can use depth-first search (DFS) or breadth-first search (BFS) algorithms.

• If during the DFS or BFS traversal, we encounter a back edge or a cycle, then the graph does not have a un...read more

I have faced incidents related to system crashes, network failures, and security breaches.

• System crash due to hardware failure

• Network failure due to misconfiguration

• Security breach due to weak password policy

• DDoS attack causing website downtime