Given k toys and n students sitting in a circle, return the index of the first child who doesn't receive a toy. Assume students are indexed from 0 to n-1 and toys are distributed sequentially starting from student 0. If all students receive a toy and there are still toys left, distribution continues from student 0 again.

A message containing letters from A-Z can be encoded into numbers using the following mapping:

'A' -> "1"
'B' -> "2"
...
'Z' -> "26"

To decode an encoded message, all digits must be mapped back into letters using the reverse of the mapping above (and sometimes multiple digits must be used to map to a single letter).

Given a string s containing only digits, return the number of ways to decode it.

The test cases are generated so that the answer fits in a 32-bit integer.

Given two strings s and t, return the number of distinct subsequences of s which equals t.

A string's subsequence is a new string formed from the original string by deleting some (or none) of the characters without disturbing the remaining characters' relative positions. (i.e., "ACE" is a subsequence of "ABCDE" while "AEC" is not).

The test cases are generated so that the answer fits on a 32-bit integer.

Implement an in-place sorting algorithm that uses O(1) auxiliary space. Candidates were asked to suggest suitable algorithms (e.g., Quick Sort, Heap Sort) and then specifically implement Quick Sort.

Given an m x n binary matrix maximalSquare, return the largest square containing only '1's and return its area.

Given a file containing numbers, approximately 2 GB in size, and a system with only 250 MB of RAM available, describe an algorithm to sort these numbers. The solution must account for the memory constraint, meaning the entire file cannot be loaded into memory at once.

There is a ball in a maze with empty spaces and walls. The ball can go through empty spaces by rolling up, down, left or right, but it won't stop rolling until hitting a wall. When the ball stops, it could choose the next direction.

Given the maze, the start and destination of the ball, find the shortest distance for the ball to stop at the destination. If the ball cannot stop at the destination, return -1.

The maze is represented by a binary 2D array. 1 means the wall and 0 means the empty space. You may assume that the borders of the maze are all walls (see examples for details).

start and destination coordinates are represented by row and column indices.

Design a system like Splitwise, focusing on its core functionalities. This includes discussing application requirements, defining classes (e.g., User, Expense, Group, Transaction), and establishing relationships between these classes. Consider how to handle debt tracking and settlements.

Given a specific software design scenario, identify appropriate design patterns (e.g., Creational, Structural, Behavioral) that can be applied to solve the problem efficiently. Additionally, explain which Object-Oriented Programming (OOPS) principles (e.g., Encapsulation, Inheritance, Polymorphism, Abstraction, SOLID principles) are relevant and how they are utilized in the proposed solution.

Explain the primary reasons for using the Builder design pattern. Discuss its advantages, such as handling complex object construction with many optional parameters (telescoping constructors), ensuring object immutability, and performing validations before final object creation. Furthermore, elaborate on specific benefits or considerations when employing the Builder pattern in a multi-threading environment, particularly concerning thread safety and concurrency.