You are given an integer n. Your task is to break it into a sum of at least two positive integers such that the product of these integers is maximized. Return the maximum product that can be obtained.
You are given two jugs with capacities x and y liters, and an infinite supply of water. You need to determine whether you can measure exactly target liters of water using the following operations: fill, empty, and pour water between the jugs.
You are given a set of distinct positive integers. Return the largest subset where every pair of elements in the subset satisfies either ‘one element is divisible by the other’.
Given an integer a and an array b, where b represents a very large number, compute ( a^b % 1337 ). The array b stores the digits of b from most significant to least significant. You must handle extremely large values of b efficiently.