You are given an array of integers representing the weights of stones. In each turn, you can select two stones, x and y, with x <= y, and smash them together. The result of the smash is as follows: if x equals y, both stones are destroyed, otherwise, the stone with weight x is destroyed, and the stone with weight y becomes y - x. The process continues until there is at most one stone left. Your task is to return the smallest possible weight of the remaining stone, or return 0 if no stones are left.
You are given an array of books where each book is represented by a pair of integers [thickness, height]. Additionally, you have a shelf with a fixed width. Your goal is to arrange the books on the shelves such that each shelf’s total thickness is less than or equal to the shelf width, and the height of each shelf is determined by the tallest book placed on it. The books must be placed in the same order as they appear in the input array. The objective is to minimize the total height of the bookshelf.
You are given an array arr of positive integers. Consider all binary trees such that each node has either 0 or 2 children, the values of arr correspond to the values of each leaf in an in-order traversal of the tree, and the value of each non-leaf node is equal to the product of the largest leaf values in its left and right subtrees. Return the smallest possible sum of the values of the non-leaf nodes among all possible binary trees.
The Tribonacci sequence is defined by the following recurrence relation: T0 = 0, T1 = 1, T2 = 1, and Tn+3 = Tn + Tn+1 + Tn+2 for n >= 0. Given an integer n, return the value of Tn.
Given a 2D grid of 0s and 1s, return the number of elements in the largest square subgrid that has 1s on its border and 0s inside. If no such subgrid exists, return 0.
Alice and Bob are playing a game with piles of stones. Each pile contains a positive integer number of stones. On each player’s turn, they can take stones from the first X remaining piles, where 1 <= X <= 2M. The goal is to maximize the number of stones Alice can collect assuming both play optimally.