You are given an integer array ’nums’ and an integer ‘k’. You can partition the array into at most ‘k’ non-empty adjacent subarrays. The score of a partition is defined as the sum of the averages of each subarray. Your goal is to return the maximum score that can be achieved by partitioning the array in any possible way, with each partition’s score calculated as the sum of averages of its subarrays.
Given an array of unique integers, where each integer is greater than 1, we can create a binary tree using these integers. The value of each non-leaf node must be the product of the values of its children. The goal is to return the number of distinct binary trees that can be constructed. Since the result may be large, return the answer modulo 10^9 + 7.
Alice is playing a game where she starts with 0 points and randomly draws a number from the range [1, maxPts] each time. Alice continues drawing until her points reach or exceed a target value k. After each draw, she may stop if her total points reach or exceed k. The goal is to determine the probability that Alice has at most n points before reaching k points.
In a line of n dominoes, each domino is initially standing upright. Some dominoes are pushed either to the left or the right. Over time, falling dominoes will cause adjacent dominoes to fall in the same direction. If a domino is pushed from both sides, it remains standing. The task is to simulate the final state of the dominoes after all the forces are applied.
Given an integer array arr, you need to find the length of the longest subarray that forms a mountain. A mountain subarray has the following properties: it must have at least three elements, the elements strictly increase to a peak, and then strictly decrease after the peak. If no such subarray exists, return 0.
A sequence is called Fibonacci-like if for all indices i, the following condition holds: xi + xi+1 == xi+2. You are given a strictly increasing sequence of positive integers, and your task is to find the length of the longest subsequence that is Fibonacci-like. If no such subsequence exists, return 0.
