You are given a network of computers, each labeled from 0 to n-1, and a list of direct connections between these computers. The network is initially connected in some way, but some computers are not directly connected. You can remove cables from existing direct connections and reconnect them between disconnected computers to minimize the number of operations required to make the entire network fully connected. The task is to determine the minimum number of operations needed. If it’s not possible to connect all the computers, return -1.
You are given n nodes in a binary tree, numbered from 0 to n-1. Each node i has two children: leftChild[i] and rightChild[i]. If a node has no left child, its value will be -1. Similarly, if a node has no right child, its value will also be -1. Your task is to return true if and only if these nodes form exactly one valid binary tree.
A company has n employees with a unique ID for each employee from 0 to n-1. The head of the company is the one with headID. Each employee has one direct manager. The head will inform his direct subordinates, and they will inform their subordinates, and so on until all employees know about the urgent news. Each employee needs informTime[i] minutes to inform their direct subordinates. Return the total time required to inform all employees.
You are given two binary trees: an original tree and a cloned tree. The cloned tree is a copy of the original tree, and you are given a reference to a node in the original tree. Your task is to return the reference to the corresponding node in the cloned tree.
You are given an m x n grid where each cell represents a street. The streets have different connections between neighboring cells. Starting from the top-left corner of the grid, you need to find if there exists a valid path to the bottom-right corner, following the direction of the streets.
You are given an undirected tree with n vertices numbered from 0 to n-1. Some vertices in this tree contain apples. Each edge in the tree requires 1 second to traverse. Starting at vertex 0, determine the minimum time required to collect all apples and return to vertex 0. The tree structure is described by the array edges, where edges[i] = [ai, bi] indicates an edge between vertices ai and bi. Additionally, the array hasApple specifies whether a vertex contains an apple (true) or not (false).