You are given the root of a binary tree where each node has a unique value, and an integer start representing the initial infected node. At minute 0, the infection begins at the node with value start. Each minute, an adjacent uninfected node becomes infected. Your task is to return the total number of minutes it takes for the entire tree to become infected.
Given the root of a perfect binary tree, reverse the values of the nodes at each odd level of the tree. The level of a node is defined as the number of edges along the path from the root to the node. A perfect binary tree is one where all nodes have two children and all leaves are on the same level.
In a tree with n nodes labeled from 0 to n - 1, each node has a gate with a price to open. Alice starts at node 0 and Bob starts at node bob. Alice moves towards a leaf node, and Bob moves towards node 0. At every node, both Alice and Bob either pay the price to open the gate, or they receive a reward. If they reach a node simultaneously, they share the price/reward equally. Return the maximum net income Alice can achieve if she travels towards the optimal leaf node.
You are given the root of a binary tree with unique values. In one operation, you can choose any two nodes at the same level and swap their values. Return the minimum number of operations needed to make the values at each level sorted in strictly increasing order.
You are given the root of a binary search tree (BST) and an array of queries. For each query, find the largest value smaller than or equal to the query value and the smallest value greater than or equal to the query value in the tree.
A country network consists of n cities connected by n-1 bidirectional roads. The capital city is city 0, and each city has one representative with a car having a fixed number of seats. Calculate the minimum amount of fuel required for all representatives to reach the capital city.