Implement a function to check if a tree is balanced. For the purposes of this question, a balanced tree is defined to be a tree such that no two leaf nodes differ in distance from the root by more than one.

Given a directed graph, design an algorithm to find out whether there is a route between two nodes.

Given a sorted (increasing order) array, write an algorithm to create a binary tree with minimal height.

Given a binary search tree, design an algorithm which creates a linked list of all the nodes at each depth (i.e., if you have a tree with depth D, you¡¯ll have D linked lists).

Write an algorithm to find the ¡®next¡¯ node (i.e., in-order successor) of a given node in a binary search tree where each node has a link to its parent.

Design an algorithm and write code to find the first common ancestor of two nodes in a binary tree. Avoid storing additional nodes in a data structure. NOTE: This is not necessarily a binary search tree.

You have two very large binary trees: T1, with millions of nodes, and T2, with hundreds of nodes. Create an algorithm to decide if T2 is a subtree of T1.

You are given a binary tree in which each node contains a value. Design an algorithm to print all paths which sum up to that value. Note that it can be any path in the tree - it does not have to start at the root.