'''
Write a recursive function which will process a binary tree.
Check its performance by generating few trees with depth less than 7
and applying the function to each of the trees.
If a function changes the structure or the contents of the tree
print each tree twice: before the function is applied and after the function is applied.
Visually check if the function processed the tree correctly.
Follow the example in the file binTreeExamples.py.
Optionally, copy and modify the functions from the main lecture file ADTtree2.py.
1.
The function removes from the tree all leaves with odd key value.
2.
The function returns sum of all keys in the leaves tree.
3.
The function returns sum of all keys in all nodes which depth is equal to a given value D.
4.
The function returns the number of all nodes which height (see definition in the lecture code)
is equal to a given value H.
5.
The function returns the biggest value of the keys of the nodes in the maximum depth in the tree.
6.
The function returns the smallest value of the keys of all **leaves** in the minimum depth in the tree.
7.
The function returns the smallest value of the keys of all **leaves** in the minimum depth in the tree.
8.
The function creates a tree which contains 2*N+1 nodes and contains only two leaves, the depth
of both leaves is N.
_________x_________
___x x___
__x x_
X x
9.
The function creates a duplicate of the given tree.
The input parameter is the root of the original tree.
10.
The function substitutes the key value of a node
by the sum of depths of all nodes in its left and right subtrees.
11.
The function adds to the tree some number of nodes. After the operation, the depths of all
leaves in the tree is equal and also the number of added nodes is minimum possible.
'''