Creates a complete (a.k.a. "perfect") binary tree from a given array.

alphabet_tree.py

# Sample array
alpha = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O']

# Note from Alan: 
# the array will always be the right length to produce
# a balanced tree where every node has two children.

# Decided on a list representation
# The end result will look like: [['A', ['B', 'I']], ['B', ['C', 'F']] . . . ]
final_tree = []

# Siblings are determined as a function of their depth and
# the index number they were assigned in the initial array.
def tree_metadata(alpha):
  index_interval = []
	i = len(alpha)
	while i > 1:
		i = (i - 1)/2
		index_interval.append(i) # final output: [7, 3, 1]
	return index_interval 

def get_children(parent, depth):
	index_interval = tree_metadata(alpha)
	i = alpha.index(parent)
	left_child = alpha[i + 1]
	right_child = alpha[i + 1 + index_interval[depth]]
	# print [parent, [left_child, right_child]] # test
	final_tree.append([parent, [left_child, right_child]])
	if depth < (len(index_interval) - 1): # excludes leaf nodes
		for item in [left_child, right_child]:
			get_children(item, depth + 1)
	return final_tree

if __name__ == "__main__":
	result = get_children(alpha[0], 0)
	for element in result:
		print element