KEYS = some random list of numbers
key = the number we're looking for in KEYS

binary_search(KEYS, key):
	middle_index = get_middle_index_index(length of KEYS)
	lower_KEYS = get_below(middle_index, KEYS)
	upper_KEYS = get_above(middle_index, KEYS)
	if key < KEYS[middle_index]
		binary_search(lower_KEYS, key)
	else if key > KEYS[middle_index]
		binary_search(upper_KEYS, key)
	else
		return middle_index
	end