def build_minimal_bst(array, start, end):
"""Build a minimal height binary search tree given a sorted arry.
Child trees have equal size, so the resulted bst might not be complete.
"""
if start >= end:
return None
mid = (start + end) // 2
root = Node(array[mid])
root.left = build_minimal_bst(array, start, mid)
root.right = build_minimal_bst(array, mid + 1, end)
return root
def build_minimal_bst(array, start, end):
"""Build a minimal height binary search tree given a sorted arry.
Child trees have equal size, so the resulted bst might not be complete.
"""
if start >= end:
return None
mid = (start + end) // 2
root = Node(array[mid])
root.left = build_minimal_bst(array, start, mid)
root.right = build_minimal_bst(array, mid + 1, end)
return root
def build_complete_bst(array, start, end):
"""Build a complete binary search tree given a sorted array."""
if start >= end:
return None
# find the root node index in the given array
l = end - start
height = int(math.log(l, 2))
num_of_leafs = l - (2**height - 1)
if num_of_leafs > 2**(height - 1):
left_tree_size = 2**height - 1
else:
left_tree_size = l - 2**(height - 1)
root_index = start + left_tree_size
# recursively build bst
root = Node(array[root_index])
root.left = build_complete_bst(array, start, root_index)
root.right = build_complete_bst(array, root_index + 1, end)
return root
def build_complete_bst(array, start, end):
"""Build a complete binary search tree given a sorted array."""
if start >= end:
return None
# find the root node index in the given array
l = end - start
height = int(math.log(l, 2))
num_of_leafs = l - (2 ** height - 1)
if num_of_leafs > 2 ** (height - 1):
left_tree_size = 2 ** height - 1
else:
left_tree_size = l - 2 ** (height - 1)
root_index = start + left_tree_size
# recursively build bst
root = Node(array[root_index])
root.left = build_complete_bst(array, start, root_index)
root.right = build_complete_bst(array, root_index + 1, end)
return root