Redirected from Binary tree sort
If we write our binary tree nodes as triples (left subtree, node, right subtree), and the null pointer as None, we can build and search them as follows (in Python):
def binary_tree_insert(treenode, value): if treenode is None: return (None, value, None) left, nodevalue, right = treenode if nodevalue > value: return (binary_tree_insert(left, value), nodevalue, right) else: return (left, nodevalue, binary_tree_insert(right, value)) def build_binary_tree(values): tree = None for v in values: tree = binary_tree_insert(tree, v) return tree def search_binary_tree(treenode, value): if treenode is None: return None # failure left, nodevalue, right = treenode if nodevalue > value: return search_binary_tree(left, value) elif value > nodevalue: return search_binary_tree(right, value) else: return nodevalue
Note that the worst case of this build_binary_tree routine is O(n2) --- if you feed it a sorted list of values, it chains them into a linked list with no left subtrees. For example, build_binary_tree([1, 2, 3, 4, 5]) yields the tree (None, 1, (None, 2, (None, 3, (None, 4, (None, 5, None))))). There are a variety of schemes for overcoming this flaw with simple binary trees.
Once we have a binary tree in this form, a simple inorder traversal can give us the node values in sorted order:
def traverse_binary_tree(treenode): if treenode is None: return [] else: left, value, right = treenode return (traverse_binary_tree(left) + [value] + traverse_binary_tree(right))
So the binary tree sort algorithm is just the following:
def treesort(array): array[:] = traverse_binary_tree(build_binary_tree(array))
There are many types of binary search trees. AVL trees and Red-Black trees are both forms of balanced binary search trees. A B-tree grows from the bottom up as elements are inserted. A splay tree is a self-adjusting binary search tree. In a treap ("tree heap"), each node also holds a priority and the parent node has higher priority than its children.
Search Encyclopedia
|
Featured Article
|