Binary Search Trees

From 6.006 Introduction to Algorithms

Latest revision as of 18:10, 14 February 2008

This page contains various implementations of different Binary Search Trees (BSTs).

Simple BST (no balancing)

• bst.py
  • Features: insert, find, delete_min, ASCII art
• bstsize.py
  • Imports and extends bst.py
  • Augmentation to compute subtree sizes
• bstsize_r.py
  • Recursive version from recitation for computing subtree sizes
  • Features: insert, find, rank, delete

AVL tree

• avl.py
  • Imports and extends bst.py
  • Features: insert, find, delete_min, ASCII art

Testing

Both bst.py and avl.py (as well as bstsize.py) can be tested interactively from a UNIX shell as follows:

• python bst.py 10 — do 10 random insertions, printing BST at each step
• python avl.py 10 — do 10 random insertions, printing AVL tree at each step

Alternatively, you can use them from a Python shell as follows:

>>> import bst
>>> t = bst.BST()
>>> print t
<empty tree>
>>> for i in range(4):
...   t.insert(i);
...
>>> print t
0
/\
 1
 /\
  2
  /\
   3
   /\
>>> t.delete_min()
>>> print t
1
/\
 2
 /\
  3
  /\

>>> import avl
>>> t = avl.AVL()
>>> print t
<empty tree>
>>> for i in range(4):
...   t.insert(i);
...
>>> print t
  1
 / \
0  2
/\ /\
    3
    /\
>>> t.delete_min()
>>> print t
  2
 / \
1  3
/\ /\