2019-04-09 in class

notes.md

@@ -216,7 +216,7 @@ Instead of using keys directly, the index returned by the hash function is used.
 **Pigeon hole problem:** More keys (pigeons) in the universe than holes (indexes
 for table t)
 
-### Solution
+## The solution: the *chained hash table*
 
 For every cell in table T don't store True/False but a linked list of keys for
 each index in the table. This is called *Chained hash table*.
@@ -244,14 +244,16 @@ If *n*, the number of elements that we want to store in the hash table, grows,
 then *|T|* must also grow. *alpha* represents the time complexity of both
 insertion and search.
 
-## Growing a Chained hash table
+## Growing a *chained hash table*
 
-In order to grow a table, a new table must be created. The hash function (or its
+In order to grow a table, a new table must be created. The hash function (or it
+s
 range parameters) must be changed as well.
 
 ### Rehashing
 
-*Rehashing* is the process of putting all the elements of the old table in the new
+*Rehashing* is the process of putting all the elements of the old table in the
+new
 table according to the new hash function. The complexity is O(n), since
 `Chained-hash-insert` is constant.
 
@@ -265,3 +267,16 @@ then the complexity of insertion is O(n^2) due to all the *rehashing* needed.
 If the table size is doubled when *overfloiwng*, then the complexity for
 insertion becomes linear again by sacrificing some memory complexity.
 
+# Binary search trees
+
+Implementation of a dynamic set over a *totally ordered* (with an order relation
+that has ...)
+
+## Interface
+
+- `Tree-Insert(T, k)` adds a key K to tree T;
+- `Tree-Delete(T, k)` deletes the key K from tree T;
+- `Tree-Search(T, k)` returns if key K is in the tree T;
+- `Tree-Minimum(T)` finds the smallest element in the tree;
+- `Tree-Maximum(T)` finds the biggest element in the tree;
+- `Tree-successor(T, k)` `Tree-predecessor(T, k)

tree.py

@@ -0,0 +1,10 @@
+#!/usr/bin/env python3
+# vim: set ts=2 sw=2 et tw=80:
+
+class Node:
+  def __init__(self, k):
+    self.key = k
+    self.left = None
+    self.right = None
+
+