1. Binary Search Trees (13.1/12.1)
Support Search, Minimum, Maximum, Predecessor, Successor, Insert, Delete
In addition to key each node has
left = left child, right = right child, p = parent
Binary search tree property:
all keys in the left subtree of x  key[x]
all keys in the right subtree of x  key[x]
Resembles quicksort

2. In-Order-Tree Walk Procedure In-Order-Tree(x) (O(n))
In-Order-Tree(left[x])
print key[x]
In-Order-Tree(right[x]) 7 5 8 3 6 9 2 4 6

3. Searching (13.2/12.2) Searching (O(h)): Procedure Tree-Search(x,k)
Given pointer to the root and key
Find pointer to a nod with key or nil
Procedure Tree-Search(x,k)
if k = key[x], then return x
if k < key[x]
then return Tree-Search(left[x])
else return Tree-Search(right[x])
Iterative Tree-Search(x,k)
while k  key[x] do
if k < key[x] then x  left[x]
else x  right[x]
return x 7 5 8 3 6 9 2 4 6

4. Min-Max, Successor-Predecessor
MIN: go to the left x  left[x]
MAX: go to the right x  right[x]
Procedure Tree-Successor(x)
if right[x]  nil then return MIN(right[x])
y = p[x]
while y  nil and x = right[y]
x  y
y  p[y]
return y 7 5 8 3 6 9 2 4 6

5. Insertion (13.3/12.3)
O(h) operation 7 5 8 3 6 9 2 4 6

6. Deletion (13.3/12.3) Tree-Delete (T, z):
z has no children, has 1 child,
has two children: then its successor has only child (which?) 7 5 6 3 2 8 9 4 7 7 7 5 8 5 8 5 8 2 6 9 3 6 9 3 6 9 1 3 6 1 6 1 4 6 4 4