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# Algorithms Homework 10

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Homework 10

Describe a modification of a Binary Search Tree dictionary that can return
the minimum value in the dictionary in Θ(1) time. This change should not
increase the asymptotic complexity of any other dictionary operation.
1. What new field(s) does the data structure need?
2. How does this change impact the min, insert, and delete methods of the
BST? Note that insertion and deletion may change the minimum value in
the BST.
Reference implementations of the min, insert, and delete functions appear
below.
1 Algorithm: BSTDict.min()
2 node = root
3 while node has a left child do
4 node = node.left
5 end
6 return node
1
1 Algorithm: BSTDict.insert(new)
2 node = root
3 while node isn’t NIL do
4 if node.value ≤ new then
5 if node.left = NIL then
6 Add new as left child of node
7 node = node.left
8 end
9 node = node.left
10 else
11 if node.right = NIL then
12 Add new as right child of node
13 node = node.right
14 end
15 node = node.right
16 end
17 end
2
1 Algorithm: BSTDict.delete(node)
2 if node has two children then
3 swapnode = right
4 while swapnode has a left child do
5 swapnode = swapnode.left
6 end
7 Swap node’s parent and children links with swapnode
8 if node is the BST root then
9 Set root to be swapnode
10 end
11 end
12 if node has no children then
13 if node is the root then
14 Set root to be NIL
15 else
16 Set node.parent’s child to be NIL
17 end
18 else
/* node must have one child */
19 if node is the root then
20 Set root to be node’s child
21 else
22 Set node.parent’s child to be node’s child
23 end
24 Set node’s child’s parent to be node.parent
25 end
3

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