1. (100 pts) Write a program to nd the kth smallest element in a binary search tree. Since we don't know how many elements are in each subtree, we can add a new eld count to each node that stores the total number of elements that are in the left subtree and the current node. You need the update count eld of the nodes when you insert and delete from the tree. To nd the kth smallest node, you need to use the count eld of the current node and decide whether kth smallest node is in the left subtree or the right subtree and follow that subtree. Node structure with count eld is as follows
struct node {
int key;
int count;
struct node *left, *right;
};
typedef struct node node;
Consider the binary search tree given below. Count eld for a node is shown on top left of the node.
4
10
2
2
6
14
1
1
1
1
4
8
12
16
Figure 1: Binary Search Tree
Sample execution for above tree is given below
fox01assign4
Enter the set of numbers for the tree
10 6 14 4 8 12 16
Enter k
5
Result = 12
