In a Binary Search Tree (BST), an in-order traversal visits nodes in ascending order. To find the kth smallest element, perform an in-order traversal and count the nodes until you reach the kth one.
Time Complexity: O(n), Space Complexity: O(n) (due to recursion stack in worst case).
1function TreeNode(val, left, right) {
2 this.val = (val===undefined ? 0 : val)
3 this.left = (left===undefined ? null : left)
4 this.right = (right===undefined ? null : right)
5}
6
7var kthSmallest = function(root, k) {
8 let count = 0;
9 let result = null;
10
11 function inorder(node) {
12 if (!node) return;
13 inorder(node.left);
14 if (++count === k) {
15 result = node.val;
16 return;
17 }
18 inorder(node.right);
19 }
20
21 inorder(root);
22 return result;
23};This JavaScript solution operates recursively. A counter keeps track of the number of visited nodes during an in-order traversal. Once the kth node is visited, the counter matches k, and the result is set to the current node's value.
Morris Traversal is a way to perform in-order traversal with O(1) extra space. This method modifies the tree's structure temporarily to avoid the recursive call stack. This approach uses the concept of threading where leaf nodes point to their in-order successor to facilitate traversal.
Time Complexity: O(n), Space Complexity: O(1).
1#include <stdio.h>
2
3struct TreeNode {
4 int val;
5 struct TreeNode *left;
6 struct TreeNode *right;
7};
8
9int kthSmallest(struct TreeNode* root, int k) {
10 struct TreeNode* curr = root;
11 struct TreeNode* pre;
12 int count = 0;
13 int result;
14
15 while (curr != NULL) {
16 if (curr->left == NULL) {
17 if (++count == k) result = curr->val;
18 curr = curr->right;
19 } else {
20 pre = curr->left;
21 while (pre->right != NULL && pre->right != curr) pre = pre->right;
22
23 if (pre->right == NULL) {
24 pre->right = curr;
25 curr = curr->left;
26 } else {
27 pre->right = NULL;
28 if (++count == k) result = curr->val;
29 curr = curr->right;
30 }
31 }
32 }
33 return result;
34}This C implementation uses the Morris Traversal to avoid recursion. The traversal temporarily alters the tree's structure to keep track of each node's predecessor, thereby facilitating efficient space management.