Solving Kth Smallest Element in a BST: Navigating Tree Order

The "Kth Smallest Element in a BST" problem requires finding the kth smallest element in a Binary Search Tree (BST). This problem can be effectively tackled by understanding and utilizing the properties of BSTs, particularly inorder traversal.

Problem Statement

Given the root of a binary search tree and an integer k, return the kth smallest value (1-indexed) of all the values of the nodes in the tree.

Example

Consider a binary search tree: Example 1:

Input: root = [3,1,4,null,2], k = 1 Output: 1

Example 2:

Input: root = [5,3,6,2,4,null,null,1], k = 3 Output: 3

Solution Approach - Inorder Traversal

class TreeNode {
  val: number;
  left: TreeNode | null;
  right: TreeNode | null;

  constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
    this.val = val === undefined ? 0 : val;
    this.left = left === undefined ? null : left;
    this.right = right === undefined ? null : right;
  }
}

function kthSmallest(root: TreeNode | null, k: number): number {
  const stack: TreeNode[] = [];
  let current = root;
  let count = 0;

  while (current || stack.length > 0) {
    while (current) {
      stack.push(current);
      current = current.left;
    }

    let poppedValue = stack.pop();

    if (poppedValue !== undefined) {
      current = poppedValue;
      count++;
      if (count === k) return current.val;

      current = current.right;
    } else {
      current = null; // or however you want to handle the undefined case
    }
  }

  return -1;
}

Breaking Down the Solution

• Map for Inorder Indices: Create a map to quickly find the index of each value in the inorder sequence.
• Recursive Construction: Recursively build the left and right subtrees using the indices in the map to find the dividing point.
• Preorder Traversal: The preorder array guides the creation of each node, starting from the root.

Conclusion

Constructing a binary tree from preorder and inorder traversals is an intriguing challenge that tests understanding of tree properties and traversal techniques.