LF.51.Insert In Binary Search Tree

Insert a key in a binary search tree if the binary search tree does not already contain the key. Return the root of the binary search tree.

Assumptions

There are no duplicate keys in the binary search tree

If the key is already existed in the binary search tree, you do not need to do anything

Examples

        5

      /    

    3        8

  /   

 1     4

insert 11, the tree becomes

        5

      /    

    3        8

  /           

 1     4       11

insert 6, the tree becomes

        5

      /    

    3        8

  /        /  

 1     4   6    11

DFS recursive:

public class Solution {
  public TreeNode insert(TreeNode root, int key) {
    // Write your solution here
    //this is the base case
    if (root == null ) {
        return new TreeNode(key) ;
    }
    if (root.key == key){
        return root ;
    }
    if (root.key > key) {
        //go to left
        root.left = insert(root.left, key) ;
    }
    if (root.key < key ) {
        //go to right
        root.right = insert(root.right, key) ;
    }
    //back -> upper -> upper upper to the top then return
    return root ;
  }
}

since this is called tail recursion, you are recommended to do it in interative: time: O(h) space: O(1)

Interative:

/*iterative: time o(h) space: o(1)
  note, here requires: Return the root of the binary search tree.
  so you need to maintain the reference of the root
  */
  public TreeNode insert_iter2(TreeNode root, int key) {
    // Write your solution here
    //this is the base case
    TreeNode newNode = new TreeNode(key);
    if (root == null ) {
        return newNode;
    }
    TreeNode curr = root ;
    while(curr != null){
        if (curr.key == key) {
            return root ; //do nothing
        } else if(curr.key < key){
            if (curr.right == null) {
                curr.right = newNode;
                break ;
            } else{
                curr = curr.right ;
            }
        } else {
            if (curr.left == null) {
                curr.left = newNode ;
                break ;
            } else {
                curr = curr.left ;
            }
        }
    }
    //return the root
    return root ;
  }