[Leetcode] Binary search/tree-230. Kth Smallest Element in a BST

Given a binary search tree, write a function kthSmallest to find the kth smallest element in it.

Note: 
You may assume k is always valid, 1 ? k ? BST's total elements.

Follow up:
What if the BST is modified (insert/delete operations) often and you need to find the kth smallest frequently? How would you optimize the kthSmallest routine?

Solution:

1.  #1st naive idea is to use inorder traversal, because of the characteristics of binary search tree, when the kth number is visited,
#it is the kth smallest value time complexity o(k), worst time complexity o(n)

  

  (1). use recursive way

 def bfsInorderRecursive(node, ansLst):
            if node:
                bfsInorderRecursive(node.left, ansLst)
                #print ("d: ", k, node.val)
                ansLst.append(node.val)
                bfsInorderRecursive(node.right, ansLst)
        
        ansLst = []
        bfsInorderRecursive(root, ansLst)
        return ansLst[k-1]

 （2) use iterative way: use stack to add all left node into a stack, then   iterate to pop out to check the node's right node existing or not to insert into stack

      current = root
        stk = []            #stack
        cnt = 1
        done = 0
        while (not done):
            if current is not None:       #Reach the left most Node of the current Node
                stk.append(current)
                current = current.left
            else:
                if (len(stk) > 0):
                    current = stk.pop(-1)
                    if cnt == k:
                       return current.val
                    cnt += 1
                    current = current.right
                else: done = 1
        return 0
        

reference:

http://www.geeksforgeeks.org/inorder-tree-traversal-without-recursion/

 

follow up problem:

add another count property  for current node,  left subtree's node number as current node's count

we can keep track of count in a subtree of any node while building the tree.

reference:

http://www.geeksforgeeks.org/find-k-th-smallest-element-in-bst-order-statistics-in-bst/