Kth Smallest Element in a BST in Python

Suppose we have a binary search tree. We have to find the Kth smallest element in that BST. So if the tree is like −

So if we want to find 3rd smallest element, then k = 3, and result will be 7.

To solve this, we will follow these steps −

• create one empty list called nodes
• call solve(root, nodes)
• return k – 1th element of nodes
• the solve method is created, this takes root and nodes array, this will work as follows −
• if root is null, then return
• solve(left of root, nodes)
• add value of root into the nodes array
• solve(right of root, nodes)

Let us see the following implementation to get better understanding −

Example

class TreeNode:
   def __init__(self, data, left = None, right = None):
      self.data = data
      self.left = left
      self.right = right
def insert(temp,data):
   que = []
   que.append(temp)
   while (len(que)):
      temp = que[0]
      que.pop(0)
      if (not temp.left):
         temp.left = TreeNode(data)
         break
      else:
         que.append(temp.left)
      if (not temp.right):
         temp.right = TreeNode(data)
         break
      else:
         que.append(temp.right)
def make_tree(elements):
   Tree = TreeNode(elements[0])
   for element in elements[1:]:
      insert(Tree, element)
   return Tree
class Solution(object):
   def kthSmallest(self, root, k):
      nodes = []
      self.solve(root,nodes)
      return nodes[k-1]
   def solve(self, root,nodes):
      if root == None:
         return
      self.solve(root.left,nodes)
      nodes.append(root.data)
      self.solve(root.right,nodes)
ob1 = Solution()
tree = make_tree([10,5,15,2,7,13])
print(ob1.kthSmallest(tree, 3))

Input

[10,5,15,2,7,13]
3

Output

7