Construct a Binary Tree from Postorder and Inorder in Python

Suppose we have the inorder and postorder traversal sequence of a binary tree. We have to generate the tree from these sequences. So if the postorder and inorder sequences are [9,15,7,20,3] and [9,3,15,20,7], then the tree will be −

Let us see the steps −

• Define a method build_tree(), this will take inorder, postorder −

• If inorder list is not empty −

  • root := make a tree node with the last value of postorder, then delete that element

  • ind := index of root data in inorder list

  • right of root := build_tree(inorder from index ind to end, postorder)

  • left of root := build_tree(inorder from 0 to index ind - 1, postorder)

• return root

Example

Let us see the following implementation to get better understanding −

class TreeNode:
   def __init__(self, data, left = None, right = None):
      self.data = data
      self.left = left
      self.right = right
def print_tree(root):
   if root is not None:
      print_tree(root.left)
      print(root.data, end = ', ')
      print_tree(root.right)
class Solution(object):
   def buildTree(self, inorder, postorder):
      if inorder:
         root = TreeNode(postorder.pop())
         ind = inorder.index(root.data)
         root.right = self.buildTree(inorder[ind+1:],postorder)
         root.left = self.buildTree(inorder[:ind],postorder)
         return root
ob1 = Solution()
print_tree(ob1.buildTree([9,3,15,20,7], [9,15,7,20,3]))

Input

[9,3,15,20,7]
[9,15,7,20,3]

Output

[9,3,15,20,7]