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Find largest subtree having identical left and right subtrees in Python
Suppose we have a binary tree; we have to find the largest subtree having identical left and right subtree. Preferred time complexity is O(n).
So, if the input is like
then the output will be
To solve this, we will follow these steps −
Define a function solve() . This will take root, encode, maxSize, maxNode
if root is None, then
return 0
left_list := list with a blank string
right_list := list with a blank string
ls := solve(root.left, left_list, maxSize, maxNode)
rs := solve(root.right, right_list, maxSize, maxNode)
size := ls + rs + 1
if left_list[0] is same as right_list[0], then
if size > maxSize[0], then
maxSize[0] := size
maxNode[0] := root
encode[0] := encode[0] concatenate "|" concatenate left_list[0] concatenate "|"
encode[0] := encode[0] concatenate "|" concatenate str(root.data) concatenate "|"
encode[0] := encode[0] concatenate "|" concatenate right_list[0] concatenate "|"
return size
From the main method, do the following −
maximum := [0]
encode := list with a blank string
solve(node, encode, maximum, maxNode)
return maximum
Example
Let us see the following implementation to get better understanding −
class TreeNode:
def __init__(self, data):
self.data = data
self.left = self.right = None
def solve(root, encode, maxSize, maxNode):
if (root == None):
return 0
left_list = [""]
right_list = [""]
ls = solve(root.left, left_list, maxSize, maxNode)
rs = solve(root.right, right_list, maxSize, maxNode)
size = ls + rs + 1
if (left_list[0] == right_list[0]):
if (size > maxSize[0]):
maxSize[0] = size
maxNode[0] = root
encode[0] = encode[0] + "|" + left_list[0] + "|"
encode[0] = encode[0] + "|" + str(root.data) + "|"
encode[0] = encode[0] + "|" + right_list[0] + "|"
return size
def largestSubtree(node, maxNode):
maximum = [0]
encode = [""]
solve(node, encode, maximum,maxNode)
return maximum
root = TreeNode(55)
root.left = TreeNode(15)
root.right = TreeNode(70)
root.left.left = TreeNode(10)
root.left.right = TreeNode(25)
root.right.left = TreeNode(75)
root.right.left.left = TreeNode(65)
root.right.left.right = TreeNode(80)
root.right.right = TreeNode(75)
root.right.right.left = TreeNode(65)
root.right.right.right = TreeNode(80)
maxNode = [None]
maximum = largestSubtree(root, maxNode)
print("Root of largest sub-tree",maxNode[0].data)
print("and its size is ", maximum)Input
root = TreeNode(55) root.left = TreeNode(15) root.right = TreeNode(70) root.left.left = TreeNode(10) root.left.right = TreeNode(25) root.right.left = TreeNode(75) root.right.left.left = TreeNode(65) root.right.left.right = TreeNode(80) root.right.right = TreeNode(75) root.right.right.left = TreeNode(65) root.right.right.right = TreeNode(80)
Output
Root of largest sub-tree 70 and its size is [7]
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