Lowest Common Ancestor of Deepest Leaves in Python\\n

Suppose we have a rooted binary tree, we have to return the lowest common ancestor of its deepest leaves. We have to keep in mind that −

• The node of a binary tree is a leaf node if and only if it has no children

• The depth of the root of the tree is 0, and when the depth of a node is d, the depth of each of its children is d+1.

• The lowest common ancestor of a set S of nodes in the node A with the largest depth such that every node in S is in the subtree with root A.

If the input is [1,2,3,4,5],

then the output will be [2,4,5]

To solve this, we will follow these steps −

• Define a method called solve(), this will take node, this will work as follows −

• if node is not present, then return a list with [0, None]

• if left and right subtrees are empty of node, then return a list with [1, None]

• d1, l := solve(left of node), d2, r := solve(right of node)

• if d1 > d2 , then return a list with values [d1 + 1, l]

• otherwise when d2 > d1, then return a list with values [d2 + 1, r]

• return a list with values [d1 + 1, node]

• In the main method, we will perform −

• list := solve(root)

• return list[1]

Example(Python)

Let us see the following implementation to get a better understanding −

 Live Demo

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):          if data is not None:             temp.left = TreeNode(data)          else:             temp.left = TreeNode(0)          break       else:          que.append(temp.left)       if (not temp.right):          if data is not None:             temp.right = TreeNode(data)          else:             temp.right = TreeNode(0)          break       else:          que.append(temp.right) def make_tree(elements):    Tree = TreeNode(elements[0])    for element in elements[1:]:       insert(Tree, element)    return Tree def print_tree(root):    #print using inorder traversal    if root is not None:       print_tree(root.left)       print(root.data, end = ', ')       print_tree(root.right) class Solution(object):    def lcaDeepestLeaves(self, root):       return self.solve(root)[1]    def solve(self,node):       if not node:          return [0,None]       if not node.left and not node.right:          return [1,node]       d1,l = self.solve(node.left)       d2,r = self.solve(node.right)       if d1>d2:          return [d1+1,l]       elif d2>d1:          return [d2+1,r]       return [d1+1,node] ob = Solution() root = make_tree([1,2,3,4,5]) print_tree(ob.lcaDeepestLeaves(root))

Input

[1,2,3,4,5]

Output

4, 2, 5,