Find Difference Between Node and Descendant in Python

Suppose we have a binary tree, we have to find the largest absolute difference between any node and its descendants.

So, if the input is like

then the output will be 7 as largest absolute difference is between nodes 8 and 1.

To solve this, we will follow these steps −

• Define a function dfs() . This will take node
• if node is not null, then
  • return a list with positive and negative infinity
• left := dfs(left of node)
• right := dfs(right of node)
• res := a pair with (minimum of left[0], right[0] and value of node, and maximum of left[1], right[1] and value of node)
• ans := maximum of ans, (value of node - res[0]) and (res[1] - value of node)
• return res
• From the main method, do the following −
• ans := 0
• dfs(root)
• return ans

Let us see the following implementation to get better understanding −

Example

 Live Demo

class TreeNode:
   def __init__(self, data, left = None, right = None):
      self.val = data
      self.left = left
      self.right = right
class Solution:
   def solve(self, root):
      def dfs(node):
         if not node:
            return [float("inf"), float("-inf")]
         left = dfs(node.left)
         right = dfs(node.right)
         res = [min(left[0], right[0], node.val), max(left[1], right[1], node.val)]
         self.ans = max(self.ans, node.val - res[0], res[1] - node.val)
         return res
      self.ans = 0
      dfs(root)
      return self.ans
ob = Solution()
root = TreeNode(1)
root.left = TreeNode(5)
root.right = TreeNode(3)
root.right.left = TreeNode(2)
root.right.right = TreeNode(8)
root.right.left.left = TreeNode(7)
root.right.left.right = TreeNode(4)
print(ob.solve(root))

Input

root = TreeNode(1)
root.left = TreeNode(5)
root.right = TreeNode(3)
root.right.left = TreeNode(2)
root.right.right = TreeNode(8)
root.right.left.left = TreeNode(7)
root.right.left.right = TreeNode(4)

Output

7