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Program to find the largest sum of the path between two nodes in a binary tree in Python

Suppose we have a binary tree; we have to find the maximum sum of any path between any two nodes.

So, if the input is like

Program to find the largest sum of the path between two nodes in a binary tree in Python

then the output will be 62 as the nodes are [12,13,14,16,7].

To solve this, we will follow these steps −

  • Define a function utils() . This will take root

  • if root null, then

    • return 0

  • l := utils(left of root)

  • r := utils(right of root)

  • max_single := maximum of (max of l and r) + value of root) and value of root

  • max_top := maximum of max_single and l + r + value of root

  • res := maximum of res and max_top

  • return max_single

  • From the main method, do the following −

  • if root is null, then

    • return 0

  • res := infinity

  • utils(root)

  • return res

Let us see the following implementation to get better understanding −

Example

class TreeNode:
   def __init__(self, value):
      self.val = value
      self.left = None
      self.right = None
class Solution:
   def solve(self, root):
      if root is None:
         return 0
      self.res = float("-inf")
      self.utils(root)
      return self.res
   def utils(self, root):
      if root is None:
         return 0
      l = self.utils(root.left)
      r = self.utils(root.right)
      max_single = max(max(l, r) + root.val, root.val)
      max_top = max(max_single, l + r + root.val)
      self.res = max(self.res, max_top)
      return max_single
ob = Solution()
root = TreeNode(13)
root.left = TreeNode(12)
root.right = TreeNode(14)
root.right.left = TreeNode(16)
root.right.right = TreeNode(22)
root.right.left.left = TreeNode(4)
root.right.left.right = TreeNode(7)
print(ob.solve(root))

Input

root = TreeNode(13)
root.left = TreeNode(12)
root.right = TreeNode(14)
root.right.left = TreeNode(16)
root.right.right = TreeNode(22)
root.right.left.left = TreeNode(4)
root.right.left.right = TreeNode(7)

Output

62