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

PythonServer Side ProgrammingProgramming

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 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

Live Demo

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