Binary Tree Maximum Path Sum in Python

Suppose we have one non-empty binary tree. We have to find the path sum. So here, a path is any sequence of nodes from some starting node to any node in the where the parent-child connections are present. The path must contain at least one node and does not need to go through the root node. So if the input tree is −

Here the output will be 32.

To solve this, we will follow these steps −

• Define one method called solve(), this will take node

• if node is null or the value of node is 0, then return 0

• left := max of 0 and solve(left of node)

• right := max of 0 and solve(right of node)

• ans := max of ans and left + right + data of the node

• return node data + max of left and right

• From the main method, set ans := -inf, then call solve(root) and return ans

Example

Let us see the following implementation to get 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 class Solution(object):    def maxPathSum(self, root):       self.ans = -float('inf')       self.solve(root)       return self.ans    def solve(self,node):       if not node or node.data == 0:          return 0       left = max(0,self.solve(node.left))       right = max(0,self.solve(node.right))       self.ans = max(self.ans,left+right+node.data)       return node.data + max(left,right) ob = Solution() root = make_tree([-10,9,10,None,None,15,7]) print(ob.maxPathSum(root))

Input

[-10,9,10,None,None,15,7]

Output

32