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Decode the Coding Interview in Scala: Real-World Examples

Binary Tree Maximum Path Sum

Explore how to compute the maximum path sum in a binary tree by understanding recursive contributions from nodes and subtrees. Learn to handle cases where the path may exclude the root, optimize with global tracking, and analyze time and space complexities of the solution.

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Description

A path in a binary tree is defined as:

A sequence of nodes such that each pair of adjacent nodes must have an edge connecting them. A node can only be included in a path at most once. Moreover, including the root in the path is not compulsory.

The path sum can be calculated by adding up all nodes’ values in the path. To solve this problem, we will calculate the maximum path sum given the root of a binary tree so that there won’t be any greater path than it in the tree.

Example

Let’s discuss the example below:

Coding exercise

Scala
class TreeNode(var value:Int=0, var left:TreeNode=null, var right:TreeNode=null) {
}
object Solution {
  def maxPathSum(root: TreeNode): Int = {
    // write your code here
    -1
  }
}
Binary Tree Maximum Path Sum

Solution

We’ll start by simplifying the problem and looking at the implementation of the maxContrib(node) function which takes a node as an argument and computes a maximum contribution that this node and ...