High Trees Question 162 of 224

How do you find the maximum path sum in a binary tree, where a path can start and end at any nodes?

DSA interview set · Speak this in 60–90 seconds · Faridabad & Delhi NCR

IdeaTrees

HowWhat happens inside

Why they askShows real use

DFS returns the best downward gain through one child (or zero if negative).

Why interviewers care about Trees:

This is a process

question about Trees.

Panels listen for order,

trade-offs, and what you would actually do on a DSA project - not buzzwords.

Stay structured

Name the idea, why it exists, then one short example.

Close cleanly

End with when you use it and one common pitfall.

Before you speak the answer, walk the interviewer through these steps:

1
DFS returns the best
downward gain through one child (or zero if negative).
2
At each node update
a global max with node + left_gain + right_gain.
3
Time is O(n) and
space is O(h).
4
Returning the through-path instead
of the one-side gain is the usual bug.
5
Common mistake
What juniors usually get wrong.
6
Close
When you pick this over the alternative.

Here's a short line you can speak, broken into clear beats:

Say this line

“Time is O(n) and space is O(h).”

Break into beats

TimeisOnandspace

Speaking order

2987408337471632900

Note: Adapt this scaffold to your own project — keep it under 60–90 seconds.

DFS returns the best downward gain through one child (or zero if negative). At each node update a global max with node + left_gain + right_gain.