Cut The Tree Hackerrank Solution Python Info

To solve this efficiently, we use a mathematical shortcut. Let's define:

If we cut an edge, the tree splits into two parts. Let's say the smaller part represents a subtree rooted at node $V$. Let $SubtreeSum(V)$ be the sum of the nodes in that subtree. cut the tree hackerrank solution python

Your goal is to find the edge to remove such that the absolute difference between $Sum_1$ and $Sum_2$ is minimized. To solve this efficiently, we use a mathematical shortcut

If the tree has $N$ nodes, you have $N-1$ edges. If you traverse the tree for every edge, your time complexity becomes roughly $O(N^2)$. Given that $N$ can be up to $10^5$, $N^2$ operations ($10^10$) will result in a "Time Limit Exceeded" error. We need a linear time solution, $O(N)$. Let $SubtreeSum(V)$ be the sum of the nodes in that subtree

The other part of the tree is simply "everything else." We don't need to traverse the other part to find its sum. We can derive it mathematically: $$Sum_other_part = TotalSum - SubtreeSum(V)$$