710066. Largest subtree sum in a tree
Largest Subtree Sum in a Tree
Summary
Given a tree, find the largest subtree sum. A subtree is a subset of nodes in the original tree. The problem involves traversing and manipulating the tree to find the maximum subtree sum.
Detailed Explanation
The approach to solve this problem involves a recursive function that calculates the maximum subtree sum for each node in the tree. We start by considering the current node as the root of a subtree, then recursively calculate the maximum subtree sums for its left and right children. The maximum subtree sum is the maximum of these three cases: 1) the current node itself, 2) the maximum subtree sum of its left child, and 3) the maximum subtree sum of its right child.
Here's a step-by-step breakdown of the solution:
- For each node in the tree:
- Initialize the maximum subtree sum to be the value of the current node.
- Recursively calculate the maximum subtree sums for its left and right children.
- Update the maximum subtree sum if any of these recursive calls return a larger value.
- Return the maximum subtree sum calculated for the root node.
Time complexity: O(n), where n is the number of nodes in the tree. This is because we visit each node once.
Space complexity: O(h), where h is the height of the tree. This is because the recursive function call stack can go up to a depth of h.
Here's an ASCII art diagram of a sample tree:
1
/ \
2 3
/ \ \
4 5 6
Optimized Solutions
Java
public int largestSubtreeSum(TreeNode root) {
if (root == null) return 0;
int sum = root.val;
for (TreeNode child : root.children) {
int childSum = largestSubtreeSum(child);
sum = Math.max(sum, childSum + root.val);
}
return sum;
}