Most Frequent Subtree Sum

Problem Description

Given the root of a binary tree, return the most frequent subtree sum. If there is a tie, return all the values with the highest frequency in any order. The subtree sum of a node is defined as the sum of all the node values formed by the subtree rooted at that node (including the node itself).

Key Insights

• A subtree sum is calculated by summing the values of all nodes in a subtree.
• We can use Depth-First Search (DFS) to traverse the tree and calculate subtree sums.
• A hash table (or dictionary) can be used to count the frequency of each subtree sum.
• The result can have multiple values if there is a tie in frequency.

Space and Time Complexity

Time Complexity: O(N) - where N is the number of nodes in the tree, as we visit each node once. Space Complexity: O(N) - for storing the counts of the subtree sums in a hash table.

Solution

To solve this problem, we can use a Depth-First Search (DFS) approach to compute the subtree sums for each node in the binary tree. While computing the sums, we will maintain a hash table (or dictionary) to keep track of the frequency of each sum encountered. After traversing the entire tree, we can determine which sums occurred most frequently and return them.

1. Define a recursive function that computes the subtree sum for a given node.
2. Use a hash table to store the frequency of each subtree sum.
3. Traverse the tree using DFS, updating the hash table with each computed subtree sum.
4. After completing the traversal, identify the maximum frequency from the hash table and gather all sums that match this frequency.

Code Solutions