It's a variant of the standard path sum problem.
Use a depth-first search (DFS) to traverse the tree, maintaining the current path sum. At each leaf, compare the sum with the minimum found so far and update accordingly. Return the minimum sum after the traversal.
Pro tip: Clarify edge cases upfront, such as an empty tree or negative values, and discuss how your solution handles them. Mention that you can optimize space by not storing all paths, only the current sum.
Ask if the tree can be empty, if node values can be negative, and if the path must end at a leaf (node with no children). Confirm the definition of 'minimum sum'.
Decide between recursive DFS or iterative stack-based DFS. Explain that DFS is suitable because it explores each root-to-leaf path exactly once.
Outline a recursive function that takes a node and the current sum. If the node is a leaf, update the global minimum. Otherwise, recurse on left and right children with the updated sum.
State that time complexity is O(n) since each node is visited once, and space complexity is O(h) for the recursion stack, where h is the tree height.
Discuss how to handle an empty tree (return 0 or infinity depending on definition) and trees with negative values (the algorithm still works).
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