Sum of Left Leaves
The Sum of Left Leaves problem asks you to compute the sum of all left leaf nodes in a binary tree. A left leaf is a node that is both a leaf, meaning it has no children, and also the left child of its parent. The output is the total of the values stored in these specific nodes.
This problem looks simple, but it tests whether you can correctly interpret tree relationships. You are not summing all leaves, and you are not summing all left children. You are summing only the nodes that satisfy both conditions at once.
Why the definition matters more than the traversal
Many mistakes on this problem come from mixing up definitions. A node can be on the left side of the tree without being a left leaf, and a node can be a left child without being a leaf. The only nodes that count are those that are left children and also have no children themselves.
Because of this, the core work is not choosing a traversal method. The core work is identifying left leaves accurately while traversing.
Recognizing the pattern: parent-child context is required
You cannot determine whether a node is a left leaf by looking at the node alone. You must know whether it is a left child of its parent, and you must know whether it has children.
This means your traversal must preserve some context. Either you check each parent and inspect its left child, or you carry a flag indicating whether the current node was reached via a left edge.
A clean approach: check the left child at each node
One practical way to solve this is to traverse the tree and, at each node, look at its left child. If the left child exists and it is a leaf, then you add its value to the total. Then you continue traversing both the left and right subtrees.
This approach is appealing because it avoids passing extra flags around. The “left leaf” condition can be checked directly from the parent’s perspective, which aligns with the definition that a left leaf is the left child of some parent.
Depth-first traversal fits naturally
Depth-first traversal works well here because it explores the tree systematically and keeps the logic simple. You visit a node, check whether its left child is a leaf, and then recursively process its children.
This style matches how you would reason about the tree manually. You look at each node, decide whether it contributes to the sum through its left child, and then move deeper.
An equivalent approach: pass an “is left child” flag
Another equally valid strategy is to traverse the tree while carrying a Boolean flag that indicates whether the current node is a left child. When you reach a leaf, you add its value only if the flag is true.
This approach is conceptually clean because it evaluates the left-leaf condition exactly at the leaf. It also makes it obvious why parent context matters, since the decision to add depends on how you arrived at the node.
Why the approach is correct
Correctness comes from exhaustive traversal and precise filtering. Every node is visited, so no potential left leaf is missed. The algorithm adds a node’s value only when it is confirmed to be both a left child and a leaf.
Because the condition is evaluated consistently and only once per leaf, there is no double-counting, and there is no risk of including nodes that do not qualify.
Time and space complexity considerations
The runtime is linear in the number of nodes because each node is processed at most once. Space complexity depends on the height of the tree due to recursion depth or an explicit stack if you implement traversal iteratively.
This is optimal, since you must inspect the tree structure to identify which nodes qualify as left leaves.
Why this problem is common in interviews
The Sum of Left Leaves problem is popular in interviews because it is deceptively easy to misunderstand. It tests careful reading of definitions, tree traversal fundamentals, and the ability to incorporate parent-child relationships into traversal logic.
Interviewers also like it because it reveals how candidates handle edge cases, such as empty trees or trees where left children exist but are not leaves.
What this problem teaches beyond leaf sums
Beyond this specific sum, the problem teaches a general lesson: many tree problems require context that is not stored in the node itself. Whether a node “counts” often depends on its relationship to its parent or how it was reached.
If you can clearly explain what qualifies as a left leaf, why parent context matters, and how traversal checks the condition reliably, you demonstrate strong fundamentals in tree reasoning. That depth of understanding makes Sum of Left Leaves an excellent exercise in precise tree traversal and relationship-based filtering.
If you want more coding problems explained, check out:
Top comments (0)