The “Binary Tree Paths” problem asks you to return all root-to-leaf paths in a binary tree. Each path should be represented as a string that lists the node values from the root down to a leaf, connected in order. A leaf is defined as a node with no children, and only paths that end at a leaf should be included in the result.
This problem is not about computing sums, depths, or balances. It is about enumeration and representation. You must explore every valid root-to-leaf route and capture it in a human-readable form, which makes it a traversal and path-building problem rather than a numerical one.
Why this is more than simple tree traversal
At first glance, this problem might look like a standard tree traversal task. However, instead of visiting nodes independently, you must preserve the context of how you arrived at each node. A node’s value alone is not enough; what matters is the full sequence of nodes from the root to that point.
This requirement means you cannot simply collect values as you traverse. You must actively build and manage a path as you move down the tree and finalize that path only when you reach a leaf.
Recognizing the root-to-leaf structure
The key structural insight is that every valid output corresponds exactly to one root-to-leaf path. There are no cycles, no revisits, and no branching once you reach a leaf. This makes the problem naturally suited to a top-down traversal where you carry the current path along with you.
Each recursive call or traversal step represents moving one level deeper in the tree, extending the current path by one node.
Want to explore more coding problem solutions? Check out the Single Number III and Remove Duplicate Letters.
Depth-first search as the natural approach
Depth-first search is the most natural strategy for this problem because it explores one complete path at a time. Starting from the root, you move down one branch, building the path as you go. When you reach a leaf, you record the path as a completed result. You then backtrack and explore the next branch.
This approach aligns perfectly with the problem’s definition. Each DFS branch corresponds to exactly one potential path, and each leaf marks a successful endpoint.
Building and managing the path correctly
As you traverse the tree, you maintain a representation of the current path. Conceptually, this is a list or string that grows as you move down and shrinks as you backtrack.
The critical detail is that the path must be updated incrementally. When you move to a child, you add that child’s value to the path. When you return from that child, you remove it. This ensures that the path always reflects the exact route you are currently exploring and prevents values from leaking between different paths.
Identifying leaf nodes as stopping points
A path is only complete when you reach a leaf node. Internal nodes do not produce output on their own, even if they have only one child. This distinction is important for correctness.
When a leaf is reached, the current path represents a full root-to-leaf route and can be safely converted into the required string format and added to the result set.
Why this approach guarantees correctness
The correctness of this solution comes from exhaustive exploration. DFS ensures that every root-to-leaf path is visited exactly once. Because you only record paths at leaves, every output corresponds to a valid path by definition.
No valid path is missed because DFS explores all branches, and no invalid path is added because only leaf-ending paths are recorded.
Time and space complexity considerations
The time complexity depends on the number of nodes and the number of root-to-leaf paths. Each node is visited once, but path construction and output generation depend on how many leaves exist.
Space complexity is driven by the recursion depth, which depends on the height of the tree, and by the storage of the output paths. This overhead is unavoidable because the problem explicitly asks you to return all paths.
Why this problem is common in interviews
Binary Tree Paths is a popular interview problem because it tests whether candidates can manage state during recursion. Many people understand tree traversal but struggle with carrying and backtracking a path correctly.
The problem also checks attention to detail, such as identifying leaf nodes correctly and formatting the output consistently.
What this problem teaches beyond tree paths
Beyond its immediate goal, this problem reinforces an important pattern in recursive algorithms: when output depends on the path taken, not just the current node, you must carry context through recursive calls and clean it up carefully.
If you can clearly explain why depth-first search is appropriate, how paths are built and backtracked, and why leaves define completion, you demonstrate strong fundamentals in tree traversal and recursive reasoning. That depth of understanding makes “Binary Tree Paths” an excellent exercise for mastering context-aware traversal problems.
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