Binary Tree Paths
To solve the problem of finding all roottoleaf paths in a binary tree, we can use a depthfirst search (DFS) approach. We can start from the root of the tree and recursively visit all nodes, keeping track of the current path. Once a leaf node is reached, we add the path to the result.
Here’s the code to achieve this:


The dfs
function recursively visits all nodes and constructs the path from the root to each leaf node. The current_path
variable keeps track of the current path as a string, and the paths
list stores all the roottoleaf paths.


Identifying Problem Isomorphism
“Binary Tree Paths” can be approximately mapped to “Path Sum II”.
Both problems deal with finding paths in a binary tree, but they have different objectives. In “Binary Tree Paths”, you’re asked to find all roottoleaf paths and return them as a list of string representations. In “Path Sum II”, you need to find all roottoleaf paths where each path’s sum equals a target sum, returning these paths as a list of integer arrays.
Despite the difference in the final output, both problems involve traversing a binary tree from the root to each leaf node and maintaining a record of the path taken. Hence, the main skills being tested are tree traversal and path recording.
“Path Sum II” is more complex as it introduces the concept of a target sum, which requires additional checking and calculation at each step.
“Binary Tree Paths” requires knowledge of binary trees, depthfirst search (DFS), and how to manipulate and generate strings. Here are 10 problems as preparation:
100. Same Tree: This problem can help you practice how to traverse a tree using DFS.
101. Symmetric Tree: You can practice DFS while comparing two different branches of a tree.
104. Maximum Depth of Binary Tree: This will give you a good understanding of DFS in a tree.
107. Binary Tree Level Order Traversal II: Practicing breadthfirst search (BFS) can help you understand the difference between DFS and BFS, which can be useful for binary tree problems.
108. Convert Sorted Array to Binary Search Tree: This problem will give you a better understanding of the structure of binary trees.
110. Balanced Binary Tree: Understanding what a balanced binary tree looks like can be useful for solving binary tree problems.
111. Minimum Depth of Binary Tree: This is another problem that helps practice tree traversal.
112. Path Sum: This problem is similar to “Binary Tree Paths” but only asks whether a path exists, rather than requiring you to return all paths.
257. Binary Tree Paths: Although not a lesser complexity problem, solving this would directly help you understand the problem at hand.
226. Invert Binary Tree: Inverting a binary tree is a good exercise for understanding tree traversal and manipulation.
These cover binary trees, perform depthfirst searches, and handle strings.
Clarification Questions
What are the clarification questions we can ask about this problem?
Identifying Problem Isomorphism


Problem Classification
This problem can be classified based on the terminology used in the problem statement as follows:
 Problem Domain: Binary Trees, Path Finding.
 Techniques Used: Tree Traversal (DepthFirst Search or BreadthFirst Search may be implied).
 Concepts Involved: Root, Leaf, Path (from root to leaf).
 Data Structures: Trees, Paths (often represented as arrays or lists of nodes).
This problem falls under the category of tree traversal where the main goal is to identify all paths from the root of a binary tree to its leaves. This involves understanding the concept of root, leaf, and path in the context of a binary tree, which is a critical part of the problem domain. Depending on the specifics of the problem, techniques used could include different types of tree traversal such as depthfirst search (DFS) or breadthfirst search (BFS). Finally, the problem uses trees as the main data structure, and paths are often represented as arrays or lists of nodes.
Language Agnostic Coding Drills
Understanding Tree Nodes: The first step is to understand the structure of a tree node. In this case, each node contains a value, and two pointers, one for the left child and one for the right child.
Basic Tree Traversal: Get comfortable with the basics of tree traversal. In this problem, a depthfirst approach is taken where we traverse down each branch as far as possible before backtracking.
Path Tracking: In the traversal process, we need to keep track of the path from the root to the current node. In the helper function,
cur
is the variable used for this purpose, which stores the path from the root to the current node.Identifying Leaf Nodes: A key aspect of this problem is identifying leaf nodes (nodes with no children). This is done with the check
if not node.left and not node.right
.Adding Paths to Result: Once a leaf node is reached, the path from the root to this leaf node (which is stored in
cur
) is added to the final result.Recursive Function: A helper function is used to perform the traversal, path tracking, leaf node identification, and result storage. This function is recursively called on the left and right children of each node, with the current path updated accordingly.
Formatting Paths: Finally, the paths, which are stored as lists of strings, are joined with ‘>’ to match the desired output format.
To create a solution, you would follow these steps:
 Create a helper function to perform the depthfirst traversal and handle the path tracking and result storage.
 Call this helper function on the root of the tree to start the process.
 Once all paths have been found, format them correctly.
 Return the result.
This problem is an application of tree traversal techniques, and the associated concepts of path tracking, leaf node identification, and result storage. It demonstrates how a seemingly complex problem can be broken down into smaller, manageable tasks.
Targeted Drills in Python
Understanding Tree Nodes: We start by understanding and implementing a binary tree node.
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class TreeNode: def __init__(self, val=0, left=None, right=None): self.val = val self.left = left self.right = right
Basic Tree Traversal: The next step is practicing tree traversal. Here’s a simple recursive depthfirst traversal which prints the value of each node.
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def print_values(node): if not node: return print(node.val) print_values(node.left) print_values(node.right)
Path Tracking: Now, let’s track the path from root to current node while traversing.
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def print_paths(node, cur=[]): if not node: return cur.append(str(node.val)) print(">".join(cur)) print_paths(node.left, cur) print_paths(node.right, cur) cur.pop()
Identifying Leaf Nodes: Let’s modify the above function to only print the paths when a leaf node is reached.
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def print_leaf_paths(node, cur=[]): if not node: return cur.append(str(node.val)) if not node.left and not node.right: print(">".join(cur)) else: print_leaf_paths(node.left, cur) print_leaf_paths(node.right, cur) cur.pop()
Adding Paths to Result: Now, instead of printing the paths, we store them in a list.
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def get_leaf_paths(node, cur=[], result=[]): if not node: return result cur.append(str(node.val)) if not node.left and not node.right: result.append(">".join(cur)) else: get_leaf_paths(node.left, cur, result) get_leaf_paths(node.right, cur, result) cur.pop() return result
Finally, these concepts can be combined and slightly adjusted to solve the problem in the question.
You’ll need to create a new list for cur
and result
each time you call the final function, as Python uses the same list across different calls to the function if it’s used as a default parameter.