Same Tree
To determine if two binary trees are the same, you need to compare both the structure and the values of the corresponding nodes. Here’s a simple approach using recursion to check if two trees are the same:
 If both the current nodes are
None
, returnTrue
.  If one of the nodes is
None
while the other is not, returnFalse
.  If the values of the current nodes are not equal, return
False
.  Recursively compare the left subtree of
p
with the left subtree ofq
.  Recursively compare the right subtree of
p
with the right subtree ofq
.  If all these conditions pass, return
True
.
Here’s the code:


The time complexity of this function is (O(n)), where (n) is the number of nodes in the tree, and the space complexity is (O(h)), where (h) is the height of the tree.
Identifying Problem Isomorphism
“Same Tree” can be mapped to “Subtree of Another Tree”.
In “Same Tree” problem, you have to determine if two given binary trees are exactly identical in structure and node values.
In “Subtree of Another Tree”, the problem is to identify whether one tree is a complete subtree of another. In essence, this problem involves a similar but slightly more complicated version of the “Same Tree” problem because it checks if a smaller tree is the same as any subtree in the larger tree.
Both problems require you to compare the structure and values of binary trees. “Same Tree” is simpler as you are only comparing two trees. “Subtree of Another Tree” adds complexity by asking if a smaller tree matches any subtree of the larger tree, not just the tree as a whole.


Problem Classification
Binary Trees: The problem involves comparing two binary trees. Understanding how binary trees work, including concepts such as nodes, left and right children, is crucial to this problem.
Tree Traversal: More specifically, this problem involves tree traversal as we need to compare each corresponding node in the two trees. It is a form of DepthFirst Search (DFS) where you traverse the tree from the root, to the left subtree, and finally the right subtree.
Recursion: The problem uses recursion to traverse and compare nodes in the binary trees. Recursion involves a function calling itself in its definition, which is a common approach to solve problems in tree data structures.
Boolean Logic: The problem deals with boolean logic as we are checking whether two trees are the same, i.e., all corresponding nodes in the two trees are equal. This involves using logical AND and logical OR operations.
These classifications help to understand the underlying concepts and techniques typically used to solve such problems.
Language Agnostic Coding Drills
Binary Trees: Understanding the concept of binary trees is crucial to this problem. This includes the concept of tree nodes, left and right children, and tree traversal methods.
Recursion: This problem involves using recursion to solve the problem. Understanding the base and recursive cases in a recursive function is key.
Conditional Statements: The ifelse logic in this problem is simple yet crucial. It checks whether a node exists before accessing its properties.
Targeted Drills in Python
 Binary Trees:


 Recursion:


 Conditional Statements:


ProblemSpecific Drill:
Now let’s combine all of these concepts into a drill specific to the problem at hand:


This drill exercises all the necessary concepts and builds up to the final solution. Each concept is demonstrated in isolation and then integrated into the final solution.
Coding Skill Exercise #26
Same Tree
Write a method to check if a given tree is the same tree.
Knowledge Gap Finder
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