Symmetric Tree
To check if a binary tree is symmetric, we need to ensure that the left subtree of the root is a mirror reflection of the right subtree of the root. We can do this by recursively comparing corresponding nodes in these two subtrees. Here’s a stepbystep guide:
 If both the current nodes from the left and right subtrees are
None
, returnTrue
.  If one of the nodes is
None
while the other is not, or if the values of the nodes are not equal, returnFalse
.  Recursively compare the left child of the left subtree with the right child of the right subtree.
 Recursively compare the right child of the left subtree with the left child of the right subtree.
 If all these conditions pass, return
True
.
Here’s the code:


This function’s time complexity 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
“Symmetric Tree” can be mapped to “Same Tree”.
Here’s why:
Both problems involve traversing trees and comparing nodes, but they do it in slightly different ways. In “Symmetric Tree”, we’re looking to see if the tree is a mirror image of itself. This means that we’re effectively comparing the left and right subtrees for each node to see if they are mirror images of each other.
In “Same Tree”, we’re comparing two different trees to see if they’re identical. This involves comparing the corresponding nodes in both trees to see if they are equal.
Both of these problems involve a depthfirst traversal of the trees and a comparison of the nodes. The key difference is that in “Symmetric Tree”, we’re comparing nodes within the same tree, while in “Same Tree”, we’re comparing nodes in two different trees.
They both involve a simple depthfirst traversal of the trees and comparison of nodes. “Symmetric Tree” is more complex due to the fact that it involves comparing mirrored nodes within the same tree.
Despite these differences, the fundamental structure and techniques used to solve these problems are very similar, hence the isomorphic mapping between them.


Problem Classification
Binary Trees: The problem involves working with binary trees. Understanding the structure of binary trees including concepts of root, left child, and right child nodes is crucial.
Tree Traversal: This problem requires traversing a binary tree. This involves visiting each node in a tree in a specific order. Here, we’re checking for symmetry, which requires a kind of mirrored traversal of two subtrees.
Symmetry Checking: The problem requires checking whether the binary tree is symmetric around its center. This involves understanding the property of symmetry in the context of binary trees.
Recursion: The problem uses a recursive approach to solve the problem. A function within the solution refers to itself to solve smaller instances of the same problem.
Boolean Logic: This problem fundamentally requires determining a true or false value – whether or not a given binary tree is symmetric. This involves using logical operations like AND and OR to combine conditions.
This classification helps to understand the core concepts and techniques that underpin the problem, and can guide appropriate approaches to problemsolving and algorithm design.
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.
Tree Symmetry: This problem is specifically about determining whether a binary tree is symmetric. A binary tree is symmetric if the left subtree is a mirror reflection of the right subtree.
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:


 Tree Symmetry:
For this concept, you should understand the symmetry property of a binary tree and how to check for it. However, writing code for this without using recursion would not be straightforward, so let’s move on to recursion.
 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.