symmetric tree leetcode 101 python

certainly! the "symmetric tree" problem is a common problem on leetcode (problem 101) that tests your understanding of binary trees. in this problem, you're asked to determine if a given binary tree is symmetric around its center.

problem statement
a binary tree is symmetric if the left subtree is a mirror reflection of the right subtree. more formally, a tree is symmetric if:

1. the left subtree is a mirror reflection of the right subtree.
2. the left and right children of the nodes are equal.

example
consider the following binary tree:

this tree is symmetric, so the output should be `true`.

conversely, the following tree is not symmetric:

this tree is not symmetric, so the output should be `false`.

approach
to determine if a binary tree is symmetric, we can use a recursive approach. the idea is to compare the left and right subtrees of the tree.

1. if both subtrees are `none`, they are symmetric.
2. if one subtree is `none` and the other is not, they are not symmetric.
3. if the values of the current nodes in both subtrees are equal, we need to recursively check:
- the left child of the left subtree with the right child of the right subtree.
- the right child of the left subtree with the left child of the right subtree.

implementation
below is the python implementation of the above approach.

explanation of the code
1. **treenode class**: this is a basic class definition for a tree node, which includes the value and pointers to the left and right children.
2. **issymmetric function**: this is the main function that checks if the tree is symmetric. it calls the helper function `ismirror`.
3. **ismirror helper function**: this function checks if two trees are mirrors of each other by comparing their values and recursively checking their children.
4. **example usage**: the code demonstrates how to create a symmetric and a non-symmetric tree and checks their symmetry using the `issymmetric` function.

time complexity
the time complexity of ...

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