Replace instance variable state tracking with nonlocal pattern in kthSmallest

[Copilot]

The kthSmallest method uses self.k to track traversal state, which breaks when the same Solution instance is called multiple times as self.k retains its mutated state between calls.

Changes

• Replace self.k instance variable with local count variable using nonlocal pattern
• Move docstring to proper position (first statement in method body)
• Add test case verifying solution reusability

Before:

def kthSmallest(self, root, k):
    self.k = k
    def traverse(root):
        self.k -= 1
        if self.k == 0:
            return root.val

After:

def kthSmallest(self, root, k):
    """..."""
    count = k
    def traverse(root):
        nonlocal count
        count -= 1
        if count == 0:
            return root.val

The method is now stateless and safe for reuse across multiple calls.

Original prompt

Context

In PR #88, a review comment identified an issue with the kthSmallest method in src/tree/kth_smallest_element_in_a_bst.py:

Using an instance variable self.k for state tracking can cause issues if the same Solution instance is reused for multiple calls to kthSmallest. After the first call, self.k will be 0 (or some other value), leading to incorrect results on subsequent calls. Consider using a local variable instead by passing k as a parameter to the traverse function or using a nonlocal variable pattern. This would make the function stateless and safer for reuse.

Current Code

The current implementation at src/tree/kth_smallest_element_in_a_bst.py uses self.k as an instance variable to track state during traversal:

class Solution:
    def kthSmallest(self, root, k):
        self.k = k
        """
        Find the kth smallest element in a BST.
        ...
        """
        def traverse(root):
            if root is None:
                return

            left_result = traverse(root.left)            
            # Check "is not None" so that 0 is accepted as a valid answer            
            if left_result is not None:
                return left_result

            self.k -= 1
            if self.k == 0:            
                return root.val

            return traverse(root.right)            

        return traverse(root)

Required Changes

1. Replace self.k with a local variable using Python's nonlocal keyword pattern. This eliminates the dependency on instance state and makes the function safe for reuse across multiple calls on the same Solution instance.

2. Also fix the docstring placement — self.k = k is currently placed before the docstring (line 31), which prevents the docstring from being recognized as the method's docstring. After removing self.k = k, ensure the docstring is the first statement in the method body.

3. Remove trailing whitespace on lines 49, 50, 55, and 58 (as noted in another review comment on the same PR).

The refactored code should use a pattern like:

def kthSmallest(self, root, k):
    """
    Find the kth smallest element in a BST.
    ...
    """
    count = [k]  # or use nonlocal pattern

    def traverse(root):
        if root is None:
            return

        left_result = traverse(root.left)
        # Check "is not None" so that 0 is accepted as a valid answer
        if left_result is not None:
            return left_result

        count[0] -= 1
        if count[0] == 0:
            return root.val

        return traverse(root.right)

    return traverse(root)

Either a mutable container (list) or the nonlocal keyword approach is acceptable.

This pull request was created from Copilot chat.

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