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Given a Binary Search Tree (BST), you need to find the minimum absolute difference between values of any two nodes in the BST.

Clarifying Questions:

1. Input Type:
   • Can the BST contain duplicate values? (Typically, a BST should not contain duplicate values.)
   • How large can the tree be? (This helps to consider time and space complexity constraints.)
2. Output Type:
   • Should we return the minimum absolute difference as an integer?

Strategy:

To find the minimum absolute difference in a BST:

1. Inorder Traversal: Utilize the properties of BST where an inorder traversal yields nodes in sorted order. This helps in evaluating the difference between subsequent elements easily.
2. Calculate Min Difference: As we traverse, keep track of the previous node value and compute the difference with the current node value. Track the minimum of these differences.

Code:

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def getMinimumDifference(root: TreeNode) -> int:
    def inorder_traversal(node):
        nonlocal prev, min_diff
        if not node:
            return
        inorder_traversal(node.left)
        if prev is not None:
            min_diff = min(min_diff, node.val - prev)
        prev = node.val
        inorder_traversal(node.right)
    
    prev = None
    min_diff = float('inf')
    inorder_traversal(root)
    return min_diff

Strategy Explanation:

1. Inorder Traversal:
   • Traverse the left subtree.
   • Process the current node.
   • Traverse the right subtree.
   • This ensures that the nodes are processed in ascending order of their values, due to the properties of the BST.
2. Tracking Minimum Difference:
   • Maintain a prev variable to store the value of the previously visited node.
   • Compute the difference between the current node’s value and prev.
   • Update min_diff if the computed difference is smaller than the current min_diff.
3. Initialization:
   • Start with prev as None.
   • Set min_diff to a large value (float('inf')), to ensure any actual difference found will be smaller.
4. Recursive Function:
   • The inorder_traversal function is called recursively, ensuring the entire tree is traversed and compared.

Time Complexity:

• Time Complexity: O(n) where n is the number of nodes in the BST, as each node is visited once.
• Space Complexity: O(h) where h is the height of the tree, due to the recursion stack. In the worst case (unbalanced tree), this could be O(n). In the average case (balanced tree), this is O(log n).

This approach ensures an efficient and straightforward way to compute the minimum absolute difference in a BST.

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