Shortest distance between two nodes in BST
Given a Binary Search Tree and two keys in it. Find the distance between two nodes with given two keys. It may be assumed that both keys exist in BST.
Input: Root of above tree a = 3, b = 9 Output: 4 Distance between 3 and 9 in above BST is 4. Input: Root of above tree a = 9, b = 25 Output: 3 Distance between 9 and 25 in above BST is 3.
We have discussed distance between two nodes in binary tree. The time complexity of this solution is O(n)
In the case of BST, we can find the distance faster. We start from the root and for every node, we do following.
- If both keys are greater than the current node, we move to the right child of the current node.
- If both keys are smaller than current node, we move to left child of current node.
- If one keys is smaller and other key is greater, current node is Lowest Common Ancestor (LCA) of two nodes. We find distances of current node from two keys and return sum of the distances.
Time Complexity: O(h) where h is the height of the Binary Search Tree.
Auxiliary Space: O(h) as well, since we need a recursive stack of size h.
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