Given a binary tree and a node in the binary tree, find Postorder predecessor of the given node.
Examples: Consider the following binary tree 20 / \ 10 26 / \ / \ 4 18 24 27 / \ 14 19 / \ 13 15 Input : 4 Output : 10 Postorder traversal of given tree is 4, 13, 15, 14, 19, 18, 10, 24, 27, 26, 20. Input : 24 Output : 10
A simple solution is to first store Postorder traversal of the given tree in an array then linearly search given node and print node next to it.
Time Complexity : O(n)
Auxiliary Space : O(n)
An efficient solution is based on below observations.
- If right child of given node exists, then the right child is postorder predecessor.
- If right child does not exist and given node is left child of its parent, then its sibling is its postorder predecessor.
- If none of above conditions are satisfied (left child does not exist and given node is not right child of its parent), then we move up using parent pointers until one of the following happens.
- We reach root. In this case, postorder predecessor does not exiss
- Current node (one of the ancestors of given node) is right child of its parent, in this case postorder predecessor is sibling of current node.
Postorder predecessor of 19 is 14
Time Complexity : O(h) where h is height of given Binary Tree
Auxiliary Space : O(1)
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