Given a binary tree, find the sum of all parent-child differences for all the non-leaf nodes of the given binary tree.
Note that parent-child difference is (parent node’s value – (sum of child node’s values)).
Input: 1 / \ 2 3 / \ / \ 4 5 6 7 \ 8 Output: -23 1st parent-child difference = 1 -(2 + 3) = -4 2nd parent-child difference = 2 -(4 + 5) = -7 3rd parent-child difference = 3 -(6 + 7) = -10 4th parent-child difference = 6 - 8 = -2 Total sum = -23 Input: 1 / \ 2 3 \ / 5 6 Output: -10
Naive Approach: The idea is to traverse the tree in any fashion and check if the node is the leaf node or not. If the node is non-leaf node, add (node data – sum of children node data) to result.
Efficient Approach: In the final result, a close analysis suggests that each internal node ( nodes which are neither root nor leaf) once gets treated as a child and once as a parent hence their contribution in the final result is zero. Also, the root is only treated as a parent once and in a similar fashion, all leaf nodes are treated as children once. Hence, the final result is (value of root – sum of all leaf nodes).
Below is the implementation of the above approach:
- Complexity of different operations in Binary tree, Binary Search Tree and AVL tree
- Minimum swap required to convert binary tree to binary search tree
- Check whether a binary tree is a full binary tree or not | Iterative Approach
- Convert a Binary Tree to Threaded binary tree | Set 1 (Using Queue)
- Convert a Binary Tree to Threaded binary tree | Set 2 (Efficient)
- Binary Tree to Binary Search Tree Conversion
- Binary Tree to Binary Search Tree Conversion using STL set
- Check whether a binary tree is a full binary tree or not
- Check whether a given binary tree is skewed binary tree or not?
- Check if a binary tree is subtree of another binary tree | Set 1
- Check if a binary tree is subtree of another binary tree | Set 2
- Convert an arbitrary Binary Tree to a tree that holds Children Sum Property
- Given level order traversal of a Binary Tree, check if the Tree is a Min-Heap
- Print Binary Tree levels in sorted order | Set 3 (Tree given as array)
- Check whether a binary tree is a complete tree or not | Set 2 (Recursive Solution)
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