Given a binary tree, the task is to count the number of ways to remove a single edge from the tree such that the tree gets divided into two halves with equal sum.
Input: 1 / \ -1 -1 \ 1 Output: 1 Only way to do this will be to remove the edge from the right of the root. After that we will get 2 sub-trees with sum = 0. 1 / -1 and -1 \ 1 will be the two sub-trees. Input: 1 / \ -1 -1 \ -1 Output: 2
A simple solution will be to remove all the edges of the tree one by one and check if that splits the tree into two halves with the same sum. If it does, we will increase the final answer by 1. This will take O(N2) time in the worst case where “N” is the number of nodes in the tree.
- Create a variable ‘sum’ and store the sum of all the elements of the Binary tree in it. We can find the sum of all the elements of a Binary tree in O(N) time as discussed in this article.
- Now we perform the following steps recursively starting from root node:
- Find the sum of all the elements of its right sub-tree (“R”). If it’s equal to half of the total sum, we increase the count by 1. This is because removing the edge connecting the current node with its right child will divide the tree into two trees with equal sum.
- Find the sum of all the elements of its left sub-tree (“L”). If it’s equal to half of the total sum, we increase the count by 1.
Below is the implementation of the above approach:
Time complexity of this approach will be O(N) and space complexity will O(H) where “N” equals number of node in Binary tree and “H” equals height of the Binary Tree.
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- Check if removing an edge can divide a Binary Tree in two halves
- Check if max sum level of Binary tree divides tree into two equal sum halves
- Maximum cost of splitting given Binary Tree into two halves
- Divide N segments into two non-empty groups such that given condition is satisfied
- Complexity of different operations in Binary tree, Binary Search Tree and AVL tree
- Convert a Binary Tree into its Mirror Tree
- Convert a Binary Search Tree into a Skewed tree in increasing or decreasing order
- Maximum sub-tree sum in a Binary Tree such that the sub-tree is also a BST
- Convert a Generic Tree(N-array Tree) to Binary Tree
- Check if a binary tree is subtree of another binary tree | Set 1
- Binary Tree to Binary Search Tree Conversion
- Check if a binary tree is subtree of another binary tree | Set 2
- Convert a Binary Tree to Threaded binary tree | Set 1 (Using Queue)
- Check whether a binary tree is a full binary tree or not
- Convert a Binary Tree to Threaded binary tree | Set 2 (Efficient)
- Minimum swap required to convert binary tree to binary search tree
- Check whether a given binary tree is skewed binary tree or not?
- Difference between Binary Tree and Binary Search Tree
- Binary Tree | Set 3 (Types of Binary Tree)
- Check if a binary tree is subtree of another binary tree using preorder traversal : Iterative
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