Check If Binary Tree Is Sum Tree Or Not

Moderate
0/80
Average time to solve is 15m
profile
Contributed by
30 upvotes
Asked in companies
AdobeGoldman SachsAmazon

Problem statement

You are given an arbitrary binary tree consisting of N nodes where each node is associated with a certain value. You need to check whether the given tree is a sum tree or not.

A binary tree is a sum tree if the value of each node is equal to the sum of nodes present in the left and the right subtree. An empty tree is a sum tree with 0 sums. A leaf node is also considered a sum tree with a sum equal to the value of the leaf node.

Detailed explanation ( Input/output format, Notes, Images )

Input Format :

The first line of the input contains a single integer T, representing the number of test cases. 

The first line of each test case will contain the values of the tree’s nodes in the level order form ( -1 for NULL node). Refer to the example for further clarification.

Example :

Consider the binary tree

altImage

The input of the tree depicted in the image above will be like: 

1
2 3
4 -1 5 6
-1 7 -1 -1 -1 -1
-1 -1

Explanation :
Level 1 :
The root node of the tree is 1

Level 2 :
Left child of 1 = 2
Right child of 1 = 3

Level 3 :
Left child of 2 = 4
Right child of 2 = null (-1)
Left child of 3 = 5
Right child of 3 = 6

Level 4 :
Left child of 4 = null (-1)
Right child of 4 = 7
Left child of 5 = null (-1)
Right child of 5 = null (-1)
Left child of 6 = null (-1)
Right child of 6 = null (-1)

Level 5 :
Left child of 7 = null (-1)
Right child of 7 = null (-1)

The first not-null node (of the previous level) is treated as the parent of the first two nodes of the current level. The second not-null node (of the previous level) is treated as the parent node for the next two nodes of the current level and so on.

The input ends when all nodes at the last level are null (-1).

Output Format :

For each test case, print ‘true’ if the given binary tree is a sum tree else, print ‘false’. The output of each test case will be printed in a separate line.

Note :

You do not need to print anything. It has already been taken care of. Just implement the given function.

Constraints :

1 <= T <= 5
1 <= N <= 3000

Time Limit: 1sec

Sample Input 1 :

2
3 1 2 -1 -1 -1 -1
3 -1 1 2 -1 -1 -1

Sample Output 1 :

true
false
Explanation for sample input 1 :
For the first test case, the given tree is


For each level, we can see that the value of each node is equal to the sum of the left and the right subtree.

For the second test case, the given tree is


We can see that the sum of a subtree of a node with root 1 is not equal to the value of the node. Hence, the answer is ‘false’.
Hint

Can you use any kind of tree traversal to find the answer.

Approaches (2)
Depth-first search.
  • The simple approach is to use DFS for finding the sum for each subtree.
  • Let getSubtreeSum() be an integer function that takes the tree’s root as input and returns the sum of the given subtree.
  • Let isSumTree() a boolean function which returns true if the given tree is sum tree or not.
  • The base case will be when the root does not exist, or the current node is a leaf node, then the answer will be true.
  • Let 'leftSum' = 0, denote the sum of the left subtree of the given node and 'rightSum' = 0, denotes the sum of the right subtree of the given node,
  • Recursively call for left and right subtrees, i.e. ‘leftSum’  = getSubtreeSum(root->left) and 'rightSum' = getSubtreeSum(root->right)
  • Now if ‘leftSum’ + ‘rightSum’ = root->data, root->left and root->right is also a sumTree then return true.
  • Else, return false.
Time Complexity

O(N ^ 2), where N is the number of nodes in the tree.

 

We will be calculating the sum of the same subtrees again and again in case of a skewed tree. Thus, the effective time complexity will be O(N ^ 2).

Space Complexity

O(N), where N is the number of nodes in the tree.

 

There will be N nodes at max at any given point of time in the recursion stack. Thus, the effective space complexity will be O(N).

Code Solution
(100% EXP penalty)
Check If Binary Tree Is Sum Tree Or Not
Full screen
Console