Count Subtrees

Easy

0/40

Average time to solve is 15m

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Asked in companies

Problem statement

You have been given a Binary Search Tree (BST) of integer values and 2 integers 'LOW' and 'HIGH' denoting range ['LOW', 'HIGH'].

Your task is to return the count of nodes where all the nodes under that node (or subtree rooted with that node) lie in the given range.

A binary search tree (BST) is a binary tree data structure with the following properties.

• The left subtree of a node contains only nodes with data less than the node’s data.

• The right subtree of a node contains only nodes with data greater than the node’s data.

• Both the left and right subtrees must also be binary search trees.

Example:

Consider the following binary search tree. Suppose the given range is [ 15, 32 ] so we return ‘2’ as an answer as there are two nodes whose subtree is in the given range, the nodes are 20 and 30.

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

Input Format:

The first line contains an integer ‘T' which denotes the number of test cases or queries to be run. Then the test cases follow.

The first line of each test case contains the elements of the tree in the level order form separated by a single space.
If any node does not have a left or right child, take -1 in its place. Refer to the example below.

The second line of each test case contains two space-separated integers containing the range 'LOW' and 'HIGH'.

Example:

Elements are in the level order form. The input consists of values of nodes separated by a single space in a single line. In case a node is null, we take -1 in its place.

For example, the input for the tree depicted in the below image would be :

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).

Note :

The above format was just to provide clarity on how the input is formed for a given tree. 

The sequence will be put together in a single line separated by a single space. Hence, for the above-depicted tree, the input will be given as:

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

Output Format :

For each test case, print a single integer denoting the count of subtrees.

Output for every test case will be printed in a separate line.

Note:

You are not required to print the output, it has already been taken care of. Just implement the function.

Constraints:

1 <= T <= 10
1 <= N <= 3*10^3
1 <= data <= 10^9 (data != -1)

Where 'N' denotes the number of nodes in the given BST and 'data' denotes the value of those nodes.

Time Limit: 1 sec

Sample Input 1:

2
10 5 50 1 -1 40 100 -1 -1 -1 -1 -1 -1
5 45
10 5 50 1 -1 40 100 -1 -1 -1 -1 -1 -1
1 45

Sample Output 1:

1
3

Explanation For Sample Input1:

For the first test case :
As there is only 1 node (40) whose subtree is in the given range. 

For the second test case :
As there are three nodes (1, 5, and 40) whose subtree is in the given range.

Sample Input 2 :

2
10 5 50 -1 -1 -1 -1
20 25
10 5 50 -1 -1 -1 -1
1 25

Sample Output 2:

0
1

Console