Pairs Violating BST

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Deutsche Bank

Problem statement

You are given a binary tree and you need to find the number of pairs violating BST property.

BST tree has the following properties:-

1. For every node, it is greater than or equal to its left child and less than or equal to its right child.
2. Node is greater than equal to the maximum value of its left subtree and less than the minimum value of its right subtree.
3. The maximum in the left sub-tree must be less than equal to the minimum in the right subtree.
For example in the following tree:- 

The numbers of pairs violating BST property are:-

(1,5) : 1 should be greater than its left child value.

(4,3) : 4 should be less than its right child value.

(5,4),(5,3):  Maximum of left subtree of 1 is 5 greater 
than 2 and 3 of its right subtree.
Detailed explanation ( Input/output format, Notes, Images )
Input Format: 
The first line contains an integer 'T' which denotes the number of test cases. Then the test cases are as follows.

The first line of each test case contains elements of the tree in the level order form. The line consists of values of nodes separated by a single space. In case a node is null, we take -1 in its place.


For example, the input for the tree depicted in the above 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)
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 4 -1 5 6 -1 7 -1 -1 -1 -1 -1 -1

Output format :

For each test case, print a single line containing a single integer denoting the number of pairs violating the BST property.

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' <= 10
1 <= Number of nodes in Tree <= 5000
1 <= Value of nodes <= 10 ^ 5

Where 'T' is the number of test cases.

Time Limit: 1 sec.
Sample Input 1:
1
8 4 3 2 -1 6 7 -1 -1 -1 -1 -1 -1
Sample Output 1:
5
Sample Output Explanation
 For the above input tree is:-


Thus pairs violating BST property are:-
(8,3) :- Greater than its right child.
(8,6) :- Greater than node on its right side.
(8,7) :- Greater than node on its right side.
(3,6):- The value of 3 is not more than its left child.
(4,3):- The value in the left subtree is greater than the 
value of the right subtree.

Thus the number of pairs is 5.
Sample Input 2:
2
35 44 26 -1 50 37 20 -1 -1 43 36 -1 -1 -1 -1 -1 -1 
49 48 26 32 36 40 31 30 -1 25 40 -1 -1 -1 40 -1 -1 -1 -1 -1 -1 -1 -1
Sample Output 2:
24
25
Hint

Do the inorder traversal of the given tree.

Approaches (2)
In-order traversal approach

The main idea is to find the inorder traversal of the given tree and find number of pairs of form arr[i] > arr[j] for i < j because in the level order form of BST the array will be sorted. So the number of pairs that are violating BST property.


 Algorithm :

  • Store the inorder form of the tree in an array ‘arr’.
  • Create a variable ans with intial value 0.
  • Run a loop from i equal to 0 to n where n is the number of nodes in the tree.
  • Run a nested loop from i+1 to N .
  • If arr[i] > arr[j] then increase the count of ans.
  • In the end return ans.
Time Complexity

O(N * N) where ‘N’ is the number of nodes in a tree.

 

We are running a nested loop from i=0 to n and then i+1 to n.

Space Complexity

O(N) where ‘N’ is the number of nodes in a tree.

 

We are creating an array to store the level order traversal of an array .

Code Solution
(100% EXP penalty)
Pairs Violating BST
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