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Check If Two Nodes Are Cousins

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Average time to solve is 10m

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Problem statement

You are given an arbitrary binary tree consisting of N nodes, where each node is associated with a certain value, and two node values, a and b, you need to check if these nodes are cousins.

Two nodes are cousins of each other if they are at the same level and have different parents. Two nodes are said to be at the same level if the distance of both the nodes from the root node is the same.

A binary tree (BT) is a data structure in which each node has at most two children.

For the given binary tree:

4 and 7 are cousins of each other since they are at the same level and have different parents, 3 and 2 respectively.

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 follow.

The first line of each test case contains the elements of the tree in the level order form separated by a single space.

The second line of each contains two space-separated integers which are values present as nodes in the Binary Tree. It is guaranteed that all nodes will have distinct values.

Refer to the example below to understand the input format.
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 4 -1 5 6 -1 7 -1 -1 -1 -1 -1 -1

Output Format:

For each test case, you need to return “YES” if the given two nodes are cousins of each other and “NO”, otherwise.(return without the quotes)

Note:

The Binary Tree has only distinct elements.
You are not required to print the expected output, it has already been taken care of. Just implement the function.

Constraints:

1 <= T <= 100
1 <= N <= 1000
-10^6 <= data <= 10^6 and data != -1

Time Limit: 1 sec

Sample Input 1:

3
1 2 3 -1 4 -1 -1 -1 -1
2 3
1 2 3 4 8 5 6 -1 -1 -1 -1 -1 -1 7 -1 -1 -1
4 6
1 2 3 -1 4 -1 -1 -1 -1
3 4

Sample Output 1:

NO
YES
NO

Explanation For Sample Input 1:

Here we have 3 test cases, hence there are 2 binary trees

Test Case 1:

We can see that the nodes with values 2 and 3 are in the same level but have the same parents.

Test Case 2:

We can see that the nodes with values 4 and 6 are in the same level and have different parents, so they are cousins.

Test Case 3:

We can see that the nodes with values 3 and 4 have different parents but are not in the same level.

Sample Input 2:

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

Sample Output 2

YES
NO

Hint 1

Hint 2

Think of a recursive solution.

Approaches (2)

Approach 1

Approach 2

Recursive Solution

Find the levels of both the given nodes.
This can be done by making a separate function for finding the level/by using level order traversal.
The levels should be the same.
Check if both the nodes are siblings or not.
This can again be done by simply going through the entire Binary Tree and checking if the node’s children are the given two nodes. If this is true, then given two nodes are siblings and hence they are not cousins.
For nodes to be cousins, they should be on the same level and have different parents.

Time Complexity

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

In the worst case, we would have to traverse the given Binary Tree at most 3 times.

Space Complexity

O(H), where H is the height of the binary tree

Stack space for recursive calls of N nodes of the binary tree and H is the height of the binary tree which can become N for a skewed tree.

(100% EXP penalty)

Check If Two Nodes Are Cousins

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