Min distance between two given nodes of a Binary Tree
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  Difficulty: Medium   Marks: 4
Associated Course(s):   Amazon SDE Test Series

Given a binary tree and two node values your task is to find the minimum distance between them.

Input:

First line of input contains the number of test cases T. For each test case, there will be only a two lines of input first of which is a string representing the tree as described below: 

  1. The values in the string are in the order of level order traversal of the tree where, numbers denotes node values, and a character “N” denotes NULL child.

  2. For example:

For the above tree, the string will be: 1 2 3 N N 4 6 N 5 N N 7 N
The next line contains two integers denoting two nodes a and b.

There are multiple test cases. For each test case, this method will be called individually.

Output:
The function should return min distance between two node values .

Constraints:
1 <= T <= 100
1 <= Number of nodes <= 104
1 <= Data of a node <= 105

Example:
Input

1
2
1 2 3
2 3 

Output
2

In above example there is one test case which represent a tree with 3 nodes and 2 edges where root is 1, left child of 1 is 2 and right child of 1 is 3.  




Note:The Input/Ouput format and Example given are used for system's internal purpose, and should be used by a user for Expected Output only. As it is a function problem, hence a user should not read any input from stdin/console. The task is to complete the function specified, and not to write the full code.

** For More Input/Output Examples Use 'Expected Output' option **

Contributor: Amit Khandelwal
Author: Shubham Joshi 1


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