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BST Sequences

Difficulty: HARD
Avg. time to solve
50 min
Success Rate
50%

Problem Statement
Suggest Edit

You are given a binary search tree consisting of distinct elements. The binary search tree is created by traversing through the sequence from left to right and inserting each element. You need to print all the sequences or ways that would result in creating the given BST.

Note:
Keep in mind that while merging the sequences the relative order of elements should be preserved.
For example :
For the given binary search tree

Example

The valid BST sequences for the above BST are:
4 2 1 3 5 6 
4 2 1 5 3 6 
4 2 1 5 6 3 
4 2 3 1 5 6 
4 2 3 5 1 6 
4 2 3 5 6 1 
4 2 5 1 3 6 
4 2 5 1 6 3 
4 2 5 3 1 6 
4 2 5 3 6 1 
4 2 5 6 1 3 
4 2 5 6 3 1 
4 5 2 1 3 6 
4 5 2 1 6 3 
4 5 2 3 1 6 
4 5 2 3 6 1 
4 5 2 6 1 3 
4 5 2 6 3 1 
4 5 6 2 1 3 
4 5 6 2 3 1 


You need to print all of them.
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 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 below image would be :

Example

Input Format:   
5
4 7
2 -1 6 8
-1 3 -1 -1 -1 -1
-1 -1


 Explanation :
 Level 1 :
 The root node of the tree is 5

Level 2 :
Left child of 5 = 4
Right child of 5 = 7

Level 3 :
Left child of 4 = 2
Right child of 4 = null (-1)
Left child of 7 = 6
Right child of 7 = 8

Level 4 :
Left child of 2 = null (-1)
Right child of 2 = 3
Left child of 6 = null (-1)
Right child of 6 = null (-1)
Left child of 8 = null (-1)
Right child of 8 = null (-1)

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

5 4 7 2 -1 6 8 -1 3 -1 -1 -1 -1 -1 -1
Output Format:
For each test case, print all the valid BST sequences of the given Binary Search Tree in a separate line.

Print the output of each test case in sorted order.
Print the output of each test case in a separate line.
Note :
You do not need to print anything; it has already been taken care of. You just need to store all valid sequences of the given BST in a predefined data structure. 
Constraints:
1 <= T <= 10
0 <= N <= 10
1 <= data <= 10^4

 Where ‘T’ is the number of test cases, and ‘N’ is the total number of nodes in the binary tree, and “data” is the value of the binary tree node.


Time Limit: 1sec
Sample Input 1:
1
4 2 5 1 3 -1 6 -1 -1 -1 -1 -1 -1
Sample Output 1:
4 2 1 3 5 6 
4 2 1 5 3 6 
4 2 1 5 6 3 
4 2 3 1 5 6 
4 2 3 5 1 6 
4 2 3 5 6 1 
4 2 5 1 3 6 
4 2 5 1 6 3 
4 2 5 3 1 6 
4 2 5 3 6 1 
4 2 5 6 1 3 
4 2 5 6 3 1 
4 5 2 1 3 6 
4 5 2 1 6 3 
4 5 2 3 1 6 
4 5 2 3 6 1 
4 5 2 6 1 3 
4 5 2 6 3 1 
4 5 6 2 1 3 
4 5 6 2 3 1   
Explanation of Sample Input 1:
The binary search tree will look like this:

Example

In the above Binary Search Tree, all the valid sequences are:

4 2 1 3 5 6  
4 2 1 5 3 6  
4 2 1 5 6 3   
4 2 5 1 3 6 
4 2 5 1 6 3  
4 2 5 6 1 3  
4 5 2 1 3 6  
4 5 2 1 6 3  
4 5 2 6 1 3  
4 5 6 2 1 3  
4 2 3 1 5 6  
4 2 3 5 1 6 
4 2 3 5 6 1 
4 2 5 3 1 6 
4 2 5 3 6 1 
4 2 5 6 3 1 
4 5 2 3 1 6 
4 5 2 3 6 1 
4 5 2 6 3 1 
4 5 6 2 3 1  
Sample Input 2:
2
2 1 3 -1 -1 -1 -1
7 -1 -1
Sample Output 2:
2 1 3
2 3 1
7
Explanation of Sample Input 2:
For the first test case, the valid sequences are = 1 2 3 and 1 3 2
For the third test case, the valid sequence is = 7.
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