6

Largest Number in Binary Tree

Difficulty: EASY
Avg. time to solve
36 min
Success Rate
60%

Problem Statement
Suggest Edit

Given a Binary Tree of N nodes where the nodes have integer values, Find the largest number that could be formed by concatenating all its nodes values.

For example:
For the given binary tree:   

tree example

Output: 96553210    
Explanation: After concatenating all the numbers in the above binary tree this is the largest number that can be formed. 
Input Format:
The first line of input contains a single integer T, representing the number of test cases or queries to be run. 

Then the T test cases follow. 

The first line of each test case contains elements 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 :

alt text

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,  Print the integer represents the largest number that could be formed by concatenating all its nodes given in a binary tree. in a single line.
Constraints:
1 <= T <= 5
0 <= N <= 10^4
0 <= node data <= 10^3    

Time Limit: 1sec
Sample Input 1:
1
1 2 3 -1 -1 -1 -1
Sample Output 1:
321
Sample Input 2:
1
1 2 3 -1 4 4 -1 -1 5 6 -1 -1 -1 -1 -1
Sample Output 2:
6544321
Explanation to Sample Input 2:
The input binary tree will be represented as 

alt-text

From the above binary tree, all possible permutation of concatenated Integers largest number is 6544321  
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