Largest Tree Value

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Average time to solve is 25m
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Problem statement

You have been given the ‘ROOT’ of a binary tree having ‘N’ nodes, you need to find the largest value in each row or level of the binary tree.

For Example

Tree

For the above binary tree, 
Max value at level 0 = 6.
Max value at level 1 = max(9 , 3) = 9
Max value at level 2 = max (4, 8, 2) = 8
Detailed explanation ( Input/output format, Notes, Images )
Input Format: 
The first line contains an integer 'T' which denotes the number of test cases.     

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.

Tree

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, Print the maximum value at each row of the binary tree.

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. Just implement the given function.
Constraints: 
1 <= T <= 50
0 <= N <= 10^3
1 <= DATA <= 10^4

'DATA' is the value of the binary tree node.

Time Limit: 1 sec
Sample Input 1:
2
13 10 7 4 9 -1 -1 -1 -1 -1 -1
6 -1 -1
Sample Output 1:
13 10 9
6
Explanation Of Sample Input 1:
Test Case 1: The tree given in this case looks like this:

Tree

We can see clearly that the maximum value in the First row = 13, Second row = 10, and in the third row = 9.  

Test Case 2: There is only one node in the tree. Therefore the only 0-th level has a maximum value = 6.
Sample Input 2:
2
11 17 21 -1 -1 -1 -1
2 8 14 -1 7 -1 -1 5 -1 -1 -1
Sample Output 2:
11 21
2 14 7 5
Explanation Of Sample Input 2:
Test Case 1: We can see clearly that the maximum value in the First row = 11 and Second row = 21.  

Test Case 2: We can see clearly that the maximum value in the First row = 2, Second row = 14, Third Row = 7 and Last Row = 5.
Hint

Try to iterate over all the max possible node in one go.

Approaches (2)
Depth First Search

Approach:

  1. The main idea is to do a depth-first search with a slight modification.
  2. We will recursively traverse the tree for its left and right child.
  3. We will maintain an extra variable ‘LEVEL’ which will keep the level number of the elements and a ‘RESULT’ vector where ‘RESULT[i]’ will store the maximum value at level ‘i‘.
  4. If the value of the current ‘LEVEL’ is equal to the size of elements in the ‘RESULT’ vector that means we have encountered the element at this level first time. So we will push the current element to ‘RESULT’.
  5. Otherwise, we will compare the current element with the ‘RESULT [ LEVEL ]’. If the current element is larger than 'RESULT [ LEVEL ]', we will update 'RESULT [ LEVEL ]' = current element.
  6. In the end, the ‘RESULT’ vector will contain the maximum values at each tree row.

 

Algorithm:

 

  1. If the root is NULL we will simply return.
  2. Otherwise, compare the current ‘LEVEL’ with the size of the ‘RESULT’ vector.
    • If level = size of ‘RESULT’
      • Push root -> DATA to ‘RESULT’.
    • Else
      • ‘RESULT [ LEVEL ]’ = max( RESULT [ LEVEL ] , root -> DATA)
  3. Recursively call for left and right children for next level i.e ( root -> LEFT , LEVEL + 1) and (root - > RIGHT, LEVEL +1).
Time Complexity

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

 

Every node in the binary tree is visited only one time. Therefore time complexity is O(N).

Space Complexity

O(N), where ‘N’ is width of the binary tree.

 

The maximum levels in a binary tree can be ‘N’ so the size of recursion stack can grow up to ‘N’. Thus, Space Complexity is O(N).

Code Solution
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Largest Tree Value
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