Maximum level sum

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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, your task is to find the maximum sum for a level in the tree.

A binary tree is a tree where every node has at most two child nodes.

Two nodes are said to be at the same level in the tree if both have equal distance from the root node.

For example, consider the following binary tree:

example

Here, max level sum is 13 for level 1(17-4) and also level 3(25-12).

Detailed explanation ( Input/output format, Notes, Images )
Input Format: 
The first line of input contains an integer ‘T’ representing the number of test cases. Then the test cases follow.

The only 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 on its place.

For example, the input for the tree depicted in the below image would be:

example

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). The last line contains the value of the two nodes (7 and 5) between which we have to find the distance.
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, the output will be the maximum level sum.

The output for each test case will be in a separate line.
Note: 
You do not need to print anything; it has already been taken care of.
Constraints: 
1 <= T <= 100
1 <= N <= 3000
-1000 <= data <= 1000 
data != -1

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

Time Limit: 1 second
Sample Input 1:
3
10 17 -4 12 -5 3 -1 -1 -1 -1 -1 25 -12 -1 -1 -1 -1
8 7 -6 -2 -5 3 -1 -1 -1 -1 -1 -1 -1 -1
-10 -12 -1 -1 -13 -1 0 -1 -1
Sample Output 1:
13
8
0
Explanation of Sample Input 1:

Sample Input 1

For the first test case, the maximum level sum is for level 1 (and level 3) i.e. 13

Sample Input 1

For the second test case, the maximum level sum is for level 0 i.e. 8.

Sample Input 1

For the third test case, the maximum level sum is for level 3 i.e. 0.
Sample Input 2:
3
1 2 3 4 5 6 -7 -1 -1 -1 -1 -1 -1 -1 -1
1 -1 2 -1 3 -1 -1
1 2 -1 3 -4 5 6 7 -8 -1 -1 -1 -1 -1 -1 -1 -1
Sample Output 2:
8
3 
10
Hint

Try to reach out to each level and find the sum for that level and find the level with maximum sum.

Approaches (2)
Recursive

We try to reach out to each node and include its contribution to the level sum recursively.

Consider a function MAXLEVELSUM that accepts BinaryTreeNode ROOT as a parameter and do:

  1. Calculate the number of levels in the tree and assign it to MAXLEVEL.
  2. Define an array of integers SUM to store sum for each level.
  3. Call function MAXLEVELSUMUTIL for ROOT, MAXLEVEL, SUM and 0.
  4. Initialize RESULT to minimum integer value.
  5. Iterate over SUM[i] for each 0<= i < MAXLEVEL and assign maximum of RESULT and SUM[i] to RESULT.
  6. Return RESULT.

The function MAXLEVELSUMUTIL used above accepts as parameter, a BinaryTreeNode ROOT, Integer MAXLEVEL (representing maximum levels in tree), integer array SUM and integer CURRENTLEVEL and do:

  1. If ROOT is not NULL do:
    1. Add ROOT.DATA to SUM[CURRENTLEVEL]
    2. Call MAXLEVELSUMUTIL for ROOT.LEFT, MAXLEVEL, SUM, CURRENTLEVEL+1
    3. Call MAXLEVELSUMUTIL for ROOT.RIGHT, MAXLEVEL, SUM, CURRENTLEVEL+1
Time Complexity

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

 

Because we’ll be processing all, N nodes of the binary tree.

Space Complexity

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

 

Because in the worst case we’ll have skewed tree with N levels so, we will be storing the sum for N levels.

Code Solution
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Maximum level sum
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