Diameter Of Binary Tree

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Average time to solve is 10m

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Problem statement

You are given a Binary Tree.

Return the length of the diameter of the tree.

Note :

The diameter of a binary tree is the length of the longest path between any two end nodes in a tree.

The number of edges between two nodes represents the length of the path between them.

Example :

Input: Consider the given binary tree:

Output: 6

Explanation:
Nodes in the diameter are highlighted. The length of the diameter, i.e., the path length, is 6.

Detailed explanation ( Input/output format, Notes, Images )

Input Format:

The only line 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 will 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)

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 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:

Return a single integer i.e. the diameter of the tree.

Note :

You do not need to print anything; it has already been taken care of. Just implement the given function.

Sample Input 1 :

1 2 3 4 7 -1 -1 -1 -1 -1 -1

Sample Output 1 :

Explanation of Sample Input 1 :

The binary tree in the given test case will look like

The length of the diameter of the above tree is the length of the path between nodes 4 and 3, i.e., 4->2->1->3. Hence the output will be 3.

Sample Input 2 :

1 2 3 -1 -1 -1 -1

Sample Output 2 :

Explanation of Sample Input 2 :

The binary tree in the given test case will look like

The length of the diameter of the above tree is the length of the path between nodes 2 and 3, i.e., 2.

Expected Time Complexity:

Try to do this in O(n).

Constraints:

1 <= n <= 10000

Where 'n' is the total number of nodes in the binary tree.

Time Limit: 1 sec

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