Given an N-ary tree, the task is to find the maximum width of the given tree. The maximum width of a tree is the maximum of width among all levels.
Input:4 / | \ 2 3 -5 / \ /\ -1 3 -2 6
Width of 0th level is 1.
Width of 1st level is 3.
Width of 2nd level is 4.
Therefore, the maximum width is 4
Input:1 / | \ 2 -1 3 / \ \ 4 5 8 / / | \ 2 6 12 7
Approach: This problem can be solved using BFS. The idea is to perform level order traversal of the tree. While doing traversal, process nodes of different levels separately. For every level being processed, count the number of nodes present at each level and keep track of the maximum count. Follow the steps below to solve the problem:
- Initialize a variable, say maxWidth to store the required maximum width of the tree.
- Initialize a Queue to perform the level order traversal of the given tree.
- Push the root node into the queue.
- If size of the queue exceeds maxWidth for any level, then update maxWidth to the size of the queue.
- Traverse the queue and push all the nodes of the next level into the queue and pop all the nodes of the current level.
- Repeat the above steps until all the levels of the tree are traversed.
- Finally, return the final value of maxWidth.
Below is the implementation of the above approach:
Time Complexity: O(N)
Auxiliary Space: O(N)