Maximum Width of Binary Tree

Medium binary tree BFS

LeetCode: https://leetcode.com/contest/leetcode-weekly-contest-46/problems/maximum-width-of-binary-tree/

Question

Given a binary tree, write a function to get the maximum width of the given tree. The width of a tree is the maximum width among all levels. The binary tree has the same structure as a full binary tree, but some nodes are null.

The width of one level is defined as the length between the end-nodes (the leftmost and right most non-null nodes in the level, where the null nodes between the end-nodes are also counted into the length calculation.

Example 1:
Input:

           1
         /   \
        3     2
       / \     \
      5   3     9

Output: 4
Explanation: The maximum width existing in the third level with the length 4 (5,3,null,9).
Example 2:
Input:

          1
         /
        3
       / \
      5   3

Output: 2
Explanation: The maximum width existing in the third level with the length 2 (5,3).
Example 3:
Input:

          1
         / \
        3   2
       /
      5

Output: 2
Explanation: The maximum width existing in the second level with the length 2 (3,2).
Example 4:
Input:

          1
         / \
        3   2
       /     \
      5       9
     /         \
    6           7

Output: 8
Explanation:The maximum width existing in the fourth level with the length 8 (6,null,null,null,null,null,null,7).

Note: Answer will in the range of 32-bit signed integer.

Thinking

1. Simlar question on GeeksforGreeks which doesn’t count null value.http://www.geeksforgeeks.org/maximum-width-of-a-binary-tree/. My solution is http://ide.geeksforgeeks.org/IagSO2
2. Using two queues. One queue is for nodes, another is for node’s positions. left is pos * 2 -1 and right is pos * 2
3. Width is the last value subtract the first value in queue

Solution

Java

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public int widthOfBinaryTree(TreeNode root) {
        Queue<TreeNode> queue = new LinkedList<TreeNode>();
        Queue<Integer> posQueue = new LinkedList<Integer>();
        int maxWidth = 0;
        queue.offer(root);
        posQueue.offer(1);
        while (!queue.isEmpty()) {
            int size  = queue.size();
            int start = 0;
            int end = 0;
            for (int i = 0; i < size; i++) {
                TreeNode node = queue.poll();
                Integer pos = posQueue.poll();
                if (i == 0) {
                    start = pos;
                }
                end = pos;
                if (node.left != null) {
                    queue.offer(node.left);
                    posQueue.offer(pos * 2- 1);
                } 
                if (node.right != null) {
                    queue.offer(node.right);
                    posQueue.offer(pos * 2);
                }
            }
            maxWidth = Math.max(maxWidth, end - start + 1);
        }
        return maxWidth;
    }
}