34. Maximum Width of Binary Tree

Given the root of a binary tree, return the maximum width of the given tree.

The maximum width of a tree is the maximum width among all levels.

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

It is guaranteed that the answer will in the range of 32-bit signed integer.

Example 1:

Input: root = [1,3,2,5,3,null,9]
Output: 4
Explanation: The maximum width existing in the third level with the length 4 (5,3,null,9).

Example 2:

Input: root = [1,3,null,5,3]
Output: 2
Explanation: The maximum width existing in the third level with the length 2 (5,3).

Example 3:

Input: root = [1,3,2,5]
Output: 2
Explanation: The maximum width existing in the second level with the length 2 (3,2).

Example 4:

Input: root = [1,3,2,5,null,null,9,6,null,null,7]
Output: 8
Explanation: The maximum width existing in the fourth level with the length 8 (6,null,null,null,null,null,null,7).

Solution:

Approach: Left Child at pos = 2*i +1 Right Child at pos = 2*i + 2 Finding the distance between the 1st left and last right of a level

class Solution
{
public:
    int widthOfBinaryTree(TreeNode *root)
    {

        if (root == NULL)
        {
            return 0;
        }

        queue<TreeNode *> q;
        queue<int> idx;

        int maxWidth = 0;
        q.push(root);
        idx.push(0);

        while (!q.empty())
        {

            int s = q.size();
            int i = 0;
            int start = 0;
            int end = 0;
            int minVal = idx.front();

            while (i < s)
            {
                int pos = idx.front() - minVal;
                idx.pop();

                if (i == 0)
                {
                    start = pos - minVal;
                }

                if (i == s - 1)
                {
                    end = pos - minVal;
                }

                TreeNode *t = q.front();
                q.pop();

                if (t->left)
                {
                    q.push(t->left);
                    idx.push(2 * pos + 1);
                }

                if (t->right)
                {
                    q.push(t->right);
                    idx.push(2 * pos + 2);
                }

                i++;
            }

            maxWidth = max(maxWidth, (end - start) + 1);
        }

        return maxWidth;
    }
};