Widest Binary Tree Level

Determine the maximum width of any level in a binary tree. This tests your understanding of tree traversals and space optimization, crucial for efficient data structure manipulation.

treebreadth-first searchlevel-order traversalbinary tree

Problem Statement

Given a binary tree, find the level that has the largest width. The width of a level is defined as the number of nodes between the leftmost and rightmost non-null nodes, including any null nodes in between. Return the maximum width found in any level of the tree.

Example 1

Input: A binary tree with root 1, left child 2, right child 3, 2's left child 4, 2's right child null, 3's left child null, 3's right child 5

Output: 4

The widest level is the last level with nodes 4 and 5. Even though the number of nodes is 2, the width is calculated as the difference between the positions of 4 and 5 (assuming 4 is at index 0 and 5 is at index 2) plus 1, which is 2-0+1 = 3. The level above has nodes 2 and 3, which would have indices 0 and 1. The width is 1-0+1 = 2. The root level has only one node with a width of 1. The 2nd level has width 2 so the last level is the widest with a width of 3.

Example 2

Input: A binary tree with root 1, left child 2, right child 3, 2's left child 4, 2's right child 5, 3's left child 6, 3's right child 7, 4's left child 8, 5's right child 9

Output: 8

The widest level is the last level with nodes 8 and 9. Even though the number of nodes is 2, the width is calculated as the difference between the positions of 8 and 9 plus 1. Since 8 is at index 0 and 9 is at index 3, the width is 3-0+1 = 4. The level before that has 4, 5, 6, 7. These would have indices 0, 1, 2, 3. The width would be 3-0+1 = 4. The level before that has 2 and 3 which would have indices 0 and 1. The width is 1-0+1 = 2. The root level is 1. Level 0 has width 1, Level 1 has width 2, Level 2 has width 4, and Level 3 has width 4 so the widest is 4.

Constraints

-The number of nodes in the tree will be in the range [0, 3000].
-Node values will be integers.
-The tree structure is a valid binary tree.

Brute Force Approach

A brute-force approach would involve traversing the tree and storing all nodes at each level. Imagine you're sorting mail into different boxes, one for each floor of a building. You'd go through each piece of mail, determine its floor, and put it in the corresponding box. Once you have all the mail sorted, you'd find the floor with the most widely spaced addresses to determine the maximum width. This requires storing all nodes, leading to higher space usage.

TimeO(n)

SpaceO(n)

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