Maximum Width of Binary Tree

Description

Given a binary tree, write a function to get 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 right most non-null nodes in the level, 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: 
       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).

 

Constraints:

• The given binary tree will have between 1 and 3000 nodes.

Solution(javascript)

// 记录每个 node 的序号，然后计算每一层的宽度
const widthOfBinaryTree = function (root) {
  if (!root) {
    return 0
  }
  root.id = BigInt(1)
  let current = [root]
  let max = 1
  while (current.length > 0) {
    const next = []
    max = Math.max(
      max,
      Number(current[current.length - 1].id - current[0].id) + 1,
    )
    current.forEach((node) => {
      if (node.left) {
        node.left.id = node.id * BigInt(2)
        next.push(node.left)
      }
      if (node.right) {
        node.right.id = node.id * BigInt(2) + BigInt(1)
        next.push(node.right)
      }
    })
    current = next
  }
  return max
}