662 Maximum Width of Binary Tree

LeetCode

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).

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定义一个 id 来表示一行中的坐标，如果填满为完全二叉树，最左边 id 是 0 ，当前节点的左子树 id 为当前节点的 id 乘以 2 ，右子树为 id 乘以 2 加 1 。

使用两个 List 记录每一行的最小 id 和最大宽度。使用前序遍历，带着层数和 id 遍历，每一行的第一个遍历到的节点是最左的节点，更新当前行的最小 id ，其余节点不是最左节点，计算宽度并更新最大宽度。

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
class Solution {
    
    ArrayList<Integer> levelMin;
    ArrayList<Integer> levelMax;
    public int widthOfBinaryTree(TreeNode root) {
        if(root==null) return 0;

        levelMin = new ArrayList<>();
        levelMax = new ArrayList<>();
        preOrder(root,0,0);
        int max=0;
        for(int i:levelMax){
            if(i>max) max=i;
        }
        return max+1;
    }
    
    private void preOrder(TreeNode root, int depth, int id){

        if(levelMin.size()==depth) {
            levelMin.add(id);
            levelMax.add(0);
        } else {
            int cur = id-levelMin.get(depth);
            if(cur > levelMax.get(depth)) levelMax.set(depth,cur);
        }

        
        if(root.left!=null){
            preOrder(root.left, depth+1, id*2);
        } 
        if(root.right!=null){
            preOrder(root.right, depth+1, id*2+1);
        }
        
    }
}