[leetcode] 662. Maximum Width of Binary Tree

Description

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.

分析

题目的意思是：求一个二叉树的最大宽度。

• 对于一棵完美二叉树，如果根结点是深度1，那么每一层的结点数就是2n-1，那么每个结点的位置就是[1, 2n-1]中的一个，假设某个结点的位置是i，那么其左右子结点的位置可以直接算出来，为2i和2i+1。
• 我们从根结点进入，深度为0，位置为1，进入递归函数。
• 首先判断，如果当前结点为空，那么直接返回，然后判断如果当前深度大于start数组的长度，说明当前到了新的一层的最左结点，我们将当前位置存入start数组中。然后我们用idx - start[h] + 1来更新结果res。这里idx是当前结点的位置，start[h]是当前层最左结点的位置。然后对左右子结点分别调用递归函数，注意左右子结点的位置可以直接计算出来。

代码

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    int widthOfBinaryTree(TreeNode* root) {
        int res=0;
        vector<int> start;
        solve(root,0,1,start,res);
        return res;
    }
    void solve(TreeNode* root,int h,int idx,vector<int>& start,int& res){
        if(!root){
            return ;
        }
        if(h>=start.size()) start.push_back(idx);
        res=max(res,idx-start[h]+1);
        solve(root->left,h+1,idx*2,start,res);
        solve(root->right,h+1,idx*2+1,start,res);
    }
};

参考文献

[LeetCode] Maximum Width of Binary Tree 二叉树的最大宽度