Print Binary Tree

Print a binary tree in an m*n 2D string array following these rules:

1. The row number m should be equal to the height of the given binary tree.
2. The column number n should always be an odd number.
3. The root node's value (in string format) should be put in the exactly middle of the first row it can be put. The column and the row where the root node belongs will separate the rest space into two parts (left-bottom part and right-bottom part). You should print the left subtree in the left-bottom part and print the right subtree in the right-bottom part. The left-bottom part and the right-bottom part should have the same size. Even if one subtree is none while the other is not, you don't need to print anything for the none subtree but still need to leave the space as large as that for the other subtree. However, if two subtrees are none, then you don't need to leave space for both of them.
4. Each unused space should contain an empty string "".
5. Print the subtrees following the same rules.

Example 1:

Input:
     1
    /
   2
Output:
[["", "1", ""],
 ["2", "", ""]]

 

Example 2:

Input:
     1
    / \
   2   3
    \
     4
Output:
[["", "", "", "1", "", "", ""],
 ["", "2", "", "", "", "3", ""],
 ["", "", "4", "", "", "", ""]]

 

Example 3:

Input:
      1
     / \
    2   5
   / 
  3 
 / 
4 
Output:

[["",  "",  "", "",  "", "", "", "1", "",  "",  "",  "",  "", "", ""]
 ["",  "",  "", "2", "", "", "", "",  "",  "",  "",  "5", "", "", ""]
 ["",  "3", "", "",  "", "", "", "",  "",  "",  "",  "",  "", "", ""]
 ["4", "",  "", "",  "", "", "", "",  "",  "",  "",  "",  "", "", ""]]

 

Note: The height of binary tree is in the range of [1, 10].

1.解析

题目大意，按照固定的格式输出二叉树。

2.分析

我先拿一个简单的例子说一下：例如，例子2，我们观察发现第1层的输出为["", "", "", "1", "", "", ""]，整棵树的高度为3，可以看到第一层节点的输出root节点值位于中间，且数组中元素的大小为7，相当于2^3-1，即第n层满二叉树的所有节点个数，所以，可以确定第一点，每一层的元素个数就是第n层满二叉树所有节点的个数。第2层的输出为["", "2", "", "", "", "3", ""]，除中间之外，可以发现左右两边各有3个大小的元素，节点值2和3分别位于左右两边中间的位置，即每一层当中节点所处的位置分布为：从中间分开，左右子树分别占据左右两边的位置，若当前层左子树只有一个节点则位于中间位置，否则位于两边。

综上，首先，确定整颗树的高度，若用二维数组存储整棵树，则对应为行数；该树对应的满二叉树的个数即为列数。数组中的每个元素用空串表示，然后利用递归逐层取递归，将当前结点的值填入对应的位置即可。

具体实现：参考@Grandyang博主的思路

/**
 * 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:
    vector<vector<string>> printTree(TreeNode* root) {
        int h = getHight(root); //求解整颗树的高度
        int w = pow(2, h) - 1; //求解该树对应的满二叉树的节点个数
        vector<vector<string>> res(h, vector<string>(w, ""));
        helper(root, 0, w-1, 0, res);
        return res;
    }
    void helper(TreeNode* root, int i, int j, int curH, vector<vector<string>>& res){
        if (!root) return;
        res[curH][(i+j)/2] = to_string(root->val); //将节点的值，放入数组中对应的位置
        helper(root->left, i, (i+j)/2, curH + 1, res);
        helper(root->right, (i+j)/2+1, j, curH + 1, res);
    }
    int getHight(TreeNode* root){
        if (!root) return 0;
        return 1 + max(getHight(root->left), getHight(root->right));
    }
};

[1]https://www.cnblogs.com/grandyang/p/7489097.html