894. All Possible Full Binary Trees

Problem

A full binary tree is a binary tree where each node has exactly 0 or 2 children.

Return a list of all possible full binary trees with N nodes. Each element of the answer is the root node of one possible tree.

Each node of each tree in the answer must have node.val = 0.

You may return the final list of trees in any order.

Example

Input: 7
Output: [[0,0,0,null,null,0,0,null,null,0,0],[0,0,0,null,null,0,0,0,0],[0,0,0,0,0,0,0],[0,0,0,0,0,null,null,null,null,0,0],[0,0,0,0,0,null,null,0,0]]
Explanation:

Solution

满二叉树的节点数一定是奇数。

/**
 * 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<TreeNode*> allPossibleFBT(int N) {
        vector<TreeNode*> fbtVec;
        if(N == 0 || N%2==0)
            return fbtVec;
        if(N == 1)
        {
            TreeNode * root = new TreeNode(0);
            fbtVec.push_back(root);
            return fbtVec;
        }
        
        for(int i = 1;i<N;i+=2)
        {
            
            vector<TreeNode *> lRet= allPossibleFBT(i);
            vector<TreeNode *> rRet= allPossibleFBT(N-1-i);

            for(int j = 0;j<lRet.size();++j)
            {   
                for(int k = 0;k<rRet.size();++k)
                {
                	//root不能放在最外层循环去new
                    TreeNode * root = new TreeNode(0);
                    root->left  = lRet[j];
                    root->right = rRet[k];
                    fbtVec.push_back(root);
                }
            }
            
        }

        return fbtVec;
    
    }
    
};