leetcode_222 Count Complete Tree Nodes

题目：

Given a complete binary tree, count the number of nodes.

Definition of a complete binary tree from Wikipedia:
In a complete binary tree every level, except possibly the last, is completely filled, and all nodes in the last level are as far left as possible. It can have between 1 and 2h nodes inclusive at the last level h.

思路1：

暴力解决，遍历树的所有节点，依次统计。

会超时，题目限定了该二叉树是完全二叉树，该种思路适用于所有二叉树。

思路2：

暴力解决无法测试通过，此时需要考虑完全二叉树的特点。

完全二叉树，至少有一课子树是完美二叉树，另一课子树至少是完全二叉树。

因此可以递归的计算。

判断完美二叉树：

     最内侧的叶子结点和最外侧的叶子结点是否在同一层。

代码：

    public static int countNodes(TreeNode root){
        if(root == null){
            return 0;
        }
        
        int hl = getLeft(root)+1;
        int hr = getRight(root)+1;
        
        if(hl == hr){
            int num = (2<<(hl-1))-1;
            return num;
        }else{
            return countNodes(root.left)+countNodes(root.right)+1;
        }
    }

    public static int getRight(TreeNode root) {
        int cou = 0;
        TreeNode ptr = root;
        while(ptr.right != null){
            cou++;
            ptr = ptr.right;
        }
        return cou;
    }

    public static int getLeft(TreeNode root) {
        int cou = 0;
        TreeNode ptr = root;
        while(ptr.left != null){
            cou++;
            ptr = ptr.left;
        }
        return cou;
    }