222. Count Complete Tree Nodes

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.

首先,不管是满二叉树还是完全二叉树,一直往左遍历都能得到树的高度。第一种方法,采用递归,思路是满二叉树的节点数等于2^h-1。代码如下:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public int countNodes(TreeNode root) {
        if (root == null) {
            return 0;
        }
        TreeNode left = root, right = root;
        int hight = 0;
        while (right != null) {
            left = left.left;
            right = right.right;
            hight ++;
        }
        if (left == null) {
            return (1 << hight) - 1;
        }
        return 1 + countNodes(root.left) + countNodes(root.right);
    }
}
第二种还是递归,思路是先侦查右树高度,方法是沿着根节点右节点一路向左下找,如果右树高度是h,那么左树肯定是满树,节点数是2^(h-1),再继续侦查右树,如果右树高度是h-1,说明左树不满,右树是满树,且节点数是2^(h - 2),再继续侦查左树。代码如下:

class Solution {
    int height(TreeNode root) {
        return root == null ? -1 : 1 + height(root.left);
    }
    public int countNodes(TreeNode root) {
        int h = height(root);
        return h < 0 ? 0 :
               height(root.right) == h-1 ? (1 << h) + countNodes(root.right)
                                         : (1 << h-1) + countNodes(root.left);
    }
}
第三种是上一种方法的迭代版,省去了每次计算全树的高度。代码如下:

class Solution {
    int height(TreeNode root) {
        return root == null ? -1 : 1 + height(root.left);
    }
    public int countNodes(TreeNode root) {
        int nodes = 0, h = height(root);
        while (root != null) {
            if (height(root.right) == h - 1) {
                nodes += 1 << h;
                root = root.right;
            } else {
                nodes += 1 << h-1;
                root = root.left;
            }
            h--;
        }
        return nodes;
    }
}

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