LeetCode_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.

下面是递归，结果是TimeOut

public int countNodes(TreeNode root) {
if(root == null) return 0;
return calNodes(root);
}
private int calNodes(TreeNode root){
if(root == null) return 0;

int count = 0;
count += calNodes(root.left) + calNodes(root.right);
return count;
}

下面是改进版本

如果从某节点一直向左的高度 = 一直向右的高度, 那么以该节点为root的子树一定是complete binary tree. 而 complete binary tree的节点数,可以用公式算出 2^h - 1. 如果高度不相等, 则递归调用 return countNode(left) + countNode(right) + 1.

public int countNodes(TreeNode root) {
if(root == null) return 0;

int left = getLeft(root)+1;
int right = getRight(root)+1;

if(left == right){
return (2<<(left-1))-1;
}else {
return countNodes(root.left)+countNodes(root.right)+1;
}

}
private int getLeft(TreeNode root){
int count = 0;
if(root == null) return 0;
while (root.left!=null) {
root = root.left;
count++;
}
return count;
}
private int getRight(TreeNode root){
int count =0;
if(root == null) return 0;
while(root.right !=null){
root = root.right;
count++;
}
return count;
}