*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 2hnodes inclusive at the last level h.

思路：

Full v.s. Complete Binary Trees

According to wikipedia

• A full binary tree (sometimes proper binary tree or 2-tree) is a tree in which every node other than the leaves has two children. 
• A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible. 

Steps to solve this problem:
1) get the height of left-most part
2) get the height of right-most part
3) when they are equal, the # of nodes = 2^h -1
4) when they are not equal, recursively get # of nodes from left&right sub-trees

Time complexity is O(h^2).

代码：

public int countNodes(TreeNode root) {
    if(root==null)
        return 0;
 
    int left = getLeftHeight(root)+1;    
    int right = getRightHeight(root)+1;
 
    if(left==right){
        return (2<<(left-1))-1;
    }else{
        return countNodes(root.left)+countNodes(root.right)+1;
    }
}
 
public int getLeftHeight(TreeNode n){
    if(n==null) return 0;
 
    int height=0;
    while(n.left!=null){
        height++;
        n = n.left;
    }
    return height;
}
 
public int getRightHeight(TreeNode n){
    if(n==null) return 0;
 
    int height=0;
    while(n.right!=null){
        height++;
        n = n.right;
    }
    return height;
}

reference：http://www.programcreek.com/2014/06/leetcode-count-complete-tree-nodes-java/