*count Complete Tree Nodes

Topic:

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, was completely filled, and all nodes As far left as possible. It can has between 1 and 2hnodes inclusive at the last level H.

Ideas:

Full v.s. Complete Binary Trees

According to Wikipedia

• A full binary tree (sometimes proper binary tree or 2-tree) are a tree in which every node other than the leaves have both ch Ildren.
• A complete binary tree was a binary tree in which every level, except possibly the last, was completely filled, and all node S is as far 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 is equal, the # of nodes = 2^h-1
4) when they is not equal, recursively get # of nodes from Left&right sub-trees

Time complexity is O (h^2).

Code:

1  Public intcountnodes (TreeNode root) {2     if(root==NULL)3         return0;4  5     intleft = Getleftheight (root) +1; 6     intright = Getrightheight (root) +1;7  8     if(left==Right ) {9         return(2<< (Left-1))-1;Ten}Else{ One         returnCountnodes (Root.left) +countnodes (root.right) +1; A     } - } -   the  Public intGetleftheight (TreeNode N) { -     if(n==NULL)return0; -   -     intHeight=0; +      while(n.left!=NULL){ -height++; +n =N.left; A     } at     returnheight; - } -   -  Public intGetrightheight (TreeNode N) { -     if(n==NULL)return0; -   in     intHeight=0; -      while(n.right!=NULL){ toheight++; +n =N.right; -     } the     returnheight; *}

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

*count Complete Tree Nodes