http://www.lintcode.com/en/problem/subtree-with-maximum-average/

Given a binary tree, find the subtree with maximum average. Return the root of the subtree.

Example Given a binary tree:

      1
    /   \
  -5     11
 / \    /  \
1   2  4    -2 

return the node 11.

解题：二叉树的一类题就是需要在二叉树的每个节点上存储一些信息，比如这道题就需要当前sum和size，好计算平均值。

/**
 * Definition of TreeNode:
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left, right;
 *     public TreeNode(int val) {
 *         this.val = val;
 *         this.left = this.right = null;
 *     }
 * }
 */


public class Solution {
    private class ResultType {
        public int sum, size;
        public ResultType(int sum, int size) {
            this.sum = sum;
            this.size = size;
        }
    }

    private TreeNode subtree = null;
    private ResultType subtreeResult = null;

    /**
     * @param root the root of binary tree
     * @return the root of the maximum average of subtree
     */
    public TreeNode findSubtree2(TreeNode root) {
        helper(root);
        return subtree;
    }

    private ResultType helper(TreeNode root) {
        if (root == null) {
            return new ResultType(0, 0);
        }

        ResultType left = helper(root.left);
        ResultType right = helper(root.right);
        //current node sum and subtree size
        ResultType result = new ResultType(
            left.sum + right.sum + root.val,
            left.size + right.size + 1
        );

        //update the average
        //subtreeResult.sum / subtreeResult.size < result.sum / result.size
        if (subtree == null ||
            subtreeResult.sum * result.size < result.sum * subtreeResult.size
        ) {
            subtree = root;
            subtreeResult = result;
        }
        return result;
    }
}