Subtree with Maximum Average

Important: using a/b < c/d => a*d < c*b to check, we don't need to do the type transfer

For the tree, if we need to get the max/min tree node, it is better to have a global variouable to remember it => traverse + divided conquer 

1) Traverse + Divided conquer version

/**
 * 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;
 *     }
 * }
 */
class ResultType {
    private int sum;
    private int size;
    public ResultType(int sum, int size) {
        this.sum = sum;
        this.size = size;
    }
    public int getSum() {
        return sum;
    }
    public int getSize() {
        return size;
    }
}

public class Solution {
    /**
     * @param root the root of binary tree
     * @return the root of the maximum average of subtree
     */
    private double maxAvg = Double.NEGATIVE_INFINITY;
    private TreeNode maxNode = null;
    
    public TreeNode findSubtree2(TreeNode root) {
        // Write your code here
        findMaxAvg(root);
        return maxNode;
    }
    
    ResultType findMaxAvg(TreeNode root) {
        if (root == null) {
            return new ResultType(0, 0);
        }
        
        ResultType left = findMaxAvg(root.left);
        ResultType right = findMaxAvg(root.right);
        
        int sum = left.getSum() + right.getSum() + root.val;
        int size = left.getSize() + right.getSize() + 1;
        double avg = sum / (double)size;
        if (avg > maxAvg) {
            maxAvg = avg;
            maxNode = root;
        }
        return new ResultType(sum, size);
    }
}

2) Divided Conquer 

/**
 * 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 {
    /**
     * @param root the root of binary tree
     * @return the root of the maximum average of subtree
     */
    private class ResultType {
        public int sum;
        public int nums;
        public int maxSum;
        public int maxNums;
        public TreeNode maxNode;
        public ResultType (int sum, int nums, int maxSum, int maxNums, TreeNode maxNode) {
            this.sum = sum;
            this.nums = nums;
            this.maxSum = maxSum;
            this.maxNums = maxNums;
            this.maxNode = maxNode;
        }
    }
    public TreeNode findSubtree2(TreeNode root) {
        // Write your code here
        if (root == null) {
            return root;
        }
        return findMaxAvg(root).maxNode;
    }
    
    private ResultType findMaxAvg(TreeNode root) {
        if (root == null) {
            return new ResultType(0, 0, Integer.MIN_VALUE, 0, root);
        }
        
        ResultType left = findMaxAvg(root.left);
        ResultType right = findMaxAvg(root.right);
        
        int sum = left.sum + right.sum + root.val;
        int nums = left.nums + right.nums + 1;
        int maxSum = sum;
        int maxNums = nums;
        TreeNode maxNode = root;
        
        if (maxSum * left.maxNums < left.maxSum * maxNums) {
            maxSum = left.maxSum;
            maxNums = left.maxNums;
            maxNode = left.maxNode;
        }
        
        if (maxSum * right.maxNums < right.maxSum * maxNums) {
            maxSum = right.maxSum;
            maxNums = right.maxNums;
            maxNode = right.maxNode;
        }
        return new ResultType(sum, nums, maxSum, maxNums, maxNode);
    }
}