package tree;

/**
 * Created by gouthamvidyapradhan on 08/05/2017.
 * <p>
 * Given a binary tree, find the largest subtree which is a Binary Search Tree (BST), where largest means subtree with largest number of nodes in it.
 * <p>
 * Note:
 * A subtree must include all of its descendants.
 * Here's an example:
 * 10
 * / \
 * 5  15
 * / \   \
 * 1   8   7
 * The Largest BST Subtree in this case is the highlighted one (5-1-8).
 * The return value is the subtree's size, which is 3.
 * <p>
 * Follow up:
 * Can you figure out ways to solve it with O(n) time complexity?
 * <p>
 * Solution: The below solution works with O(n). Validate the BST property from the leaf node and increment the count, as soon as a violation
 * of BST property is found terminate the count.
 */
public class LargestBSTSubtree {
    /**
     * Range class
     */
    private class Range {
        int min, max, count;

        Range(int min, int max, int count) {
            this.min = min;
            this.max = max;
            this.count = count;
        }
    }

    /**
     * TreeNode
     */
    public static class TreeNode {
        int val;
        TreeNode left;
        TreeNode right;

        TreeNode(int x) {
            val = x;
        }
    }

    /**
     * Count
     */
    private static int count = 0;

    /**
     * Main method
     *
     * @param args
     * @throws Exception
     */
    public static void main(String[] args) throws Exception {
        TreeNode root = new TreeNode(10);
        root.left = new TreeNode(9);
        root.left.left = new TreeNode(8);
        System.out.println(new LargestBSTSubtree().largestBSTSubtree(root));
    }

    /**
     * Largest subtree count
     *
     * @param root root node
     * @return count
     */
    public int largestBSTSubtree(TreeNode root) {
        getCount(root);
        return count;
    }

    /**
     * Get count
     *
     * @param node root node
     * @return Range
     */
    private Range getCount(TreeNode node) {
        if (node == null) return null;
        Range left = getCount(node.left);
        Range right = getCount(node.right);
        if (left == null && right == null) {
            count = Math.max(count, 1);
            return new Range(node.val, node.val, 1);
        } else if (left == null) {
            if (node.val < right.min && right.count != -1) //check for -1 ensures that there is no violation of BST property
                return countMaxAndBuildNewRange(right.count + 1, node.val, right.max);
        } else if (right == null) {
            if (node.val > left.max && left.count != -1)
                return countMaxAndBuildNewRange(left.count + 1, left.min, node.val);
        } else if (node.val > left.max && node.val < right.min && right.count != -1 && left.count != -1)
            return countMaxAndBuildNewRange(left.count + right.count + 1, left.min, right.max);
        return new Range(0, 0, -1); //violation of BST property
    }

    /**
     * Record max and build new range
     *
     * @param sum total sum
     * @param min min
     * @param max max
     * @return new Range
     */
    private Range countMaxAndBuildNewRange(int sum, int min, int max) {
        count = Math.max(count, sum);
        return new Range(min, max, sum);
    }
}