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package g0501_0600.s0538_convert_bst_to_greater_tree;

// #Medium #Depth_First_Search #Tree #Binary_Tree #Binary_Search_Tree
// #2022_08_02_Time_1_ms_(88.41%)_Space_50_MB_(23.08%)

import com_github_leetcode.TreeNode;

/*
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
/**
 * 538 - Convert BST to Greater Tree\.
 *
 * Medium
 *
 * Given the `root` of a Binary Search Tree (BST), convert it to a Greater Tree such that every key of the original BST is changed to the original key plus the sum of all keys greater than the original key in BST.
 *
 * As a reminder, a _binary search tree_ is a tree that satisfies these constraints:
 *
 * *   The left subtree of a node contains only nodes with keys **less than** the node's key.
 * *   The right subtree of a node contains only nodes with keys **greater than** the node's key.
 * *   Both the left and right subtrees must also be binary search trees.
 *
 * **Example 1:**
 *
 * ![](https://assets.leetcode.com/uploads/2019/05/02/tree.png)
 *
 * **Input:** root = [4,1,6,0,2,5,7,null,null,null,3,null,null,null,8]
 *
 * **Output:** [30,36,21,36,35,26,15,null,null,null,33,null,null,null,8]
 *
 * **Example 2:**
 *
 * **Input:** root = [0,null,1]
 *
 * **Output:** [1,null,1]
 *
 * **Constraints:**
 *
 * *   The number of nodes in the tree is in the range [0, 104].
 * *   -104 <= Node.val <= 104
 * *   All the values in the tree are **unique**.
 * *   `root` is guaranteed to be a valid binary search tree.
 *
 * **Note:** This question is the same as 1038: [https://leetcode.com/problems/binary-search-tree-to-greater-sum-tree/](https://leetcode.com/problems/binary-search-tree-to-greater-sum-tree/)
**/
public class Solution {
    public TreeNode convertBST(TreeNode root) {
        if (root != null) {
            postOrder(root, 0);
        }
        return root;
    }

    private int postOrder(TreeNode node, int val) {
        int newVal = 0;
        if (node.right != null) {
            newVal += postOrder(node.right, val);
        }
        newVal += newVal == 0 ? val + node.val : node.val;
        node.val = newVal;
        if (node.left != null) {
            newVal = postOrder(node.left, newVal);
        }
        return newVal;
    }
}




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