538. Convert BST to Greater Tree

Given 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 sum of all keys greater than the original key in BST.

Example:

Input:
 The root of a Binary Search Tree like this:
              5
            /   \
           2     13


Output:
 The root of a Greater Tree like this:
             18
            /   \
          20     13

Analysis:

2 pass.

First pass just simple recursive tree scan to get the sum s of all nodes.

Second pass, in-order recursive traverse to do following at visit:

s = s - root.val;

root.val += s;

Complexity:

Time: O(N)

Space: O(logn)

Code:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    int s = 0;
    public TreeNode convertBST(TreeNode root) {
        if(root == null)
        {
            return null;
        }
        s = sum(root);
        traverse(root);
        return root;        
    }

    private int sum(TreeNode root)
    {
        if(root == null)
        {
            return 0;
        }
        return root.val + sum(root.left) + sum(root.right);
    }

    private void traverse(TreeNode root)
    {
        if(root == null){
            return;
        }
        traverse(root.left);
        s = s - root.val;
        root.val += s;
        traverse(root.right);
    }
}