538 Convert BST to Greater Tree

538. Convert BST to Greater Tree

1. Question

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

2. Implementation

(1) DFS

思路: 规律比较明显，对于每个node，先处理右子树，累加右子树的和，然后更新当前node的值，再处理左子树

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public TreeNode convertBST(TreeNode root) {
        int[] sum = new int[1];
        convertBST(root, sum);
        return root;
    }

    public void convertBST(TreeNode node, int[] sum) {
        if (node == null) {
            return;
        }

        convertBST(node.right, sum);
        node.val += sum[0];
        sum[0] = node.val;
        convertBST(node.left, sum);
    }
}

3. Time & Space Complexity

DFS: 时间复杂度O(n), 空间复杂度: O(h)