LeetCode 530. Minimum Absolute Difference in BST（二叉搜索树的最小绝对差）

题目描述

Given a binary search tree with non-negative values, find the minimum absolute difference between values of any two nodes.

Example:

Input:

   1
    \
     3
    /
   2

Output:
1

Explanation:
The minimum absolute difference is 1, which is the difference between 2 and 1 (or between 2 and 3).

Note: There are at least two nodes in this BST.

解法一

思路

既然是要找结点值之间最小的差的绝对值，那就是对每个结点值找到与其最相近的结点值，然后求差了。设想如果是一个有序数组的话，这样的最小值就是按顺序后一个元素与前一个元素的差的最小值了。看到BST第一反应就是BST的中序遍历结果是有序数组，正好对应上了，那就是中序遍历时，求当前结点与前一结点的差，差的最小值就是结果了。

Python

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None


class Solution:
    def getMinimumDifference(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """
        result = sys.maxsize
        stack = []
        prev = None
        while root or stack:
            if root:
                stack.append(root)
                root = root.left
            else:
                node = stack.pop()
                if prev is not None:
                    result = min(result, node.val - prev)
                prev = node.val
                root = node.right
        return result

Java

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public int getMinimumDifference(TreeNode root) {
        int result = Integer.MAX_VALUE;
        Stack<TreeNode> stack = new Stack<>();
        Integer prev = null;
        while (root != null || !stack.empty()) {
            if (root != null) {
                stack.add(root);
                root = root.left;
            } else {
                TreeNode node = stack.pop();
                if (prev != null) {
                    result = Math.min(result, node.val - prev);
                }
                prev = node.val;
                root = node.right;
            }
        }
        return result;
    }
}

C++

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    int getMinimumDifference(TreeNode *root) {
        int result = INT_MAX;
        stack<TreeNode *> sta;
        int prev = 0;
        bool hasPrev = false;
        while (root != nullptr || !sta.empty()) {
            if (root != nullptr) {
                sta.push(root);
                root = root->left;
            } else {
                TreeNode *node = sta.top();
                sta.pop();
                if (hasPrev) {
                    result = min(result, node->val - prev);
                }
                prev = node->val;
                hasPrev = true;
                root = node->right;
            }
        }
        return result;
    }
};