530. Minimum Absolute Difference in BST

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.

 暴力解法，但是会超时

 private readonly List<int> deltaList = new List<int>();

        private readonly List<int> sourceList = new List<int>();

        public int GetMinimumDifference(TreeNode root)
        {
            Chuck(root);
            int min = deltaList.Min();
            return min;
        }

        private void Chuck(TreeNode node)
        {
            if (node == null)
            {
                return;
            }

            int val = node.val;
            if (!sourceList.Contains(val))
            {
                foreach (var item in sourceList)
                {
                    var delta = Math.Abs(item - val);
                    if (!deltaList.Contains(delta))
                    {
                        deltaList.Add(delta);
                    }
                }
                sourceList.Add(val);
            }
            else
            {
                deltaList.Add(0);
            }
            Chuck(node.left);
            Chuck(node.right);
        }

 

https://www.cnblogs.com/grandyang/p/6540165.html

由于BST的左<根<右的性质可知，如果按照中序遍历会得到一个有序数组，那么最小绝对差肯定在相邻的两个节点值之间产生。

所以我们的做法就是对BST进行中序遍历，然后当前节点值和之前节点值求绝对差并更新结果res。

 https://anothercasualcoder.blogspot.com/2017/06/minimum-absolute-difference-in-bst-by.html

It is important to use the only crucial information in this problem: that we're dealing with a Binary-Search-Tree (BST). With that information in mind, remember that an In-Order traversal of the tree will give you all its elements in sorted order. If your tree for instance is:

  6

3  7

The In-Order traversal will give you 3,6,7. Now with that it becomes very easy to solve it:

a) Do an In-Order traversal passing in the previous value

b) The processing will consist of checking <current value> - <previous value> and keeping tracking of the min

Linear time, very fast as the response indicates. Code is down below - cheers! Marcelo

        public int GetMinimumDifference(TreeNode root)
        {
            int res = int.MaxValue ,pre = -1;
            Chuck(root,ref pre, ref res);
            return res;
        }

        private void Chuck(TreeNode node, ref int pre, ref int res)
        {
            if (node == null)
            {
                return;
            }

            Chuck(node.left, ref pre, ref res);
            if (pre != -1)
            {
                res = Math.Min(res, node.val - pre);
            }

            pre = node.val;
            Chuck(node.right, ref pre, ref res);
        }

Runtime: 104 ms, faster than 69.42% of C# online submissions forMinimum Absolute Difference in BST.

Memory Usage: 26.2 MB, less than 33.33% of C# online submissions forMinimum Absolute Difference in BST.

 注意事项

prev必须是ref类型，

[5,4,7]

   5

 /    \

4     7

 

不是ref类型，左边在递归的时候，退出时会丢失value

prev = -1
prev = -1
prev = 5
7 - 5 = 2
2

ref类型

prev = -1
prev = 4
5 - 4 = 1
prev = 5
7 - 5 = 2
1

 

使用全局变量

  private int pre = -1;

        private int res = int.MaxValue;

        public int GetMinimumDifference(TreeNode root)
        {
            Chuck(root);
            return res;
        }

        private void Chuck(TreeNode node)
        {
            if (node == null)
            {
                return;
            }

            Chuck(node.left);
            Output.WriteLine($"prev = {pre}");
            if (pre != -1)
            {
                int delta = node.val - pre;
                Output.WriteLine($"{node.val} - {pre} = {delta}");
                res = Math.Min(res, delta);
            }

            pre = node.val;
            Chuck(node.right);
        }

 

作者:Chuck Lu    GitHub