0783-Minimum Distance Between BST Nodes.md

Minimum Distance Between BST Nodes

Given a Binary Search Tree (BST) with the root node root,
return the minimum difference between the values of any two different nodes in the tree.

Example:

Input: root = [4,2,6,1,3,null,null]
Output: 1
Explanation:
Note that root is a TreeNode object, not an array.

The given tree [4,2,6,1,3,null,null] is represented by the following diagram:

          4
        /   \
      2      6
     / \    
    1   3  

while the minimum difference in this tree is 1, it occurs between node 1 and node 2, also between node 3 and node 2.

Note:

1. The size of the BST will be between 2 and 100.
2. The BST is always valid, each node's value is an integer, and each node's value is different.

Solution

O(n+n) Time, O(n) Space - In-Order Montonic Array Construction:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     public var val: Int
 *     public var left: TreeNode?
 *     public var right: TreeNode?
 *     public init(_ val: Int) {
 *         self.val = val
 *         self.left = nil
 *         self.right = nil
 *     }
 * }
 */
class Solution {
    func getMinimumDifference(_ root: TreeNode?) -> Int {
        var input : [Int] = []
        inOrder(root, &input)
        var result = Int.max
        for i in stride(from: 0, to: input.count-1, by: 1) {
            result = min(result, abs(input[i]-input[i+1]))
        }
        return result
    }
    
    func inOrder(_ node: TreeNode?, _ result: inout [Int]) {
        guard let node = node else { return }
        inOrder(node.left, &result)
        result.append(node.val)
        inOrder(node.right, &result)
    }
}

O(n) Time, O(1) Space - In-Order Traversal + Update:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     public var val: Int
 *     public var left: TreeNode?
 *     public var right: TreeNode?
 *     public init(_ val: Int) {
 *         self.val = val
 *         self.left = nil
 *         self.right = nil
 *     }
 * }
 */
class Solution {
    func getMinimumDifference(_ root: TreeNode?) -> Int {
        var prev : Int?, result = Int.max
        inOrder(root, &prev, &result)
        return result
    }
    
    func inOrder(_ node: TreeNode?, _ prev: inout Int?, _ result: inout Int) {
        guard let node = node else { return }
        inOrder(node.left, &prev, &result)
        if let prev = prev {
            result = min(result, abs(node.val-prev))
        }
        prev = node.val
        inOrder(node.right, &prev, &result)
    }
}