# 03192020

Given a binary tree, determine if it is a valid binary search tree (BST).

Assume a BST is defined as follows:

The left subtree of a node contains only nodes with keys less than the node's key.
The right subtree of a node contains only nodes with keys greater than the node's key.
Both the left and right subtrees must also be binary search trees.

10
/\
5 18
/\ /\
2 7 15 20

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public boolean isValidBST(TreeNode root) {
        return helper(root, Integer.MIN_VALUE, Integer.MAX_VALUE);
    }
    
    public boolean helper(TreeNode root, long min, long max) {
        if (root == null) return true;
        if (root.val >= max || root.val <= min) return false;
        return helper(root.left, min, root.val) && helper(root.right, root.val, max);
    }
}

min =    
max = 5

public List<Integer> inorderTraversal(TreeNode root) {
    List<Integer> list = new ArrayList<>();
    if(root == null) return list;
    Stack<TreeNode> stack = new Stack<>();
    while(root != null || !stack.empty()){
        while(root != null){
            stack.push(root);
            root = root.left;
        }
        root = stack.pop();
        list.add(root.val);
        root = root.right;
        
    }
    return list;
}

public boolean isValidBST(TreeNode root) {
   if (root == null) return true;
   Stack<TreeNode> stack = new Stack<>();
   TreeNode pre = null;
   while (root != null || !stack.isEmpty()) {
      while (root != null) {
         stack.push(root);
         root = root.left;
      }
      root = stack.pop();
      if(pre != null && root.val <= pre.val) return false;
      pre = root;
      root = root.right;
   }
   return true;
}

10
/\
5 18
/\ /\
2 7 15 20

stack : 10 -> 5 -> 2

root: 2
pre: null

stack : 10 -> 5
root: null
pre: 2

stack : 10
root: 7
pre: 5

public boolean isValidBST(TreeNode root) {
   if (root == null) return true;
   Stack<TreeNode> stack = new Stack<>();
   TreeNode pre = null;
   while (root != null || !stack.isEmpty()) {
      while (root != null) {
         stack.push(root);
         root = root.left;
      }
      root = stack.pop();
      if(pre != null && root.val <= pre.val) return false;
      pre = root;
      root = root.right;
   }
   return true;
}