Validate BST

refer to : https://www.algoexpert.io/questions/Validate%20BST

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1. Problem statement.

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

A valid 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 or equal to the node's key.
• Both the left and right subtrees must also be binary search trees.

2. Analysis.

          10              10 is in (-inf, inf)

      /       \

     5         15.     5 is in (-inf, 10).  maxValue = 10       15 is in (10, inf)   minValue = 10

  /   \      /   \

2      5  13    22.      2 is in(minValue,5).   5 is in [5, 10).     13 is in (minValue, 15).  22 is in [15, maxValue)

3. code.  O(n) time || O(d) space, d is the depth of the BST.

class BST:
    def __init__(self, value):
        self.value = value
        self.left = None
        self.right = None


def validateBst(tree):
    return helper(tree, float("-inf"), float("inf"))
    
def helper(tree, minValue, maxValue):
    if tree is None:
        return True
    if tree.value < minValue or tree.value >= maxValue:
        return False
    leftIsValid = helper(tree.left, minValue, tree.value)
    return leftIsValid and helper(tree.right, tree.value, maxValue)

import java.util.*;

class Program {
  public static boolean validateBst(BST tree) {
    return helper(tree, Integer.MIN_VALUE,Integer.MAX_VALUE);
  }
    public static boolean helper(BST tree, int minValue, int maxValue){
        if(tree.value < minValue || tree.value >= maxValue){
            return false;
        }
        if(tree.left != null && !helper(tree.left, minValue, tree.value)){
            return false;
        }
        if(tree.right != null && !helper(tree.right, tree.value, maxValue)){
            return false;
        }
        return true;
    }

  static class BST {
    public int value;
    public BST left;
    public BST right;

    public BST(int value) {
      this.value = value;
    }
  }
}