[Algorithm] Check if a binary tree is binary search tree or not

What is Binary Search Tree (BST)

A binary tree in which for each node, value of all the nodes in left subtree is less or equal and value of all the nodes in right subtree is greater

The idea:

We can use set boundry for each node. We take C tree for example:

For root node, the B (bountry) = [MIN, MAX]

node 4: B = [MIN, 7] // cannot be greater than 7

node 1: B = [MIN, 4]

node 6: B = [4, 7] // cannot less than 4, but should less than 7.

node 9: B = [7, MAX] // cannot less than 7

function Node(val) {
  return {
    val,
    left: null,
    right: null
  };
}

function Tree() {
  return {
    root: null,
    addLeft(val, root) {
      const node = Node(val);
      root.left = node;
      return root.left;
    },
    addRight(val, root) {
      const node = Node(val);
      root.right = node;
      return root.right;
    }
  };
}

function isBinarySearchTree(root) {
  function helper(root, max, min) {
    if (root == null) {
      return true;
    }

    if (
      root.val >= min &&
      root.val <= max &&
      helper(root.left, root.val, min) &&
      helper(root.right, max, root.val)
    ) {
      return true;
    } else {
      return false;
    }
  }

  return helper(root, Number.MAX_VALUE, Number.MIN_VALUE);
}

const tree = new Tree();
const root = Node();
tree.root = root;
const ll1 = tree.addLeft(, tree.root);
tree.addRight(, tree.root);
const ll2 = tree.addLeft(, ll1);
const lr2 = tree.addRight(, ll1);
tree.addLeft(, ll2);
tree.addRight(, lr2);
tree.addRight(, tree.root);

/*
             10
           /    \
         5       16
       /   \
     4      7
    /        \
  1           11  

11 is greater than 10, which is false

*/

const res1 = isBinarySearchTree(root); // false
console.log(res1);

const tree2 = new Tree();
const root2 = Node();
tree2.root = root2;
const _ll1 = tree.addLeft(, tree.root);
tree.addRight(, tree.root);
tree.addLeft(, _ll1);
tree.addRight(, _ll1);

/*

          7
         / \
       4    9
      / \
     1   6
*/

const res2 = isBinarySearchTree(root2); // true
console.log(res2);