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

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(10);
tree.root = root;
const ll1 = tree.addLeft(5, tree.root);
tree.addRight(16, tree.root);
const ll2 = tree.addLeft(4, ll1);
const lr2 = tree.addRight(7, ll1);
tree.addLeft(1, ll2);
tree.addRight(11, lr2);
tree.addRight(16, 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(7);
tree2.root = root2;
const _ll1 = tree.addLeft(4, tree.root);
tree.addRight(9, tree.root);
tree.addLeft(1, _ll1);
tree.addRight(6, _ll1);

/*

          7
         / \  
       4    9 
      / \
     1   6
*/

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