Checking if a tree is binary search tree

Question

I am not able to understand how the Java function HERE (Please scroll to the very end of the page) checks if a tree is BST or not, as the code does not look like making using of min and max at all. I am copy pasting the code here as well

/** 
 Tests if a tree meets the conditions to be a 
 binary search tree (BST). Uses the efficient 
 recursive helper. 
*/ 
public boolean isBST2() { 
 return( isBST2(root, Integer.MIN_VALUE, Integer.MAX_VALUE) ); 
}
/** 
  Efficient BST helper -- Given a node, and min and max values, 
  recurs down the tree to verify that it is a BST, and that all 
  its nodes are within the min..max range. Works in O(n) time -- 
  visits each node only once. 
*/ 
private boolean isBST2(Node node, int min, int max) { 
  if (node==null) { 
    return(true); 
  } 
  else { 
   // left should be in range  min...node.data 
    boolean leftOk = isBST2(node.left, min, node.data);

    // if the left is not ok, bail out 
    if (!leftOk) return(false);

    // right should be in range node.data+1..max 
    boolean rightOk = isBST2(node.right, node.data+1, max);

    return(rightOk); 
  } 
} 

Answer 1

A tree is a BST if and only if the nodes of an inorder traversal are monotonic. The easiest way to think of this is that if the root has value n , then the left-hand branch should also be a BST whose nodes are at most n , and the right-hand side should be a BST whose nodes are at least n . If those conditions are satisfied then the tree as a whole is a BST.

That's exactly what your code nearly does. It checks that a tree is a BST with a given minimum a given maximum. It recursively calls itself by looking at the root node with value data , and then checks that the left-hand branch is a BST none of whose nodes exceeds data , and that the right-hand branch is a BST none of whose nodes is smaller than data .

But actually it doesn't quite do this... it misses out the min/max check! Perhaps you're supposed to add that yourself? Is this homework?

The place to add it would be in here:

if (node==null) { 
  return(true); 
}

You just need a couple of extra conditions for if node!=null ...

Answer 2

boolean checkBST(Node root) {
    return  c(root, Integer.MIN_VALUE, Integer.MAX_VALUE);
}

boolean c(Node n, int s, int b) {
    return n == null || (n.data > s && n.data < b && c(n.left, s, n.data) && c(n.right, n.data, b));
}