# How to find if given binary tree is a valid binary search tree?

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Assuming that each node contains a pointer to its left child, a pointer to its right child, and an integer, but not a pointer to its parent? How to find out if given tree is a binary tree or not.

posted Sep 28, 2013

Which language or just algorithm.

``````boolean isValidTree(Node *root)
{
if (root->left)
if (root->left->data > root->data) ||  (!isValidTree(root->left))
return FALSE;

if (root->right)
if (root->right->data < root->data) || (!isValidTree(root->right))
return FALSE;

return TRUE;
}
``````

Note that it is not enough to write a recursive function that just checks if the left and right nodes of each
node are less than and greater than the current node (and calls that recursively). You need to make sure that all the nodes of the subtree starting at your current node are within the valid range of values allowed
by the current node's ancestors. Therefore you can solve this recursively by writing a helper function that accepts a current node, the smallest allowed value, and the largest allowed value for that subtree.
Example for this:-

``````boolean isValid(Node root) {
return isValidHelper(root, Integer.MIN_VALUE,
Integer.MAX_VALUE);
}
boolean isValidHelper(Node curr, int min, int max) {
if (curr.left != null) {
if (curr.left.value < min ||
!isValidHelper(curr.left, min, curr.value))
return false;
}
if (curr.right != null) {
if (curr.right.value > max ||
!isValidHelper(curr.right, curr.value, max))
return false;
}
return true;
}
``````

The running time of this algorithm is O(n).

Is it (curr.left.value) ok in c.
because left is pointer.

if (curr.right.value > max || !isValidHelper(curr.right, curr.value, max))

If "curr.right.value" is greate than "max" then function "isValidHelper" will not be called because of short circuit .