# Validating A Binary Search Tree (BST) The logic behind validating a BST is :

• The in-order traversal of a binary search tree will always have the nodes in increasing order. Thus, given a tree we traverse it in an in-order manner and look at the sequence of nodes. If the nodes are in increasing order then the traversed tree is a valid Binary Search Tree.

Example : Consider a valid and an invalid BST as shown.

Inorder traversal of valid binary search tree : 3 5 6 7 10. ( The numbers are in ascending order )
Inorder traversal of an invalid binary search tree : 3 5 7 6 10. ( The numbers are not in ascending order )

Time Complexity of validating a BST with N nodes : O ( N ), as the in-order traversal visits each node of the binary search tree once, the time complexity is O ( N ).

C++ : Program for validating a BST

``````#include<iostream>
#include<vector>
using namespace std;

class Node {

public:
int data;
Node * left;
Node * right;
Node(int x) : data(x), left(NULL), right(NULL)
{}
Node(int x, Node* left_node, Node* right_node) : data(x), left(left_node), right(right_node)
{}
};

class Tree {

public:

vector<int> order;

/* The in-order traversal of a valid binary search tree
is always in increasing order (sorted) */
void InOrder (Node * node) {

if (node != NULL) {
InOrder(node->left);
order.push_back(node->data);
InOrder(node->right);
}
}

bool IsValidBST (Node * node) {

InOrder(node);
for (int i=1; i < order.size(); i++) {
if (order[i-1] > order[i])
return false;
}
return true;
}
};

int main() {

/*   5
/ \
1   7
/ \
6   8  */
Node node6(6), node8(8), node1(1);
Node node7(6, &node6, &node8);
Node root_node5(5, &node1, &node6);

Tree t;

/*  3
/
4   */
Node node4(4);
Node root_node3(3, &node4, nullptr);

/*   10
/  \
2    15
/  \
9   20 */

Node node9(9), node20(20), node2(2);
Node node15(15, &node9, &node20);
Node root_node10(10, &node2, &node15);

vector<Node> roots = { root_node5, root_node3, root_node10 };

for (auto root : roots) {
if (t.IsValidBST(&root)) {
cout << "Tree with root node (" << root.data << ") is a valid binary search tree" << endl;
} else {
cout << "Tree with root node (" << root.data << ") is not a valid binary search tree" << endl;
}
}
return 0;
}
``````

Output

``````Tree with root node (5) is a valid binary search tree
Tree with root node (3) is not a valid binary search tree
Tree with root node (10) is not a valid binary search tree
``````