We have a binary search tree and a number N. Our task is to find the greatest number in the binary search tree that is less than or equal to N. Print the value of the element if it exists otherwise print -1.

Examples:For the above given binary search tree-

Input : N = 24 Output :result = 21 (searching for 24 will be like-5->12->21) Input : N = 4 Output : result = 3 (searching for 4 will be like-5->2->3)

We follow recursive approach for solving this problem. We start searching for element from root node. If we reach a leaf and its value is greater than N, element does not exist so return -1. Else if node’s value is less than or equal to N and right value is NULL or greater than N, then return the node value as it will be the answer.

Otherwise if node’s value is greater than N, then search for the element in the left subtree else search for the element in the right subtree by calling the same function by passing the left or right values accordingly.

// C++ code to find the largest value smaller // than or equal to N #include <bits/stdc++.h> using namespace std; struct Node { int key; Node* left, *right; }; // To create new BST Node Node* newNode(int item) { Node* temp = new Node; temp->key = item; temp->left = temp->right = NULL; return temp; } // To insert a new node in BST Node* insert(Node* node, int key) { // if tree is empty return new node if (node == NULL) return newNode(key); // if key is less then or grater then // node value then recur down the tree if (key < node->key) node->left = insert(node->left, key); else if (key > node->key) node->right = insert(node->right, key); // return the (unchanged) node pointer return node; } // function to find max value less then N int findMaxforN(Node* root, int N) { /* If leaf node reached and is greater than N*/ if (root->left == NULL && root->right == NULL && root->key > N) return -1; /* If node's value is less than N and right value is NULL or grater than then return the node value*/ if ((root->key <= N && root->right == NULL) || (root->key <= N && root->right->key > N)) return root->key; // if node value is grater than N search in the // left subtree if (root->key >= N) return findMaxforN(root->left, N); // if node value is less than N search in the // right subtree else return findMaxforN(root->right, N); } // Driver code int main() { int N = 4; // creating following BST /* 5 / \ 2 12 / \ / \ 1 3 9 21 / \ 19 25 */ Node* root = insert(root, 25); insert(root, 2); insert(root, 1); insert(root, 3); insert(root, 12); insert(root, 9); insert(root, 21); insert(root, 19); insert(root, 25); printf("%d", findMaxforN(root, N)); return 0; }

Output:

3

Time complexity = O(h) where h is height of BST.

**Reference : **

https://www.careercup.com/question?id=5765237112307712

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