#### Inorder Successor of Bst

N
```/**
* @file
* @brief An implementation for finding the [Inorder successor of a binary
* successor of a node is the next node in Inorder traversal of the Binary Tree.
* Inorder Successor is NULL for the last node in Inorder traversal.
* @details
* ### Case 1: The given node has the right node/subtree
*
*      * In this case, the left-most deepest node in the right subtree will
* come just after the given node as we go to left deep in inorder.
*      - Go deep to left most node in right subtree.
*        OR, we can also say in case if BST, find the minimum of the subtree
* for a given node.
*
* ### Case 2: The given node does not have a right node/subtree
*
* #### Method 1: Use parent pointer (store the address of parent nodes)
*      * If a node does not have the right subtree, and we already visited the
* node itself, then the next node will be its parent node according to inorder
* traversal, and if we are going to parent from left, then the parent would be
* unvisited.
*      * In other words, go to the nearest ancestor for which given node would
* be in left subtree.
*
* #### Method 2: Search from the root node
*      * In case if there is no link from a child node to the parent node, we
* need to walk down the tree starting from the root node to the given node, by
* doing so, we are visiting every ancestor of the given node.
*      * In order successor would be the deepest node in this path for which
* given node is in left subtree.
*
* @author [Nitin Sharma](https://github.com/foo290)
* */

#include <cassert>   ///  for assert
#include <iostream>  ///  for IO Operations
#include <vector>    ///  for std::vector

/**
* @namespace operations_on_datastructures
* @brief Operations on data structures
*/
namespace operations_on_datastructures {

/**
* @namespace inorder_successor_of_bst
* @brief Functions for the [Inorder successor of a binary search
*/
namespace inorder_traversal_of_bst {

/**
* @brief A Node structure representing a single node in BST
*/
class Node {
public:
int64_t data;  ///< The key/value of the node
Node *left;    ///< Pointer to Left child
Node *right;   ///< Pointer to right child
};

/**
* @brief Allocates a new node in heap for given data and returns it's pointer.
* @param data Data for the node.
* @returns A pointer to the newly allocated Node.
* */
Node *makeNode(int64_t data) {
Node *node = new Node();
node->data = data;      ///< setting data for node
node->left = nullptr;   ///< setting left child as null
node->right = nullptr;  ///< setting right child as null
return node;
}

/**
* @brief Inserts the given data in BST while maintaining the properties of BST.
* @param root Pointer to the root node of the BST
* @param data Data to be inserted.
* @returns Node* Pointer to the root node.
* */
Node *Insert(Node *root, int64_t data) {
if (root == nullptr) {
root = makeNode(data);
} else if (data <= root->data) {
root->left = Insert(root->left, data);
} else {
root->right = Insert(root->right, data);
}
return root;
}

/**
* @brief Searches the given data in BST and returns the pointer to the node
* containing that data.
* @param root Pointer to the root node of the BST
* @param data Data to be Searched.
* @returns Node* pointer to the found node
* */
Node *getNode(Node *root, int64_t data) {
if (root == nullptr) {
return nullptr;
} else if (root->data == data) {
return root;  /// Node found!
} else if (data > root->data) {
/// Traverse right subtree recursively as the given data is greater than
/// the data in root node, data must be present in right subtree.
return getNode(root->right, data);
} else {
/// Traverse left subtree recursively as the given data is less than the
/// data in root node, data must be present in left subtree.
return getNode(root->left, data);
}
}

/**
* @brief Finds and return the minimum node in BST.
* @param root A pointer to root node.
* @returns Node* Pointer to the found node
* */
Node *findMinNode(Node *root) {
if (root == nullptr) {
return root;
}
while (root->left != nullptr) {
root = root->left;
}
return root;
}

/**
* @brief Prints the BST in inorder traversal using recursion.
* @param root A pointer to the root node of the BST.
* @returns void
* */
void printInorder(Node *root) {
if (root == nullptr) {
return;
}

printInorder(root->left);  /// recursive call to left subtree
std::cout << root->data << " ";
printInorder(root->right);  /// recursive call to right subtree
}

/**
* @brief This function is used in test cases to quickly create BST containing
* large data instead of hard coding it in code. For a given root, this will add
* all the nodes containing data passes in data vector.
* @param root Pointer to the root node.
* @param data A vector containing integer values which are suppose to be
* inserted as nodes in BST.
* @returns Node pointer to the root node.
* */
Node *makeBST(Node *root, const std::vector<int64_t> &data) {
for (int64_t values : data) {
root = Insert(root, values);
}
return root;
}

/**
* @brief Inorder successor of a node is the next node in inorder traversal of
* the Binary Tree. This function takes the root node and the data of the node
* for which we have to find the inorder successor, and returns the inorder
* successor node.
* @details Search from the root node as we need to walk the tree starting from
* the root node to the given node, by doing so, we are visiting every ancestor
* of the given node. In order successor would be the deepest node in this path
* for which given node is in left subtree. Time complexity O(h)
* @param root A pointer to the root node of the BST
* @param data The data (or the data of node) for which we have to find inorder
* successor.
* @returns Node pointer to the inorder successor node.
* */
Node *getInorderSuccessor(Node *root, int64_t data) {
Node *current = getNode(root, data);
if (current == nullptr) {
return nullptr;
}

// Case - 1
if (current->right != nullptr) {
return findMinNode(current->right);
}
// case - 2
else {
Node *successor = nullptr;
Node *ancestor = root;

while (ancestor != current && ancestor != nullptr) {
// This means my current node is in left of the root node
if (current->data < ancestor->data) {
successor = ancestor;
ancestor = ancestor->left;  // keep going left
} else {
ancestor = ancestor->right;
}
}
return successor;  // Nodes with maximum vales will not have a successor
}
}

/**
* @brief This function clears the memory allocated to entire tree recursively.
* Its just for clean up the memory and not relevant to the actual topic.
* @param root Root node of the tree.
* @returns void
* */
void deallocate(Node *rootNode) {
if (rootNode == nullptr) {
return;
}
deallocate(rootNode->left);
deallocate(rootNode->right);
delete (rootNode);
}

}  // namespace inorder_traversal_of_bst
}  // namespace operations_on_datastructures

/**
* @brief class encapsulating the necessary test cases
*/
class TestCases {
private:
/**
* @brief A function to print given message on console.
* @tparam T Type of the given message.
* @returns void
* */
template <typename T>
void log(T msg) {
// It's just to avoid writing cout and endl
std::cout << "[TESTS] : ---> " << msg << std::endl;
}

public:
/**
* @brief Executes test cases
* @returns void
* */
void runTests() {
log("Running Tests...");

testCase_1();
testCase_2();
testCase_3();

log("Test Cases over!");
std::cout << std::endl;
}

/**
* @brief A test case contains edge case, printing inorder successor of last
* node.
* @returns void
* */
void testCase_1() {
const operations_on_datastructures::inorder_traversal_of_bst::Node
*expectedOutput = nullptr;  ///< Expected output of this test

log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
log("This is test case 1 : ");
log("Description:");
log("   EDGE CASE : Printing inorder successor for last node in the "
"BST, Output will be nullptr.");

operations_on_datastructures::inorder_traversal_of_bst::Node *root =
nullptr;
std::vector<int64_t> node_data{
20, 3, 5, 6, 2, 23, 45, 78, 21};  ///< Data to make nodes in BST

root = operations_on_datastructures::inorder_traversal_of_bst::makeBST(
root,
node_data);  ///< Adding nodes to BST

std::cout << "Inorder sequence is : ";
operations_on_datastructures::inorder_traversal_of_bst::printInorder(
root);  ///< Printing inorder to cross-verify.
std::cout << std::endl;

operations_on_datastructures::inorder_traversal_of_bst::Node
*inorderSuccessor = operations_on_datastructures::
inorder_traversal_of_bst::getInorderSuccessor(
root, 78);  ///< The inorder successor node for given data

log("Checking assert expression...");
assert(inorderSuccessor == expectedOutput);
log("Assertion check passed!");

operations_on_datastructures::inorder_traversal_of_bst::deallocate(
root);  /// memory cleanup!

log("[PASS] : TEST CASE 1 PASS!");
log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
}

/**
* @brief A test case which contains main list of 100 elements and sublist
* of 20.
* @returns void
* */
void testCase_2() {
const int expectedOutput = 21;  ///< Expected output of this test

log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
log("This is test case 2 : ");

operations_on_datastructures::inorder_traversal_of_bst::Node *root =
nullptr;
std::vector<int64_t> node_data{
20, 3, 5, 6, 2, 23, 45, 78, 21};  ///< Data to make nodes in BST

root = operations_on_datastructures::inorder_traversal_of_bst::makeBST(
root,
node_data);  ///< Adding nodes to BST

std::cout << "Inorder sequence is : ";
operations_on_datastructures::inorder_traversal_of_bst::printInorder(
root);  ///< Printing inorder to cross-verify.
std::cout << std::endl;

operations_on_datastructures::inorder_traversal_of_bst::Node
*inorderSuccessor = operations_on_datastructures::
inorder_traversal_of_bst::getInorderSuccessor(
root, 20);  ///< The inorder successor node for given data

log("Checking assert expression...");
assert(inorderSuccessor->data == expectedOutput);
log("Assertion check passed!");

operations_on_datastructures::inorder_traversal_of_bst::deallocate(
root);  /// memory cleanup!

log("[PASS] : TEST CASE 2 PASS!");
log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
}

/**
* @brief A test case which contains main list of 50 elements and sublist
* of 20.
* @returns void
* */
void testCase_3() {
const int expectedOutput = 110;  ///< Expected output of this test

log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
log("This is test case 3 : ");

operations_on_datastructures::inorder_traversal_of_bst::Node *root =
nullptr;
std::vector<int64_t> node_data{
89,  67,  32, 56, 90, 123, 120,
110, 115, 6,  78, 7,  10};  ///< Data to make nodes in BST

root = operations_on_datastructures::inorder_traversal_of_bst::makeBST(
root,
node_data);  ///< Adding nodes to BST

std::cout << "Inorder sequence is : ";
operations_on_datastructures::inorder_traversal_of_bst::printInorder(
root);  ///< Printing inorder to cross-verify.
std::cout << std::endl;

operations_on_datastructures::inorder_traversal_of_bst::Node
*inorderSuccessor = operations_on_datastructures::
inorder_traversal_of_bst::getInorderSuccessor(
root, 90);  ///< The inorder successor node for given data

log("Checking assert expression...");
assert(inorderSuccessor->data == expectedOutput);
log("Assertion check passed!");

operations_on_datastructures::inorder_traversal_of_bst::deallocate(
root);  /// memory cleanup!

log("[PASS] : TEST CASE 3 PASS!");
log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
}
};

/**
* @brief Self-test implementations
* @returns void
*/
static void test() {
TestCases tc;
tc.runTests();
}

/**
* @brief Main function
* @param argc commandline argument count (ignored)
* @param argv commandline array of arguments (ignored)
* @returns 0 on exit
*/
int main(int argc, char *argv[]) {
test();  // run self-test implementations

operations_on_datastructures::inorder_traversal_of_bst::Node *root =
nullptr;  ///< root node of the bst
std::vector<int64_t> node_data{3,  4, 5,
89, 1, 2};  ///< Data to add nodes in BST

int64_t targetElement = 4;  ///< An element to find inorder successor for.
root = operations_on_datastructures::inorder_traversal_of_bst::makeBST(
root, node_data);  ///< Making BST

operations_on_datastructures::inorder_traversal_of_bst::Node
*inorderSuccessor = operations_on_datastructures::
inorder_traversal_of_bst::getInorderSuccessor(root, targetElement);

std::cout << "In-order sequence is : ";
operations_on_datastructures::inorder_traversal_of_bst::printInorder(root);
std::cout << std::endl;

if (inorderSuccessor == nullptr) {
std::cout << "Inorder successor for last node is NULL" << std::endl;
} else {
std::cout << "Target element is : " << targetElement << std::endl;
std::cout << "Inorder successor for target element is : "
<< inorderSuccessor->data << std::endl;
}

deallocate(root);  /// memory cleanup!

return 0;
}
```