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operations_on_datastructures/inorder_successor_of_bst.cpp
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@ -1,27 +1,32 @@
/** /**
* @file * @file
* @brief An implementation for finding [Inorder successor of binary search * @brief An implementation for finding the [Inorder successor of a binary search
* tree](https://www.youtube.com/watch?v=5cPbNCrdotA&t=904s) Inorder successor * tree](https://www.youtube.com/watch?v=5cPbNCrdotA&t=904s) Inorder successor
* of a node is the next node in Inorder traversal of the Binary Tree. Inorder * 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. * Successor is NULL for the last node in Inorder traversal.
* *
* ### Case 1 : The given node has right node/subtree * ### Case 1
*
* The given node has right node/subtree
*
* In this case the left most deepest node in the right subtree will come * 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. * just after the given node as we go to left deep in inorder.
* - Go deep to left most node in right subtree. * - Go deep to left most node in right subtree.
* OR, we can also say in case if BST, find the minimum of the subtree * OR, we can also say in case if BST, find the minimum of the subtree
* for a given node. * for a given node.
* *
* ### Case 2 : The given node does not have a right node/subtree * ### Case 2
* *
* #### Method 1 : Use parent pointer (store the address of parent nodes) * 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 right subtree, and we already visited the node * If a node does not have right subtree, and we already visited the node
* itself, then the next node will be its parent node according to inorder * 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 * 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 * unvisited. In other words, go to the nearest ancestor for which given node
* would be in left subtree. * would be in left subtree.
* *
* #### Method 2 : Search from the root node * #### Method 2: Search from the root node
* In case if there is no link to the parent, we need to walk the tree * In case if there is no link to the parent, we need to walk the tree
* starting from the root node to the given node, by doing so, we are visiting * 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 * every ancestor of the given node. In order successor would be the deepest
@ -31,32 +36,44 @@
* */ * */
#include <cassert> /// For assert #include <cassert> /// For assert
#include <iostream> /// For IO Operations #include <iostream> /// For IO Operations
#include <vector> /// For std::vector #include <vector> /// For std::vector
namespace binary_search_tree {
/** /**
* @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
* tree](https://www.youtube.com/watch?v=5cPbNCrdotA) implementation
*/
namespace inorder_traversal_of_bst {
/**
* @brief A Node structure representing a single node in bst. * @brief A Node structure representing a single node in bst.
*/ */
class Node { class Node {
public: public:
int64_t data; ///< The key/value of the node int64_t data; ///< The key/value of the node
Node *left; ///< Pointer to Left child Node *left; ///< Pointer to Left child
Node *right; ///< Pointer to right child Node *right; ///< Pointer to right child
}; };
/** /**
* @brief Allocates a new node in heap for given data and returns it's pointer. * @brief Allocates a new node in heap for given data and returns it's pointer.
* @param data Data for the node. * @param data Data for the node.
* @returns A pointer to the newly allocated Node. * @returns A pointer to the newly allocated Node.
* */ * */
Node *makeNode(int64_t data) { Node *makeNode(int64_t data) {
Node *node = new Node(); Node *node = new Node();
node->data = data; ///< setting data for node node->data = data; ///< setting data for node
node->left = nullptr; ///< setting left child as null node->left = nullptr; ///< setting left child as null
node->right = nullptr; ///< setting right child as null node->right = nullptr; ///< setting right child as null
return node; return node;
} }
/** /**
* @brief Inserts the given data in BST while maintaining the properties of BST. * @brief Inserts the given data in BST while maintaining the properties of BST.
@ -64,16 +81,16 @@ Node *makeNode(int64_t data) {
* @param data Data to be inserted. * @param data Data to be inserted.
* @returns Node* Pointer to the root node. * @returns Node* Pointer to the root node.
* */ * */
Node *Insert(Node *root, int64_t data) { Node *Insert(Node *root, int64_t data) {
if (root == nullptr) { if (root == nullptr) {
root = makeNode(data); root = makeNode(data);
} else if (data <= root->data) { } else if (data <= root->data) {
root->left = Insert(root->left, data); root->left = Insert(root->left, data);
} else { } else {
root->right = Insert(root->right, data); root->right = Insert(root->right, data);
} }
return root; return root;
} }
/** /**
* @brief Searches the given data in BST and returns the pointer to the node * @brief Searches the given data in BST and returns the pointer to the node
@ -82,34 +99,65 @@ Node *Insert(Node *root, int64_t data) {
* @param data Data to be Searched. * @param data Data to be Searched.
* @returns Node* pointer to the found node * @returns Node* pointer to the found node
* */ * */
Node *getNode(Node *root, int64_t data) { Node *getNode(Node *root, int64_t data) {
if (root == nullptr) { if (root == nullptr) {
return nullptr; return nullptr;
} else if (root->data == data) { } else if (root->data == data) {
return root; return root;
} else if (data > root->data) { } else if (data > root->data) {
/// recursive call /// recursive call
return getNode(root->right, data); return getNode(root->right, data);
} else { } else {
/// recursive call /// recursive call
return getNode(root->left, data); return getNode(root->left, data);
} }
} }
/** /**
* @brief Finds and return the minimum node in BST. * @brief Finds and return the minimum node in BST.
* @param root A pointer to root node. * @param root A pointer to root node.
* @returns Node* Pointer to the found node * @returns Node* Pointer to the found node
* */ * */
Node *findMinNode(Node *root) { Node *findMinNode(Node *root) {
if (root == nullptr) { if (root == nullptr) {
return root; return root;
} }
while (root->left != nullptr) { while (root->left != nullptr) {
root = root->left; root = root->left;
} }
return root; 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 Search from the root node as we need to walk the tree starting from * @brief Search from the root node as we need to walk the tree starting from
@ -122,69 +170,41 @@ Node *findMinNode(Node *root) {
* successor. * successor.
* @returns Node pointer to the inorder successor node. * @returns Node pointer to the inorder successor node.
* */ * */
Node *getInorderSuccessor(Node *root, int64_t data) { Node *getInorderSuccessor(Node *root, int64_t data) {
Node *current = getNode(root, data); Node *current = getNode(root, data);
if (current == nullptr) if (current == nullptr) {
return nullptr; return nullptr;
}
// Case - 1 // Case - 1
if (current->right != nullptr) { if (current->right != nullptr) {
return findMinNode(current->right); return findMinNode(current->right);
} }
// case - 2 // case - 2
else { else {
Node *successor = nullptr; Node *successor = nullptr;
Node *ancestor = root; Node *ancestor = root;
while (ancestor != current && ancestor != nullptr) { while (ancestor != current && ancestor != nullptr) {
// This means my current node is in left of the root node // This means my current node is in left of the root node
if (current->data < ancestor->data) { if (current->data < ancestor->data) {
successor = ancestor; successor = ancestor;
ancestor = ancestor->left; // keep going left ancestor = ancestor->left; // keep going left
} else { } else {
ancestor = ancestor->right; ancestor = ancestor->right;
}
}
return successor; // Nodes with maximum vales will not have a successor
} }
} }
return successor; // Nodes with maximum vales will not have a successor } // namespace inorder_traversal_of_bst
} } // namespace operations_on_datastructures
}
/**
* @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;
}
} // namespace binary_search_tree
/** /**
* @brief class encapsulating the necessary test cases * @brief class encapsulating the necessary test cases
*/ */
class TestCases { class TestCases {
private: private:
/** /**
* @brief A function to print given message on console. * @brief A function to print given message on console.
* @tparam T Type of the given message. * @tparam T Type of the given message.
@ -196,7 +216,7 @@ class TestCases {
std::cout << "[TESTS] : ---> " << msg << std::endl; std::cout << "[TESTS] : ---> " << msg << std::endl;
} }
public: public:
/** /**
* @brief Executes test cases * @brief Executes test cases
* @returns void * @returns void
@ -218,8 +238,8 @@ class TestCases {
* @returns void * @returns void
* */ * */
void testCase_1() { void testCase_1() {
const binary_search_tree::Node *expectedOutput = const operations_on_datastructures::inorder_traversal_of_bst::Node *expectedOutput =
nullptr; ///< Expected output of this test nullptr; ///< Expected output of this test
log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"); log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
log("This is test case 1 : "); log("This is test case 1 : ");
@ -227,21 +247,21 @@ class TestCases {
log(" EDGE CASE : Printing inorder successor for last node in the " log(" EDGE CASE : Printing inorder successor for last node in the "
"BST, Output will be nullptr."); "BST, Output will be nullptr.");
binary_search_tree::Node *root = nullptr; operations_on_datastructures::inorder_traversal_of_bst::Node *root = nullptr;
std::vector<int64_t> node_data{ std::vector<int64_t> node_data{
20, 3, 5, 6, 2, 23, 45, 78, 21}; ///< Data to make nodes in BST 20, 3, 5, 6, 2, 23, 45, 78, 21}; ///< Data to make nodes in BST
root = binary_search_tree::makeBST(root, root = operations_on_datastructures::inorder_traversal_of_bst::makeBST(root,
node_data); ///< Adding nodes to BST node_data); ///< Adding nodes to BST
std::cout << "Inorder sequence is : "; std::cout << "Inorder sequence is : ";
binary_search_tree::printInorder( operations_on_datastructures::inorder_traversal_of_bst::printInorder(
root); ///< Printing inorder to cross-verify. root); ///< Printing inorder to cross-verify.
std::cout << std::endl; std::cout << std::endl;
binary_search_tree::Node *inorderSuccessor = operations_on_datastructures::inorder_traversal_of_bst::Node *inorderSuccessor =
binary_search_tree::getInorderSuccessor( operations_on_datastructures::inorder_traversal_of_bst::getInorderSuccessor(
root, 78); ///< The inorder successor node for given data root, 78); ///< The inorder successor node for given data
log("Checking assert expression..."); log("Checking assert expression...");
assert(inorderSuccessor == expectedOutput); assert(inorderSuccessor == expectedOutput);
@ -265,21 +285,21 @@ class TestCases {
log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"); log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
log("This is test case 2 : "); log("This is test case 2 : ");
binary_search_tree::Node *root = nullptr; operations_on_datastructures::inorder_traversal_of_bst::Node *root = nullptr;
std::vector<int64_t> node_data{ std::vector<int64_t> node_data{
20, 3, 5, 6, 2, 23, 45, 78, 21}; ///< Data to make nodes in BST 20, 3, 5, 6, 2, 23, 45, 78, 21}; ///< Data to make nodes in BST
root = binary_search_tree::makeBST(root, root = operations_on_datastructures::inorder_traversal_of_bst::makeBST(root,
node_data); ///< Adding nodes to BST node_data); ///< Adding nodes to BST
std::cout << "Inorder sequence is : "; std::cout << "Inorder sequence is : ";
binary_search_tree::printInorder( operations_on_datastructures::inorder_traversal_of_bst::printInorder(
root); ///< Printing inorder to cross-verify. root); ///< Printing inorder to cross-verify.
std::cout << std::endl; std::cout << std::endl;
binary_search_tree::Node *inorderSuccessor = operations_on_datastructures::inorder_traversal_of_bst::Node *inorderSuccessor =
binary_search_tree::getInorderSuccessor( operations_on_datastructures::inorder_traversal_of_bst::getInorderSuccessor(
root, 20); ///< The inorder successor node for given data root, 20); ///< The inorder successor node for given data
log("Checking assert expression..."); log("Checking assert expression...");
assert(inorderSuccessor->data == expectedOutput); assert(inorderSuccessor->data == expectedOutput);
@ -303,22 +323,22 @@ class TestCases {
log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"); log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
log("This is test case 3 : "); log("This is test case 3 : ");
binary_search_tree::Node *root = nullptr; operations_on_datastructures::inorder_traversal_of_bst::Node *root = nullptr;
std::vector<int64_t> node_data{ std::vector<int64_t> node_data{
89, 67, 32, 56, 90, 123, 120, 89, 67, 32, 56, 90, 123, 120,
110, 115, 6, 78, 7, 10}; ///< Data to make nodes in BST 110, 115, 6, 78, 7, 10}; ///< Data to make nodes in BST
root = binary_search_tree::makeBST(root, root = operations_on_datastructures::inorder_traversal_of_bst::makeBST(root,
node_data); ///< Adding nodes to BST node_data); ///< Adding nodes to BST
std::cout << "Inorder sequence is : "; std::cout << "Inorder sequence is : ";
binary_search_tree::printInorder( operations_on_datastructures::inorder_traversal_of_bst::printInorder(
root); ///< Printing inorder to cross-verify. root); ///< Printing inorder to cross-verify.
std::cout << std::endl; std::cout << std::endl;
binary_search_tree::Node *inorderSuccessor = operations_on_datastructures::inorder_traversal_of_bst::Node *inorderSuccessor =
binary_search_tree::getInorderSuccessor( operations_on_datastructures::inorder_traversal_of_bst::getInorderSuccessor(
root, 90); ///< The inorder successor node for given data root, 90); ///< The inorder successor node for given data
log("Checking assert expression..."); log("Checking assert expression...");
assert(inorderSuccessor->data == expectedOutput); assert(inorderSuccessor->data == expectedOutput);
@ -350,18 +370,18 @@ static void test() {
int main(int argc, char *argv[]) { int main(int argc, char *argv[]) {
test(); /// run self-test implementations test(); /// run self-test implementations
binary_search_tree::Node *root = nullptr; ///< root node of the bst operations_on_datastructures::inorder_traversal_of_bst::Node *root = nullptr; ///< root node of the bst
std::vector<int64_t> node_data{3, 4, 5, std::vector<int64_t> node_data{3, 4, 5,
89, 1, 2}; ///< Data to add nodes in BST 89, 1, 2}; ///< Data to add nodes in BST
int64_t targetElement = 4; ///< An element to find inorder successor for. int64_t targetElement = 4; ///< An element to find inorder successor for.
root = binary_search_tree::makeBST(root, node_data); ///< Making BST root = operations_on_datastructures::inorder_traversal_of_bst::makeBST(root, node_data); ///< Making BST
binary_search_tree::Node *inorderSuccessor = operations_on_datastructures::inorder_traversal_of_bst::Node *inorderSuccessor =
binary_search_tree::getInorderSuccessor(root, targetElement); operations_on_datastructures::inorder_traversal_of_bst::getInorderSuccessor(root, targetElement);
std::cout << "In-order sequence is : "; std::cout << "In-order sequence is : ";
binary_search_tree::printInorder(root); operations_on_datastructures::inorder_traversal_of_bst::printInorder(root);
std::cout << std::endl; std::cout << std::endl;
if (inorderSuccessor == nullptr) { if (inorderSuccessor == nullptr) {