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operations_on_datastructures/inorder_successor_of_bst.cpp
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@ -1,186 +1,190 @@
/** /**
* @file * @file
* @brief An implementation for finding [Inorder successor of binary search tree](https://www.youtube.com/watch?v=5cPbNCrdotA&t=904s) * @brief An implementation for finding [Inorder successor of binary search
* Inorder 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. * 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
* 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 just after the given node as we go to left * In this case the left most deepest node in the right subtree will come
* 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 for a given node. * 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 * ### Case 2 : The given node does not have a right node/subtree
* *
* #### Method 1 : Use parent pointer (store the address of parent nodes) * #### 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 itself, * If a node does not have right subtree, and we already visited the node
* then the next node will be its parent node according to inorder traversal, and if we are going to parent from left, * itself, then the next node will be its parent node according to inorder
* then the parent would be unvisited. In other words, go to the nearest ancestor for which given node would be in left subtree. * 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 * #### Method 2 : Search from the root node
* 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, * In case if there is no link to the parent, we need to walk the tree
* by doing so, we are visiting every ancestor of the given node. In order successor would be the deepest node in * starting from the root node to the given node, by doing so, we are visiting
* this path for which given node is in left subtree. * 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) * @author [Nitin Sharma](https://github.com/foo290)
* */ * */
#include <cassert> /// For assert
#include <iostream> /// For IO Operations #include <iostream> /// For IO Operations
#include <vector> /// For std::vector #include <vector> /// For std::vector
#include <cassert> /// For assert
namespace binary_search_tree { namespace binary_search_tree {
/** /**
* @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.
* @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 Inserts the given data in BST while maintaining the properties of BST. * @brief Searches the given data in BST and returns the pointer to the node
* @param root Pointer to the root node of the BST * containing that data.
* @param data Data to be inserted. * @param root Pointer to the root node of the BST
* @returns Node* Pointer to the root node. * @param data Data to be Searched.
* */ * @returns Node* pointer to the found node
Node *Insert(Node *root, int64_t data) { * */
if (root == nullptr) { Node *getNode(Node *root, int64_t data) {
root = makeNode(data); if (root == nullptr) {
} else if (data <= root->data) { return nullptr;
root->left = Insert(root->left, data); } else if (root->data == data) {
} else { return root;
root->right = Insert(root->right, data); } else if (data > root->data) {
} /// recursive call
return getNode(root->right, data);
} else {
/// recursive call
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; return root;
} }
while (root->left != nullptr) {
/** root = root->left;
* @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;
}
else if (data > root->data) {
/// recursive call
return getNode(root->right, data);
}
else {
/// recursive call
return getNode(root->left, data);
}
} }
return root;
}
/** /**
* @brief Finds and return the minimum node in BST. * @brief Search from the root node as we need to walk the tree starting from
* @param root A pointer to root node. * the root node to the given node, by doing so, we are visiting every ancestor
* @returns Node* Pointer to the found node * 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)
Node *findMinNode(Node *root) { *
if (root == nullptr) { * @param root A pointer to the root node of the BST
return root; * @param data The data (or the data of node) for which we have to find inorder
} * successor.
while (root->left != nullptr) { * @returns Node pointer to the inorder successor node.
root = root->left; * */
} Node *getInorderSuccessor(Node *root, int64_t data) {
return root; 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) {
* @brief Search from the root node as we need to walk the tree starting from the root node to the given node, // This means my current node is in left of the root node
* by doing so, we are visiting every ancestor of the given node. if (current->data < ancestor->data) {
* In order successor would be the deepest node in this path for which given node is in left subtree. successor = ancestor;
* Time complexity O(h) ancestor = ancestor->left; // keep going left
* } else {
* @param root A pointer to the root node of the BST ancestor = ancestor->right;
* @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
} }
return successor; // Nodes with maximum vales will not have a successor
} }
}
/** /**
* @brief Prints the BST in inorder traversal using recursion. * @brief Prints the BST in inorder traversal using recursion.
* @param root A pointer to the root node of the BST. * @param root A pointer to the root node of the BST.
* @returns void * @returns void
* */ * */
void printInorder(Node *root) { void printInorder(Node *root) {
if (root == nullptr) return; if (root == nullptr)
return;
printInorder(root->left); /// recursive call to left subtree printInorder(root->left); /// recursive call to left subtree
std::cout << root->data << " "; std::cout << root->data << " ";
printInorder(root->right); /// recursive call to right subtree 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 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 } // 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.
@ -192,7 +196,7 @@ private:
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
@ -209,35 +213,42 @@ public:
} }
/** /**
* @brief A test case contains edge case, printing inorder successor of last node. * @brief A test case contains edge case, printing inorder successor of last
* node.
* @returns void * @returns void
* */ * */
void testCase_1() { void testCase_1() {
const binary_search_tree::Node *expectedOutput = nullptr; ///< Expected output of this test const binary_search_tree::Node *expectedOutput =
nullptr; ///< Expected output of this test
log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"); log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
log("This is test case 1 : "); log("This is test case 1 : ");
log("Description:"); log("Description:");
log(" EDGE CASE : Printing inorder successor for last node in the BST, Output will be nullptr."); log(" EDGE CASE : Printing inorder successor for last node in the "
"BST, Output will be nullptr.");
binary_search_tree::Node *root = nullptr; binary_search_tree::Node *root = nullptr;
std::vector<int64_t> node_data {20, 3, 5, 6, 2, 23, 45 , 78, 21}; ///< Data to make nodes in BST std::vector<int64_t> node_data{
20, 3, 5, 6, 2, 23, 45, 78, 21}; ///< Data to make nodes in BST
root = binary_search_tree::makeBST(root, node_data); ///< Adding nodes to BST root = binary_search_tree::makeBST(root,
node_data); ///< Adding nodes to BST
std::cout<<"Inorder sequence is : "; std::cout << "Inorder sequence is : ";
binary_search_tree::printInorder(root); ///< Printing inorder to cross-verify. binary_search_tree::printInorder(
std::cout<<std::endl; root); ///< Printing inorder to cross-verify.
std::cout << std::endl;
binary_search_tree::Node *inorderSuccessor = binary_search_tree::Node *inorderSuccessor =
binary_search_tree::getInorderSuccessor(root, 78); ///< The inorder successor node for given data binary_search_tree::getInorderSuccessor(
root, 78); ///< The inorder successor node for given data
log("Checking assert expression..."); log("Checking assert expression...");
assert(inorderSuccessor == expectedOutput); assert(inorderSuccessor == expectedOutput);
log("Assertion check passed!"); log("Assertion check passed!");
delete(inorderSuccessor); delete (inorderSuccessor);
delete(root); delete (root);
log("[PASS] : TEST CASE 1 PASS!"); log("[PASS] : TEST CASE 1 PASS!");
log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"); log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
@ -255,23 +266,27 @@ public:
log("This is test case 2 : "); log("This is test case 2 : ");
binary_search_tree::Node *root = nullptr; binary_search_tree::Node *root = nullptr;
std::vector<int64_t> node_data {20, 3, 5, 6, 2, 23, 45 , 78, 21}; ///< Data to make nodes in BST std::vector<int64_t> node_data{
20, 3, 5, 6, 2, 23, 45, 78, 21}; ///< Data to make nodes in BST
root = binary_search_tree::makeBST(root, node_data); ///< Adding nodes to BST root = binary_search_tree::makeBST(root,
node_data); ///< Adding nodes to BST
std::cout<<"Inorder sequence is : "; std::cout << "Inorder sequence is : ";
binary_search_tree::printInorder(root); ///< Printing inorder to cross-verify. binary_search_tree::printInorder(
std::cout<<std::endl; root); ///< Printing inorder to cross-verify.
std::cout << std::endl;
binary_search_tree::Node *inorderSuccessor = binary_search_tree::Node *inorderSuccessor =
binary_search_tree::getInorderSuccessor(root, 20); ///< The inorder successor node for given data binary_search_tree::getInorderSuccessor(
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);
log("Assertion check passed!"); log("Assertion check passed!");
delete(inorderSuccessor); delete (inorderSuccessor);
delete(root); delete (root);
log("[PASS] : TEST CASE 2 PASS!"); log("[PASS] : TEST CASE 2 PASS!");
log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"); log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
@ -289,23 +304,28 @@ public:
log("This is test case 3 : "); log("This is test case 3 : ");
binary_search_tree::Node *root = nullptr; binary_search_tree::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 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 = binary_search_tree::makeBST(root, node_data); ///< Adding nodes to BST root = binary_search_tree::makeBST(root,
node_data); ///< Adding nodes to BST
std::cout<<"Inorder sequence is : "; std::cout << "Inorder sequence is : ";
binary_search_tree::printInorder(root); ///< Printing inorder to cross-verify. binary_search_tree::printInorder(
std::cout<<std::endl; root); ///< Printing inorder to cross-verify.
std::cout << std::endl;
binary_search_tree::Node *inorderSuccessor = binary_search_tree::Node *inorderSuccessor =
binary_search_tree::getInorderSuccessor(root, 90); ///< The inorder successor node for given data binary_search_tree::getInorderSuccessor(
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);
log("Assertion check passed!"); log("Assertion check passed!");
delete(inorderSuccessor); delete (inorderSuccessor);
delete(root); delete (root);
log("[PASS] : TEST CASE 3 PASS!"); log("[PASS] : TEST CASE 3 PASS!");
log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"); log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
@ -331,28 +351,29 @@ 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 binary_search_tree::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 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. int64_t targetElement = 4; ///< An element to find inorder successor for.
root = binary_search_tree::makeBST(root, node_data); ///< Making BST root = binary_search_tree::makeBST(root, node_data); ///< Making BST
binary_search_tree::Node *inorderSuccessor = binary_search_tree::Node *inorderSuccessor =
binary_search_tree::getInorderSuccessor(root, targetElement); binary_search_tree::getInorderSuccessor(root, targetElement);
std::cout<<"In-order sequence is : "; std::cout << "In-order sequence is : ";
binary_search_tree::printInorder(root); binary_search_tree::printInorder(root);
std::cout<<std::endl; std::cout << std::endl;
if (inorderSuccessor == nullptr) { if (inorderSuccessor == nullptr) {
std::cout<<"Inorder successor for last node is NULL"<<std::endl; std::cout << "Inorder successor for last node is NULL" << std::endl;
} } else {
else { std::cout << "Target element is : " << targetElement << std::endl;
std::cout<<"Target element is : "<<targetElement<<std::endl; std::cout << "Inorder successor for target element is : "
std::cout<<"Inorder successor for target element is : "<<inorderSuccessor->data; << inorderSuccessor->data;
} }
delete(inorderSuccessor); delete (inorderSuccessor);
delete(root); delete (root);
return 0; return 0;
} }