feat: add Recursive tree traversal techniques

DIRECTORY.md

@@ -278,6 +278,7 @@
   * [Pascal Triangle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/pascal_triangle.cpp)
   * [Postfix Evaluation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/postfix_evaluation.cpp)
   * [Primality Test](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/primality_test.cpp)
+  * [Recursive Tree Traversal](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/recursive_tree_traversal.cpp)
   * [Smallest Circle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/smallest_circle.cpp)
   * [Sparse Matrix](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/sparse_matrix.cpp)
   * [Spiral Print](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/spiral_print.cpp)

others/recursive_tree_traversal.cpp

@@ -0,0 +1,377 @@
+/******************************************************************************
+ * @file
+ * @brief Recursive version of Inorder, Preorder, and Postorder [Traversal of
+ * the Tree] (https://en.wikipedia.org/wiki/Tree_traversal)
+ *
+ * @details
+ *
+ * ### Iterative Inorder Traversal of a tree
+ * For traversing a (non-empty) binary tree in an inorder fashion, we must do
+ * these three things for every node n starting from the tree’s root:
+ *
+ * (L) Recursively traverse its left subtree. When this step is finished,
+ * we are back at n again.
+ * (N) Process n itself.
+ * (R) Recursively traverse its right subtree. When this step is finished,
+ * we are back at n again.
+ *
+ * In normal inorder traversal, we visit the left subtree before the right
+ * subtree. If we visit the right subtree before visiting the left subtree, it
+ * is referred to as reverse inorder traversal.
+ *
+ * ### Iterative Preorder Traversal of a tree
+ * For traversing a (non-empty) binary tree in a preorder fashion, we must do
+ * these three things for every node n starting from the tree’s root:
+ *
+ * (N) Process n itself.
+ * (L) Recursively traverse its left subtree. When this step is finished,
+ * we are back at n again.
+ * (R) Recursively traverse its right subtree. When this step is finished,
+ * we are back at n again.
+ *
+ * In normal preorder traversal, visit the left subtree before the right
+ * subtree. If we visit the right subtree before visiting the left subtree, it
+ * is referred to as reverse preorder traversal.
+ *
+ * ### Iterative Postorder Traversal of a tree
+ * For traversing a (non-empty) binary tree in a postorder fashion, we must do
+ * these three things for every node n starting from the tree’s root:
+ *
+ * (L) Recursively traverse its left subtree. When this step is finished,
+ * we are back at n again.
+ * (R) Recursively traverse its right subtree. When this step is finished,
+ * we are back at n again.
+ * (N) Process n itself.
+ *
+ * In normal postorder traversal, visit the left subtree before the right
+ * subtree. If we visit the right subtree before visiting the left subtree, it
+ * is referred to as reverse postorder traversal.
+ *
+ * @author [Lajat Manekar](https://github.com/Lazeeez)
+ *
+ ******************************************************************************/
+
+#include <cassert>   /// for assert
+#include <iostream>  /// for I/O operations
+#include <vector>    /// for vector
+
+/******************************************************************************
+ * @namespace others
+ * @brief Other algorithms
+ *******************************************************************************/
+namespace others {
+
+/******************************************************************************
+ * @namespace interpolation_search
+ * @brief Functions for the Recursive version of Inorder, Preorder, and
+ * Postorder [Traversal of the
+ * Tree](https://en.wikipedia.org/wiki/Tree_traversal) algorithm implementation
+ *******************************************************************************/
+namespace recursive_tree_traversals {
+
+/******************************************************************************
+ * @brief The structure to hold Nodes of the tree.
+ * @param data Value that will be stored in the node.
+ * @param left follow up left subtree.
+ * @param right follow up right subtree.
+ *******************************************************************************/
+struct Node {
+    uint64_t data = 0;     ///< The value/key of the node.
+    struct Node *left{};   ///< struct pointer to left subtree.
+    struct Node *right{};  ///< struct pointer to right subtree.
+};
+/******************************************************************************
+ * @brief BT used to make the entire structure of the binary tree and the
+ * functions associated with the binary tree
+ *******************************************************************************/
+class BT {
+ public:
+    std::vector<uint64_t>
+        inorder_result;  // vector to store the inorder traversal of the tree.
+    std::vector<uint64_t>
+        preorder_result;  // vector to store the preorder traversal of the tree.
+    std::vector<uint64_t> postorder_result;  // vector to store the preorder
+                                             // traversal of the tree.
+
+    Node *createNewNode(
+        uint64_t);  // function that will create new node for insertion.
+
+    std::vector<uint64_t> inorder(
+        Node *);  // function that takes root of the tree as an argument and
+                  // returns its inorder traversal.
+    std::vector<uint64_t> preorder(
+        Node *);  // function that takes root of the tree as an argument and
+                  // returns its preorder traversal.
+    std::vector<uint64_t> postorder(
+        Node *);  // function that takes root of the tree as an argument and
+                  // returns its postorder traversal.
+};
+
+/******************************************************************************
+ * @brief will allocate the memory for a node and, along the data and return the
+ * node.
+ * @param data value that a particular node will contain.
+ * @return pointer to the newly created node with assigned data.
+ *******************************************************************************/
+Node *BT::createNewNode(uint64_t data) {
+    Node *node = new Node();
+    node->data = data;
+    node->left = node->right = nullptr;
+    return node;
+}
+
+/******************************************************************************
+ * @brief inorder() function that will perform the inorder traversal
+ * recursively, and return the resultant vector that contain the inorder
+ * traversal of a tree.
+ * @param root head/root node of a tree
+ * @return result that is containing the inorder traversal of a tree
+ *******************************************************************************/
+std::vector<uint64_t> BT::inorder(Node *root) {
+    if (root == nullptr) {  // return if the current node is empty
+        return {};
+    }
+
+    inorder(root->left);  // Traverse the left subtree
+    BT::inorder_result.push_back(
+        root->data);  // Display the data part of the root (or current node)
+    inorder(root->right);  // Traverse the right subtree
+
+    return inorder_result;
+}
+
+/******************************************************************************
+ * @brief preorder function that will perform the preorder traversal
+ * recursively, and return the resultant vector that contain the preorder
+ * traversal of a tree.
+ * @param root head/root node of a tree
+ * @return result that is containing the preorder traversal of a tree
+ *******************************************************************************/
+std::vector<uint64_t> BT::preorder(Node *root) {
+    if (root == nullptr) {  // if the current node is empty
+        return {};
+    }
+
+    BT::preorder_result.push_back(
+        root->data);  // Display the data part of the root (or current node)
+    preorder(root->left);   // Traverse the left subtree
+    preorder(root->right);  // Traverse the right subtree
+
+    return preorder_result;
+}
+
+/******************************************************************************
+ * @brief postorder function that will perform the postorder traversal
+ * recursively, and return the result vector that contain the postorder
+ * traversal of a tree.
+ * @param root head/root node of a tree
+ * @return result that is containing the postorder traversal of a tree
+ *******************************************************************************/
+std::vector<uint64_t> BT::postorder(Node *root) {
+    if (root == nullptr) {  // if the current node is empty
+        return {};
+    }
+
+    postorder(root->left);   // Traverse the left subtree
+    postorder(root->right);  // Traverse the right subtree
+    BT::postorder_result.push_back(
+        root->data);  // Display the data part of the root (or current node)
+
+    return postorder_result;
+}
+
+}  // namespace recursive_tree_traversals
+
+}  // namespace others
+
+/*******************************************************************************
+ * @brief 1st test-case
+ * @returns void
+ *******************************************************************************/
+void test1() {
+    others::recursive_tree_traversals::BT obj1;
+    others::recursive_tree_traversals::Node *root = obj1.createNewNode(2);
+    root->left = obj1.createNewNode(7);
+    root->right = obj1.createNewNode(5);
+    root->left->left = obj1.createNewNode(2);
+    root->left->right = obj1.createNewNode(6);
+    root->right->right = obj1.createNewNode(9);
+    root->left->right->left = obj1.createNewNode(5);
+    root->left->right->right = obj1.createNewNode(11);
+    root->right->right->left = obj1.createNewNode(4);
+
+    std::vector<uint64_t> actual_result_inorder{2, 7, 5, 6, 11, 2, 5, 4, 9};
+    std::vector<uint64_t> actual_result_preorder{2, 7, 2, 6, 5, 11, 5, 9, 4};
+    std::vector<uint64_t> actual_result_postorder{2, 5, 11, 6, 7, 4, 9, 5, 2};
+    std::vector<uint64_t> result_inorder;    ///< result stores the inorder
+                                             ///< traversal of the binary tree
+    std::vector<uint64_t> result_preorder;   ///< result stores the preorder
+                                             ///< traversal of the binary tree
+    std::vector<uint64_t> result_postorder;  ///< result stores the postorder
+                                             ///< traversal of the binary tree
+
+    uint64_t size = actual_result_inorder.size();
+
+    // Calling inorder() function by passing a root node,
+    // and storing the inorder traversal in result_inorder.
+    result_inorder = obj1.inorder(root);
+    std::cout << "Testcase #1: Inorder Traversal...";
+    for (auto i = 0; i < size; ++i) {
+        assert(actual_result_inorder[i] == result_inorder[i]);
+    }
+    std::cout << "Passed!" << std::endl;
+
+    // Calling preorder() function by passing a root node,
+    // and storing the preorder traversal in result_preorder.
+    result_preorder = obj1.preorder(root);
+    std::cout << "Testcase #1: Preorder Traversal...";
+    for (auto i = 0; i < size; ++i) {
+        assert(actual_result_preorder[i] == result_preorder[i]);
+    }
+    std::cout << "Passed!" << std::endl;
+
+    // Calling postorder() function by passing a root node,
+    // and storing the postorder traversal in result_postorder.
+    result_postorder = obj1.postorder(root);
+    std::cout << "Testcase #1: Postorder Traversal...";
+    for (auto i = 0; i < size; ++i) {
+        assert(actual_result_postorder[i] == result_postorder[i]);
+    }
+    std::cout << "Passed!" << std::endl;
+
+    std::cout << std::endl;
+}
+
+/*******************************************************************************
+ * @brief 2nd test-case
+ * @returns void
+ *******************************************************************************/
+void test2() {
+    others::recursive_tree_traversals::BT obj2;
+    others::recursive_tree_traversals::Node *root = obj2.createNewNode(1);
+    root->left = obj2.createNewNode(2);
+    root->right = obj2.createNewNode(3);
+    root->left->left = obj2.createNewNode(4);
+    root->right->left = obj2.createNewNode(5);
+    root->right->right = obj2.createNewNode(6);
+    root->right->left->left = obj2.createNewNode(7);
+    root->right->left->right = obj2.createNewNode(8);
+
+    std::vector<uint64_t> actual_result_inorder{4, 2, 1, 7, 5, 8, 3, 6};
+    std::vector<uint64_t> actual_result_preorder{1, 2, 4, 3, 5, 7, 8, 6};
+    std::vector<uint64_t> actual_result_postorder{4, 2, 7, 8, 5, 6, 3, 1};
+    std::vector<uint64_t> result_inorder;    ///< result stores the inorder
+                                             ///< traversal of the binary tree
+    std::vector<uint64_t> result_preorder;   ///< result stores the preorder
+                                             ///< traversal of the binary tree
+    std::vector<uint64_t> result_postorder;  ///< result stores the postorder
+                                             ///< traversal of the binary tree
+
+    uint64_t size = actual_result_inorder.size();
+
+    // Calling inorder() function by passing a root node,
+    // and storing the inorder traversal in result_inorder.
+    result_inorder = obj2.inorder(root);
+    std::cout << "Testcase #2: Inorder Traversal...";
+    for (auto i = 0; i < size; ++i) {
+        assert(actual_result_inorder[i] == result_inorder[i]);
+    }
+    std::cout << "Passed!" << std::endl;
+
+    // Calling preorder() function by passing a root node,
+    // and storing the preorder traversal in result_preorder.
+    result_preorder = obj2.preorder(root);
+    std::cout << "Testcase #2: Preorder Traversal...";
+    for (auto i = 0; i < size; ++i) {
+        assert(actual_result_preorder[i] == result_preorder[i]);
+    }
+    std::cout << "Passed!" << std::endl;
+
+    // Calling postorder() function by passing a root node,
+    // and storing the postorder traversal in result_postorder.
+    result_postorder = obj2.postorder(root);
+    std::cout << "Testcase #2: Postorder Traversal...";
+    for (auto i = 0; i < size; ++i) {
+        assert(actual_result_postorder[i] == result_postorder[i]);
+    }
+    std::cout << "Passed!" << std::endl;
+
+    std::cout << std::endl;
+}
+
+/*******************************************************************************
+ * @brief 3rd test-case
+ * @returns void
+ *******************************************************************************/
+void test3() {
+    others::recursive_tree_traversals::BT obj3;
+    others::recursive_tree_traversals::Node *root = obj3.createNewNode(1);
+    root->left = obj3.createNewNode(2);
+    root->right = obj3.createNewNode(3);
+    root->left->left = obj3.createNewNode(4);
+    root->left->right = obj3.createNewNode(5);
+
+    std::vector<uint64_t> actual_result_inorder{4, 2, 5, 1, 3};
+    std::vector<uint64_t> actual_result_preorder{1, 2, 4, 5, 3};
+    std::vector<uint64_t> actual_result_postorder{4, 5, 2, 3, 1};
+    std::vector<uint64_t> result_inorder;    ///< result stores the inorder
+                                             ///< traversal of the binary tree
+    std::vector<uint64_t> result_preorder;   ///< result stores the preorder
+                                             ///< traversal of the binary tree
+    std::vector<uint64_t> result_postorder;  ///< result stores the postorder
+                                             ///< traversal of the binary tree
+
+    uint64_t size = actual_result_inorder.size();
+
+    // Calling inorder() function by passing a root node,
+    // and storing the inorder traversal in result_inorder.
+
+    result_inorder = obj3.inorder(root);
+    std::cout << "Testcase #3: Inorder Traversal...";
+    for (auto i = 0; i < size; ++i) {
+        assert(actual_result_inorder[i] == result_inorder[i]);
+    }
+    std::cout << "Passed!" << std::endl;
+
+    // Calling preorder() function by passing a root node,
+    // and storing the preorder traversal in result_preorder.
+    result_preorder = obj3.preorder(root);
+    std::cout << "Testcase #3: Preorder Traversal...";
+    for (auto i = 0; i < size; ++i) {
+        assert(actual_result_preorder[i] == result_preorder[i]);
+    }
+    std::cout << "Passed!" << std::endl;
+
+    // Calling postorder() function by passing a root node,
+    // and storing the postorder traversal in result_postorder.
+    result_postorder = obj3.postorder(root);
+    std::cout << "Testcase #3: Postorder Traversal...";
+    for (auto i = 0; i < size; ++i) {
+        assert(actual_result_postorder[i] == result_postorder[i]);
+    }
+    std::cout << "Passed!" << std::endl;
+
+    std::cout << std::endl;
+}
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void tests() {
+    std::cout << "1st test-case" << std::endl;
+    test1();  // run 1st test-case
+    std::cout << "2nd test-case" << std::endl;
+    test2();  // run 2nd test-case
+    std::cout << "3rd test-case" << std::endl;
+    test3();  // run 3rd test-case
+}
+
+/*******************************************************************************
+ * @brief Main function
+ * @returns 0 on exit
+ *******************************************************************************/
+int main() {
+    tests();  // run self-test implementations
+    return 0;
+}