Add the initial EN translation for C++ code (#1346)

en/codes/cpp/chapter_tree/CMakeLists.txt

@@ -0,0 +1,6 @@
+add_executable(avl_tree avl_tree.cpp)
+add_executable(binary_search_tree binary_search_tree.cpp)
+add_executable(binary_tree binary_tree.cpp)
+add_executable(binary_tree_bfs binary_tree_bfs.cpp)
+add_executable(binary_tree_dfs binary_tree_dfs.cpp)
+add_executable(array_binary_tree array_binary_tree.cpp)

en/codes/cpp/chapter_tree/array_binary_tree.cpp

@@ -0,0 +1,137 @@
+/**
+ * File: array_binary_tree.cpp
+ * Created Time: 2023-07-19
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Array-based binary tree class */
+class ArrayBinaryTree {
+  public:
+    /* Constructor */
+    ArrayBinaryTree(vector<int> arr) {
+        tree = arr;
+    }
+
+    /* List capacity */
+    int size() {
+        return tree.size();
+    }
+
+    /* Get the value of the node at index i */
+    int val(int i) {
+        // If index is out of bounds, return INT_MAX, representing a null
+        if (i < 0 || i >= size())
+            return INT_MAX;
+        return tree[i];
+    }
+
+    /* Get the index of the left child of the node at index i */
+    int left(int i) {
+        return 2 * i + 1;
+    }
+
+    /* Get the index of the right child of the node at index i */
+    int right(int i) {
+        return 2 * i + 2;
+    }
+
+    /* Get the index of the parent of the node at index i */
+    int parent(int i) {
+        return (i - 1) / 2;
+    }
+
+    /* Level-order traversal */
+    vector<int> levelOrder() {
+        vector<int> res;
+        // Traverse array
+        for (int i = 0; i < size(); i++) {
+            if (val(i) != INT_MAX)
+                res.push_back(val(i));
+        }
+        return res;
+    }
+
+    /* Pre-order traversal */
+    vector<int> preOrder() {
+        vector<int> res;
+        dfs(0, "pre", res);
+        return res;
+    }
+
+    /* In-order traversal */
+    vector<int> inOrder() {
+        vector<int> res;
+        dfs(0, "in", res);
+        return res;
+    }
+
+    /* Post-order traversal */
+    vector<int> postOrder() {
+        vector<int> res;
+        dfs(0, "post", res);
+        return res;
+    }
+
+  private:
+    vector<int> tree;
+
+    /* Depth-first traversal */
+    void dfs(int i, string order, vector<int> &res) {
+        // If it is an empty spot, return
+        if (val(i) == INT_MAX)
+            return;
+        // Pre-order traversal
+        if (order == "pre")
+            res.push_back(val(i));
+        dfs(left(i), order, res);
+        // In-order traversal
+        if (order == "in")
+            res.push_back(val(i));
+        dfs(right(i), order, res);
+        // Post-order traversal
+        if (order == "post")
+            res.push_back(val(i));
+    }
+};
+
+/* Driver Code */
+int main() {
+    // Initialize binary tree
+    // Use INT_MAX to represent an empty spot nullptr
+    vector<int> arr = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};
+    TreeNode *root = vectorToTree(arr);
+    cout << "\nInitialize binary tree\n";
+    cout << "Binary tree in array representation:\n";
+    printVector(arr);
+    cout << "Binary tree in linked list representation:\n";
+    printTree(root);
+
+    // Array-based binary tree class
+    ArrayBinaryTree abt(arr);
+
+    // Access node
+    int i = 1;
+    int l = abt.left(i), r = abt.right(i), p = abt.parent(i);
+    cout << "\nCurrent node's index is " << i << ", value = " << abt.val(i) << "\n";
+    cout << "Its left child's index is " << l << ", value = " << (l != INT_MAX ? to_string(abt.val(l)) : "nullptr") << "\n";
+    cout << "Its right child's index is " << r << ", value = " << (r != INT_MAX ? to_string(abt.val(r)) : "nullptr") << "\n";
+    cout << "Its parent's index is " << p << ", value = " << (p != INT_MAX ? to_string(abt.val(p)) : "nullptr") << "\n";
+
+    // Traverse tree
+    vector<int> res = abt.levelOrder();
+    cout << "\nLevel-order traversal is:";
+    printVector(res);
+    res = abt.preOrder();
+    cout << "Pre-order traversal is:";
+    printVector(res);
+    res = abt.inOrder();
+    cout << "In-order traversal is:";
+    printVector(res);
+    res = abt.postOrder();
+    cout << "Post-order traversal is:";
+    printVector(res);
+
+    return 0;
+}

en/codes/cpp/chapter_tree/avl_tree.cpp

@@ -0,0 +1,233 @@
+/**
+ * File: avl_tree.cpp
+ * Created Time: 2023-02-03
+ * Author: what-is-me (whatisme@outlook.jp)
+ */
+
+#include "../utils/common.hpp"
+
+/* AVL tree */
+class AVLTree {
+  private:
+    /* Update node height */
+    void updateHeight(TreeNode *node) {
+        // Node height equals the height of the tallest subtree + 1
+        node->height = max(height(node->left), height(node->right)) + 1;
+    }
+
+    /* Right rotation operation */
+    TreeNode *rightRotate(TreeNode *node) {
+        TreeNode *child = node->left;
+        TreeNode *grandChild = child->right;
+        // Rotate node to the right around child
+        child->right = node;
+        node->left = grandChild;
+        // Update node height
+        updateHeight(node);
+        updateHeight(child);
+        // Return the root of the subtree after rotation
+        return child;
+    }
+
+    /* Left rotation operation */
+    TreeNode *leftRotate(TreeNode *node) {
+        TreeNode *child = node->right;
+        TreeNode *grandChild = child->left;
+        // Rotate node to the left around child
+        child->left = node;
+        node->right = grandChild;
+        // Update node height
+        updateHeight(node);
+        updateHeight(child);
+        // Return the root of the subtree after rotation
+        return child;
+    }
+
+    /* Perform rotation operation to restore balance to the subtree */
+    TreeNode *rotate(TreeNode *node) {
+        // Get the balance factor of node
+        int _balanceFactor = balanceFactor(node);
+        // Left-leaning tree
+        if (_balanceFactor > 1) {
+            if (balanceFactor(node->left) >= 0) {
+                // Right rotation
+                return rightRotate(node);
+            } else {
+                // First left rotation then right rotation
+                node->left = leftRotate(node->left);
+                return rightRotate(node);
+            }
+        }
+        // Right-leaning tree
+        if (_balanceFactor < -1) {
+            if (balanceFactor(node->right) <= 0) {
+                // Left rotation
+                return leftRotate(node);
+            } else {
+                // First right rotation then left rotation
+                node->right = rightRotate(node->right);
+                return leftRotate(node);
+            }
+        }
+        // Balanced tree, no rotation needed, return
+        return node;
+    }
+
+    /* Recursively insert node (helper method) */
+    TreeNode *insertHelper(TreeNode *node, int val) {
+        if (node == nullptr)
+            return new TreeNode(val);
+        /* 1. Find insertion position and insert node */
+        if (val < node->val)
+            node->left = insertHelper(node->left, val);
+        else if (val > node->val)
+            node->right = insertHelper(node->right, val);
+        else
+            return node;    // Do not insert duplicate nodes, return
+        updateHeight(node); // Update node height
+        /* 2. Perform rotation operation to restore balance to the subtree */
+        node = rotate(node);
+        // Return the root node of the subtree
+        return node;
+    }
+
+    /* Recursively remove node (helper method) */
+    TreeNode *removeHelper(TreeNode *node, int val) {
+        if (node == nullptr)
+            return nullptr;
+        /* 1. Find and remove the node */
+        if (val < node->val)
+            node->left = removeHelper(node->left, val);
+        else if (val > node->val)
+            node->right = removeHelper(node->right, val);
+        else {
+            if (node->left == nullptr || node->right == nullptr) {
+                TreeNode *child = node->left != nullptr ? node->left : node->right;
+                // Number of child nodes = 0, remove node and return
+                if (child == nullptr) {
+                    delete node;
+                    return nullptr;
+                }
+                // Number of child nodes = 1, remove node
+                else {
+                    delete node;
+                    node = child;
+                }
+            } else {
+                // Number of child nodes = 2, remove the next node in in-order traversal and replace the current node with it
+                TreeNode *temp = node->right;
+                while (temp->left != nullptr) {
+                    temp = temp->left;
+                }
+                int tempVal = temp->val;
+                node->right = removeHelper(node->right, temp->val);
+                node->val = tempVal;
+            }
+        }
+        updateHeight(node); // Update node height
+        /* 2. Perform rotation operation to restore balance to the subtree */
+        node = rotate(node);
+        // Return the root node of the subtree
+        return node;
+    }
+
+  public:
+    TreeNode *root; // Root node
+
+    /* Get node height */
+    int height(TreeNode *node) {
+        // Empty node height is -1, leaf node height is 0
+        return node == nullptr ? -1 : node->height;
+    }
+
+    /* Get balance factor */
+    int balanceFactor(TreeNode *node) {
+        // Empty node balance factor is 0
+        if (node == nullptr)
+            return 0;
+        // Node balance factor = left subtree height - right subtree height
+        return height(node->left) - height(node->right);
+    }
+
+    /* Insert node */
+    void insert(int val) {
+        root = insertHelper(root, val);
+    }
+
+    /* Remove node */
+    void remove(int val) {
+        root = removeHelper(root, val);
+    }
+
+    /* Search node */
+    TreeNode *search(int val) {
+        TreeNode *cur = root;
+        // Loop find, break after passing leaf nodes
+        while (cur != nullptr) {
+            // Target node is in cur's right subtree
+            if (cur->val < val)
+                cur = cur->right;
+            // Target node is in cur's left subtree
+            else if (cur->val > val)
+                cur = cur->left;
+            // Found target node, break loop
+            else
+                break;
+        }
+        // Return target node
+        return cur;
+    }
+
+    /*Constructor*/
+    AVLTree() : root(nullptr) {
+    }
+
+    /*Destructor*/
+    ~AVLTree() {
+        freeMemoryTree(root);
+    }
+};
+
+void testInsert(AVLTree &tree, int val) {
+    tree.insert(val);
+    cout << "\nAfter inserting node " << val << ", the AVL tree is" << endl;
+    printTree(tree.root);
+}
+
+void testRemove(AVLTree &tree, int val) {
+    tree.remove(val);
+    cout << "\nAfter removing node " << val << ", the AVL tree is" << endl;
+    printTree(tree.root);
+}
+
+/* Driver Code */
+int main() {
+    /* Initialize empty AVL tree */
+    AVLTree avlTree;
+
+    /* Insert node */
+    // Notice how the AVL tree maintains balance after inserting nodes
+    testInsert(avlTree, 1);
+    testInsert(avlTree, 2);
+    testInsert(avlTree, 3);
+    testInsert(avlTree, 4);
+    testInsert(avlTree, 5);
+    testInsert(avlTree, 8);
+    testInsert(avlTree, 7);
+    testInsert(avlTree, 9);
+    testInsert(avlTree, 10);
+    testInsert(avlTree, 6);
+
+    /* Insert duplicate node */
+    testInsert(avlTree, 7);
+
+    /* Remove node */
+    // Notice how the AVL tree maintains balance after removing nodes
+    testRemove(avlTree, 8); // Remove node with degree 0
+    testRemove(avlTree, 5); // Remove node with degree 1
+    testRemove(avlTree, 4); // Remove node with degree 2
+
+    /* Search node */
+    TreeNode *node = avlTree.search(7);
+    cout << "\nThe found node object is " << node << ", node value =" << node->val << endl;
+}

en/codes/cpp/chapter_tree/binary_search_tree.cpp

@@ -0,0 +1,170 @@
+/**
+ * File: binary_search_tree.cpp
+ * Created Time: 2022-11-25
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Binary search tree */
+class BinarySearchTree {
+  private:
+    TreeNode *root;
+
+  public:
+    /* Constructor */
+    BinarySearchTree() {
+        // Initialize empty tree
+        root = nullptr;
+    }
+
+    /* Destructor */
+    ~BinarySearchTree() {
+        freeMemoryTree(root);
+    }
+
+    /* Get binary tree root node */
+    TreeNode *getRoot() {
+        return root;
+    }
+
+    /* Search node */
+    TreeNode *search(int num) {
+        TreeNode *cur = root;
+        // Loop find, break after passing leaf nodes
+        while (cur != nullptr) {
+            // Target node is in cur's right subtree
+            if (cur->val < num)
+                cur = cur->right;
+            // Target node is in cur's left subtree
+            else if (cur->val > num)
+                cur = cur->left;
+            // Found target node, break loop
+            else
+                break;
+        }
+        // Return target node
+        return cur;
+    }
+
+    /* Insert node */
+    void insert(int num) {
+        // If tree is empty, initialize root node
+        if (root == nullptr) {
+            root = new TreeNode(num);
+            return;
+        }
+        TreeNode *cur = root, *pre = nullptr;
+        // Loop find, break after passing leaf nodes
+        while (cur != nullptr) {
+            // Found duplicate node, thus return
+            if (cur->val == num)
+                return;
+            pre = cur;
+            // Insertion position is in cur's right subtree
+            if (cur->val < num)
+                cur = cur->right;
+            // Insertion position is in cur's left subtree
+            else
+                cur = cur->left;
+        }
+        // Insert node
+        TreeNode *node = new TreeNode(num);
+        if (pre->val < num)
+            pre->right = node;
+        else
+            pre->left = node;
+    }
+
+    /* Remove node */
+    void remove(int num) {
+        // If tree is empty, return
+        if (root == nullptr)
+            return;
+        TreeNode *cur = root, *pre = nullptr;
+        // Loop find, break after passing leaf nodes
+        while (cur != nullptr) {
+            // Found node to be removed, break loop
+            if (cur->val == num)
+                break;
+            pre = cur;
+            // Node to be removed is in cur's right subtree
+            if (cur->val < num)
+                cur = cur->right;
+            // Node to be removed is in cur's left subtree
+            else
+                cur = cur->left;
+        }
+        // If no node to be removed, return
+        if (cur == nullptr)
+            return;
+        // Number of child nodes = 0 or 1
+        if (cur->left == nullptr || cur->right == nullptr) {
+            // When the number of child nodes = 0 / 1, child = nullptr / that child node
+            TreeNode *child = cur->left != nullptr ? cur->left : cur->right;
+            // Remove node cur
+            if (cur != root) {
+                if (pre->left == cur)
+                    pre->left = child;
+                else
+                    pre->right = child;
+            } else {
+                // If the removed node is the root, reassign the root
+                root = child;
+            }
+            // Free memory
+            delete cur;
+        }
+        // Number of child nodes = 2
+        else {
+            // Get the next node in in-order traversal of cur
+            TreeNode *tmp = cur->right;
+            while (tmp->left != nullptr) {
+                tmp = tmp->left;
+            }
+            int tmpVal = tmp->val;
+            // Recursively remove node tmp
+            remove(tmp->val);
+            // Replace cur with tmp
+            cur->val = tmpVal;
+        }
+    }
+};
+
+/* Driver Code */
+int main() {
+    /* Initialize binary search tree */
+    BinarySearchTree *bst = new BinarySearchTree();
+    // Note that different insertion orders can result in various tree structures. This particular sequence creates a perfect binary tree
+    vector<int> nums = {8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15};
+    for (int num : nums) {
+        bst->insert(num);
+    }
+    cout << endl << "The initialized binary tree is\n" << endl;
+    printTree(bst->getRoot());
+
+    /* Search node */
+    TreeNode *node = bst->search(7);
+    cout << endl << "The found node object is " << node << ", node value =" << node->val << endl;
+
+    /* Insert node */
+    bst->insert(16);
+    cout << endl << "After inserting node 16, the binary tree is\n" << endl;
+    printTree(bst->getRoot());
+
+    /* Remove node */
+    bst->remove(1);
+    cout << endl << "After removing node 1, the binary tree is\n" << endl;
+    printTree(bst->getRoot());
+    bst->remove(2);
+    cout << endl << "After removing node 2, the binary tree is\n" << endl;
+    printTree(bst->getRoot());
+    bst->remove(4);
+    cout << endl << "After removing node 4, the binary tree is\n" << endl;
+    printTree(bst->getRoot());
+
+    // Free memory
+    delete bst;
+
+    return 0;
+}

en/codes/cpp/chapter_tree/binary_tree.cpp

@@ -0,0 +1,43 @@
+/**
+ * File: binary_tree.cpp
+ * Created Time: 2022-11-25
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Driver Code */
+int main() {
+    /* Initialize binary tree */
+    // Initialize node
+    TreeNode *n1 = new TreeNode(1);
+    TreeNode *n2 = new TreeNode(2);
+    TreeNode *n3 = new TreeNode(3);
+    TreeNode *n4 = new TreeNode(4);
+    TreeNode *n5 = new TreeNode(5);
+    // Construct node references (pointers)
+    n1->left = n2;
+    n1->right = n3;
+    n2->left = n4;
+    n2->right = n5;
+    cout << endl << "Initialize binary tree\n" << endl;
+    printTree(n1);
+
+    /* Insert and remove nodes */
+    TreeNode *P = new TreeNode(0);
+    // Insert node P between n1 -> n2
+    n1->left = P;
+    P->left = n2;
+    cout << endl << "After inserting node P\n" << endl;
+    printTree(n1);
+    // Remove node P
+    n1->left = n2;
+    delete P; // Free memory
+    cout << endl << "After removing node P\n" << endl;
+    printTree(n1);
+
+    // Free memory
+    freeMemoryTree(n1);
+
+    return 0;
+}

en/codes/cpp/chapter_tree/binary_tree_bfs.cpp

@@ -0,0 +1,42 @@
+/**
+ * File: binary_tree_bfs.cpp
+ * Created Time: 2022-11-25
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Level-order traversal */
+vector<int> levelOrder(TreeNode *root) {
+    // Initialize queue, add root node
+    queue<TreeNode *> queue;
+    queue.push(root);
+    // Initialize a list to store the traversal sequence
+    vector<int> vec;
+    while (!queue.empty()) {
+        TreeNode *node = queue.front();
+        queue.pop();              // Queue dequeues
+        vec.push_back(node->val); // Save node value
+        if (node->left != nullptr)
+            queue.push(node->left); // Left child node enqueues
+        if (node->right != nullptr)
+            queue.push(node->right); // Right child node enqueues
+    }
+    return vec;
+}
+
+/* Driver Code */
+int main() {
+    /* Initialize binary tree */
+    // Use a specific function to convert an array into a binary tree
+    TreeNode *root = vectorToTree(vector<int>{1, 2, 3, 4, 5, 6, 7});
+    cout << endl << "Initialize binary tree\n" << endl;
+    printTree(root);
+
+    /* Level-order traversal */
+    vector<int> vec = levelOrder(root);
+    cout << endl << "Sequence of nodes in level-order traversal = ";
+    printVector(vec);
+
+    return 0;
+}

en/codes/cpp/chapter_tree/binary_tree_dfs.cpp

@@ -0,0 +1,69 @@
+/**
+ * File: binary_tree_dfs.cpp
+ * Created Time: 2022-11-25
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+// Initialize the list for storing traversal sequences
+vector<int> vec;
+
+/* Pre-order traversal */
+void preOrder(TreeNode *root) {
+    if (root == nullptr)
+        return;
+    // Visit priority: root node -> left subtree -> right subtree
+    vec.push_back(root->val);
+    preOrder(root->left);
+    preOrder(root->right);
+}
+
+/* In-order traversal */
+void inOrder(TreeNode *root) {
+    if (root == nullptr)
+        return;
+    // Visit priority: left subtree -> root node -> right subtree
+    inOrder(root->left);
+    vec.push_back(root->val);
+    inOrder(root->right);
+}
+
+/* Post-order traversal */
+void postOrder(TreeNode *root) {
+    if (root == nullptr)
+        return;
+    // Visit priority: left subtree -> right subtree -> root node
+    postOrder(root->left);
+    postOrder(root->right);
+    vec.push_back(root->val);
+}
+
+/* Driver Code */
+int main() {
+    /* Initialize binary tree */
+    // Use a specific function to convert an array into a binary tree
+    TreeNode *root = vectorToTree(vector<int>{1, 2, 3, 4, 5, 6, 7});
+    cout << endl << "Initialize binary tree\n" << endl;
+    printTree(root);
+
+    /* Pre-order traversal */
+    vec.clear();
+    preOrder(root);
+    cout << endl << "Sequence of nodes in pre-order traversal = ";
+    printVector(vec);
+
+    /* In-order traversal */
+    vec.clear();
+    inOrder(root);
+    cout << endl << "Sequence of nodes in in-order traversal = ";
+    printVector(vec);
+
+    /* Post-order traversal */
+    vec.clear();
+    postOrder(root);
+    cout << endl << "Sequence of nodes in post-order traversal = ";
+    printVector(vec);
+
+    return 0;
+}