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Retranslate the complete English edition from Simplified Chinese (#2010)

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* Retranslate the complete English edition from Simplified Chinese

* Polish three English explanations after reader-focused review
This commit is contained in:
Yudong Jin
2026-10-31 03:35:51 +08:00
committed by GitHub
parent ef46e2ed95
commit 14c314c08c
1502 changed files with 29459 additions and 23517 deletions
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118
en/codes/cpp/chapter_tree/avl_tree.cpp
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@@ -9,93 +9,93 @@
/* AVL tree */
class AVLTree {
private:
/* Update node height */
/* Update the node height */
void updateHeight(TreeNode *node) {
// Node height equals the height of the tallest subtree + 1
// The node height equals the height of its taller subtree + 1
node->height = max(height(node->left), height(node->right)) + 1;
}
/* Right rotation operation */
/* Right rotation */
TreeNode *rightRotate(TreeNode *node) {
TreeNode *child = node->left;
TreeNode *grandChild = child->right;
// Using child as pivot, rotate node to the right
// Rotate node to the right around child
child->right = node;
node->left = grandChild;
// Update node height
// Update the node height
updateHeight(node);
updateHeight(child);
// Return root node of subtree after rotation
// Return the root of the rotated subtree
return child;
}
/* Left rotation operation */
/* Left rotation */
TreeNode *leftRotate(TreeNode *node) {
TreeNode *child = node->right;
TreeNode *grandChild = child->left;
// Using child as pivot, rotate node to the left
// Rotate node to the left around child
child->left = node;
node->right = grandChild;
// Update node height
// Update the node height
updateHeight(node);
updateHeight(child);
// Return root node of subtree after rotation
// Return the root of the rotated subtree
return child;
}
/* Perform rotation operation to restore balance to this subtree */
/* Perform rotations to restore balance in this subtree */
TreeNode *rotate(TreeNode *node) {
// Get balance factor of node
// Get the balance factor of node
int _balanceFactor = balanceFactor(node);
// Left-leaning tree
// Left-heavy tree
if (_balanceFactor > 1) {
if (balanceFactor(node->left) >= 0) {
// Right rotation
// Rotate right
return rightRotate(node);
} else {
// First left rotation then right rotation
// Rotate left, then right
node->left = leftRotate(node->left);
return rightRotate(node);
}
}
// Right-leaning tree
// Right-heavy tree
if (_balanceFactor < -1) {
if (balanceFactor(node->right) <= 0) {
// Left rotation
// Rotate left
return leftRotate(node);
} else {
// First right rotation then left rotation
// Rotate right, then left
node->right = rightRotate(node->right);
return leftRotate(node);
}
}
// Balanced tree, no rotation needed, return directly
// The tree is balanced; return without rotating
return node;
}
/* Recursively insert node (helper method) */
/* Insert a node recursively (helper method) */
TreeNode *insertHelper(TreeNode *node, int val) {
if (node == nullptr)
return new TreeNode(val);
/* 1. Find insertion position and insert node */
/* 1. Find the insertion position and insert the 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; // Duplicate node not inserted, return directly
updateHeight(node); // Update node height
/* 2. Perform rotation operation to restore balance to this subtree */
return node; // Return without inserting a duplicate node
updateHeight(node); // Update the node height
/* 2. Perform rotations to restore balance in this subtree */
node = rotate(node);
// Return root node of subtree
// Return the root of the subtree
return node;
}
/* Recursively delete node (helper method) */
/* Remove a node recursively (helper method) */
TreeNode *removeHelper(TreeNode *node, int val) {
if (node == nullptr)
return nullptr;
/* 1. Find node and delete */
/* 1. Find and remove the node */
if (val < node->val)
node->left = removeHelper(node->left, val);
else if (val > node->val)
@@ -103,18 +103,18 @@ class AVLTree {
else {
if (node->left == nullptr || node->right == nullptr) {
TreeNode *child = node->left != nullptr ? node->left : node->right;
// Number of child nodes = 0, delete node directly and return
// Number of children = 0: remove node and return
if (child == nullptr) {
delete node;
return nullptr;
}
// Number of child nodes = 1, delete node directly
// Number of children = 1: remove node directly
else {
delete node;
node = child;
}
} else {
// Number of child nodes = 2, delete the next node in inorder traversal and replace current node with it
// Number of children = 2: remove the inorder successor and use its value to replace the current node value
TreeNode *temp = node->right;
while (temp->left != nullptr) {
temp = temp->left;
@@ -124,57 +124,57 @@ class AVLTree {
node->val = tempVal;
}
}
updateHeight(node); // Update node height
/* 2. Perform rotation operation to restore balance to this subtree */
updateHeight(node); // Update the node height
/* 2. Perform rotations to restore balance in this subtree */
node = rotate(node);
// Return root node of subtree
// Return the root of the subtree
return node;
}
public:
TreeNode *root; // Root node
/* Get node height */
/* Get the node height */
int height(TreeNode *node) {
// Empty node height is -1, leaf node height is 0
// A null node has height -1; a leaf has height 0
return node == nullptr ? -1 : node->height;
}
/* Get balance factor */
/* Get the balance factor */
int balanceFactor(TreeNode *node) {
// Empty node balance factor is 0
// A null node has balance factor 0
if (node == nullptr)
return 0;
// Node balance factor = left subtree height - right subtree height
return height(node->left) - height(node->right);
}
/* Insert node */
/* Insert a node */
void insert(int val) {
root = insertHelper(root, val);
}
/* Remove node */
/* Remove a node */
void remove(int val) {
root = removeHelper(root, val);
}
/* Search node */
/* Find a node */
TreeNode *search(int val) {
TreeNode *cur = root;
// Loop search, exit after passing leaf node
// Continue searching while the current node pointer is not null
while (cur != nullptr) {
// Target node is in cur's right subtree
// The target node lies in the right subtree of cur
if (cur->val < val)
cur = cur->right;
// Target node is in cur's left subtree
// The target node lies in the left subtree of cur
else if (cur->val > val)
cur = cur->left;
// Found target node, exit loop
// The target node was found; exit the loop
else
break;
}
// Return target node
// Return the target node, or nullptr if it was not found
return cur;
}
@@ -190,23 +190,23 @@ class AVLTree {
void testInsert(AVLTree &tree, int val) {
tree.insert(val);
cout << "\nAfter inserting node " << val << ", AVL tree is" << endl;
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 << ", AVL tree is" << endl;
cout << "\nAfter removing node " << val << " , the AVL tree is" << endl;
printTree(tree.root);
}
/* Driver Code */
/* Driver code */
int main() {
/* Please pay attention to how the AVL tree maintains balance after inserting nodes */
/* Initialize an empty AVL tree */
AVLTree avlTree;
/* Insert node */
// Delete nodes
/* Insert a node */
// Observe how the AVL tree maintains balance after a node is inserted
testInsert(avlTree, 1);
testInsert(avlTree, 2);
testInsert(avlTree, 3);
@@ -218,16 +218,16 @@ int main() {
testInsert(avlTree, 10);
testInsert(avlTree, 6);
/* Please pay attention to how the AVL tree maintains balance after deleting nodes */
/* Insert a duplicate node */
testInsert(avlTree, 7);
/* Remove node */
// Delete node with degree 1
testRemove(avlTree, 8); // Delete node with degree 2
testRemove(avlTree, 5); // Remove node with degree 1
testRemove(avlTree, 4); // Remove node with degree 2
/* Remove a node */
// Observe how the AVL tree maintains balance after a node is removed
testRemove(avlTree, 8); // Remove a node with 0 children
testRemove(avlTree, 5); // Remove a node with 1 child
testRemove(avlTree, 4); // Remove a node with 2 children
/* Search node */
/* Look up a node */
TreeNode *node = avlTree.search(7);
cout << "\nFound node object is " << node << ", node value = " << node->val << endl;
cout << "\nFound node address: " << node << ", node value = " << node->val << endl;
}