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

en/codes/cpp/chapter_backtracking/CMakeLists.txt

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+add_executable(preorder_traversal_i_compact preorder_traversal_i_compact.cpp)
+add_executable(preorder_traversal_ii_compact preorder_traversal_ii_compact.cpp)
+add_executable(preorder_traversal_iii_compact preorder_traversal_iii_compact.cpp)
+add_executable(preorder_traversal_iii_template preorder_traversal_iii_template.cpp)
+add_executable(permutations_i permutations_i.cpp)
+add_executable(permutations_ii permutations_ii.cpp)
+add_executable(n_queens n_queens.cpp)
+add_executable(subset_sum_i_naive subset_sum_i_naive.cpp)
+add_executable(subset_sum_i subset_sum_i.cpp)
+add_executable(subset_sum_ii subset_sum_ii.cpp)

en/codes/cpp/chapter_backtracking/n_queens.cpp

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+/**
+ * File: n_queens.cpp
+ * Created Time: 2023-05-04
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Backtracking algorithm: n queens */
+void backtrack(int row, int n, vector<vector<string>> &state, vector<vector<vector<string>>> &res, vector<bool> &cols,
+               vector<bool> &diags1, vector<bool> &diags2) {
+    // When all rows are placed, record the solution
+    if (row == n) {
+        res.push_back(state);
+        return;
+    }
+    // Traverse all columns
+    for (int col = 0; col < n; col++) {
+        // Calculate the main and minor diagonals corresponding to the cell
+        int diag1 = row - col + n - 1;
+        int diag2 = row + col;
+        // Pruning: do not allow queens on the column, main diagonal, or minor diagonal of the cell
+        if (!cols[col] && !diags1[diag1] && !diags2[diag2]) {
+            // Attempt: place the queen in the cell
+            state[row][col] = "Q";
+            cols[col] = diags1[diag1] = diags2[diag2] = true;
+            // Place the next row
+            backtrack(row + 1, n, state, res, cols, diags1, diags2);
+            // Retract: restore the cell to an empty spot
+            state[row][col] = "#";
+            cols[col] = diags1[diag1] = diags2[diag2] = false;
+        }
+    }
+}
+
+/* Solve n queens */
+vector<vector<vector<string>>> nQueens(int n) {
+    // Initialize an n*n size chessboard, where 'Q' represents the queen and '#' represents an empty spot
+    vector<vector<string>> state(n, vector<string>(n, "#"));
+    vector<bool> cols(n, false);           // Record columns with queens
+    vector<bool> diags1(2 * n - 1, false); // Record main diagonals with queens
+    vector<bool> diags2(2 * n - 1, false); // Record minor diagonals with queens
+    vector<vector<vector<string>>> res;
+
+    backtrack(0, n, state, res, cols, diags1, diags2);
+
+    return res;
+}
+
+/* Driver Code */
+int main() {
+    int n = 4;
+    vector<vector<vector<string>>> res = nQueens(n);
+
+    cout << "Input the dimensions of the chessboard as " << n << endl;
+    cout << "Total number of queen placement solutions = " << res.size() << endl;
+    for (const vector<vector<string>> &state : res) {
+        cout << "--------------------" << endl;
+        for (const vector<string> &row : state) {
+            printVector(row);
+        }
+    }
+
+    return 0;
+}

en/codes/cpp/chapter_backtracking/permutations_i.cpp

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+/**
+ * File: permutations_i.cpp
+ * Created Time: 2023-04-24
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Backtracking algorithm: Permutation I */
+void backtrack(vector<int> &state, const vector<int> &choices, vector<bool> &selected, vector<vector<int>> &res) {
+    // When the state length equals the number of elements, record the solution
+    if (state.size() == choices.size()) {
+        res.push_back(state);
+        return;
+    }
+    // Traverse all choices
+    for (int i = 0; i < choices.size(); i++) {
+        int choice = choices[i];
+        // Pruning: do not allow repeated selection of elements
+        if (!selected[i]) {
+            // Attempt: make a choice, update the state
+            selected[i] = true;
+            state.push_back(choice);
+            // Proceed to the next round of selection
+            backtrack(state, choices, selected, res);
+            // Retract: undo the choice, restore to the previous state
+            selected[i] = false;
+            state.pop_back();
+        }
+    }
+}
+
+/* Permutation I */
+vector<vector<int>> permutationsI(vector<int> nums) {
+    vector<int> state;
+    vector<bool> selected(nums.size(), false);
+    vector<vector<int>> res;
+    backtrack(state, nums, selected, res);
+    return res;
+}
+
+/* Driver Code */
+int main() {
+    vector<int> nums = {1, 2, 3};
+
+    vector<vector<int>> res = permutationsI(nums);
+
+    cout << "Input array nums = ";
+    printVector(nums);
+    cout << "All permutations res = ";
+    printVectorMatrix(res);
+
+    return 0;
+}

en/codes/cpp/chapter_backtracking/permutations_ii.cpp

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+/**
+ * File: permutations_ii.cpp
+ * Created Time: 2023-04-24
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Backtracking algorithm: Permutation II */
+void backtrack(vector<int> &state, const vector<int> &choices, vector<bool> &selected, vector<vector<int>> &res) {
+    // When the state length equals the number of elements, record the solution
+    if (state.size() == choices.size()) {
+        res.push_back(state);
+        return;
+    }
+    // Traverse all choices
+    unordered_set<int> duplicated;
+    for (int i = 0; i < choices.size(); i++) {
+        int choice = choices[i];
+        // Pruning: do not allow repeated selection of elements and do not allow repeated selection of equal elements
+        if (!selected[i] && duplicated.find(choice) == duplicated.end()) {
+            // Attempt: make a choice, update the state
+            duplicated.emplace(choice); // Record selected element values
+            selected[i] = true;
+            state.push_back(choice);
+            // Proceed to the next round of selection
+            backtrack(state, choices, selected, res);
+            // Retract: undo the choice, restore to the previous state
+            selected[i] = false;
+            state.pop_back();
+        }
+    }
+}
+
+/* Permutation II */
+vector<vector<int>> permutationsII(vector<int> nums) {
+    vector<int> state;
+    vector<bool> selected(nums.size(), false);
+    vector<vector<int>> res;
+    backtrack(state, nums, selected, res);
+    return res;
+}
+
+/* Driver Code */
+int main() {
+    vector<int> nums = {1, 1, 2};
+
+    vector<vector<int>> res = permutationsII(nums);
+
+    cout << "Input array nums = ";
+    printVector(nums);
+    cout << "All permutations res = ";
+    printVectorMatrix(res);
+
+    return 0;
+}

en/codes/cpp/chapter_backtracking/preorder_traversal_i_compact.cpp

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+/**
+ * File: preorder_traversal_i_compact.cpp
+ * Created Time: 2023-04-16
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+vector<TreeNode *> res;
+
+/* Pre-order traversal: Example one */
+void preOrder(TreeNode *root) {
+    if (root == nullptr) {
+        return;
+    }
+    if (root->val == 7) {
+        // Record solution
+        res.push_back(root);
+    }
+    preOrder(root->left);
+    preOrder(root->right);
+}
+
+/* Driver Code */
+int main() {
+    TreeNode *root = vectorToTree(vector<int>{1, 7, 3, 4, 5, 6, 7});
+    cout << "\nInitialize binary tree" << endl;
+    printTree(root);
+
+    // Pre-order traversal
+    preOrder(root);
+
+    cout << "\nOutput all nodes with value 7" << endl;
+    vector<int> vals;
+    for (TreeNode *node : res) {
+        vals.push_back(node->val);
+    }
+    printVector(vals);
+}

en/codes/cpp/chapter_backtracking/preorder_traversal_ii_compact.cpp

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+/**
+ * File: preorder_traversal_ii_compact.cpp
+ * Created Time: 2023-04-16
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+vector<TreeNode *> path;
+vector<vector<TreeNode *>> res;
+
+/* Pre-order traversal: Example two */
+void preOrder(TreeNode *root) {
+    if (root == nullptr) {
+        return;
+    }
+    // Attempt
+    path.push_back(root);
+    if (root->val == 7) {
+        // Record solution
+        res.push_back(path);
+    }
+    preOrder(root->left);
+    preOrder(root->right);
+    // Retract
+    path.pop_back();
+}
+
+/* Driver Code */
+int main() {
+    TreeNode *root = vectorToTree(vector<int>{1, 7, 3, 4, 5, 6, 7});
+    cout << "\nInitialize binary tree" << endl;
+    printTree(root);
+
+    // Pre-order traversal
+    preOrder(root);
+
+    cout << "\nOutput all root-to-node 7 paths" << endl;
+    for (vector<TreeNode *> &path : res) {
+        vector<int> vals;
+        for (TreeNode *node : path) {
+            vals.push_back(node->val);
+        }
+        printVector(vals);
+    }
+}

en/codes/cpp/chapter_backtracking/preorder_traversal_iii_compact.cpp

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+/**
+ * File: preorder_traversal_iii_compact.cpp
+ * Created Time: 2023-04-16
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+vector<TreeNode *> path;
+vector<vector<TreeNode *>> res;
+
+/* Pre-order traversal: Example three */
+void preOrder(TreeNode *root) {
+    // Pruning
+    if (root == nullptr || root->val == 3) {
+        return;
+    }
+    // Attempt
+    path.push_back(root);
+    if (root->val == 7) {
+        // Record solution
+        res.push_back(path);
+    }
+    preOrder(root->left);
+    preOrder(root->right);
+    // Retract
+    path.pop_back();
+}
+
+/* Driver Code */
+int main() {
+    TreeNode *root = vectorToTree(vector<int>{1, 7, 3, 4, 5, 6, 7});
+    cout << "\nInitialize binary tree" << endl;
+    printTree(root);
+
+    // Pre-order traversal
+    preOrder(root);
+
+    cout << "\nOutput all root-to-node 7 paths, requiring paths not to include nodes with value 3" << endl;
+    for (vector<TreeNode *> &path : res) {
+        vector<int> vals;
+        for (TreeNode *node : path) {
+            vals.push_back(node->val);
+        }
+        printVector(vals);
+    }
+}

en/codes/cpp/chapter_backtracking/preorder_traversal_iii_template.cpp

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+/**
+ * File: preorder_traversal_iii_template.cpp
+ * Created Time: 2023-04-16
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Determine if the current state is a solution */
+bool isSolution(vector<TreeNode *> &state) {
+    return !state.empty() && state.back()->val == 7;
+}
+
+/* Record solution */
+void recordSolution(vector<TreeNode *> &state, vector<vector<TreeNode *>> &res) {
+    res.push_back(state);
+}
+
+/* Determine if the choice is legal under the current state */
+bool isValid(vector<TreeNode *> &state, TreeNode *choice) {
+    return choice != nullptr && choice->val != 3;
+}
+
+/* Update state */
+void makeChoice(vector<TreeNode *> &state, TreeNode *choice) {
+    state.push_back(choice);
+}
+
+/* Restore state */
+void undoChoice(vector<TreeNode *> &state, TreeNode *choice) {
+    state.pop_back();
+}
+
+/* Backtracking algorithm: Example three */
+void backtrack(vector<TreeNode *> &state, vector<TreeNode *> &choices, vector<vector<TreeNode *>> &res) {
+    // Check if it's a solution
+    if (isSolution(state)) {
+        // Record solution
+        recordSolution(state, res);
+    }
+    // Traverse all choices
+    for (TreeNode *choice : choices) {
+        // Pruning: check if the choice is legal
+        if (isValid(state, choice)) {
+            // Attempt: make a choice, update the state
+            makeChoice(state, choice);
+            // Proceed to the next round of selection
+            vector<TreeNode *> nextChoices{choice->left, choice->right};
+            backtrack(state, nextChoices, res);
+            // Retract: undo the choice, restore to the previous state
+            undoChoice(state, choice);
+        }
+    }
+}
+
+/* Driver Code */
+int main() {
+    TreeNode *root = vectorToTree(vector<int>{1, 7, 3, 4, 5, 6, 7});
+    cout << "\nInitialize binary tree" << endl;
+    printTree(root);
+
+    // Backtracking algorithm
+    vector<TreeNode *> state;
+    vector<TreeNode *> choices = {root};
+    vector<vector<TreeNode *>> res;
+    backtrack(state, choices, res);
+
+    cout << "\nOutput all root-to-node 7 paths, requiring paths not to include nodes with value 3" << endl;
+    for (vector<TreeNode *> &path : res) {
+        vector<int> vals;
+        for (TreeNode *node : path) {
+            vals.push_back(node->val);
+        }
+        printVector(vals);
+    }
+}

en/codes/cpp/chapter_backtracking/subset_sum_i.cpp

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+/**
+ * File: subset_sum_i.cpp
+ * Created Time: 2023-06-21
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Backtracking algorithm: Subset Sum I */
+void backtrack(vector<int> &state, int target, vector<int> &choices, int start, vector<vector<int>> &res) {
+    // When the subset sum equals target, record the solution
+    if (target == 0) {
+        res.push_back(state);
+        return;
+    }
+    // Traverse all choices
+    // Pruning two: start traversing from start to avoid generating duplicate subsets
+    for (int i = start; i < choices.size(); i++) {
+        // Pruning one: if the subset sum exceeds target, end the loop immediately
+        // This is because the array is sorted, and later elements are larger, so the subset sum will definitely exceed target
+        if (target - choices[i] < 0) {
+            break;
+        }
+        // Attempt: make a choice, update target, start
+        state.push_back(choices[i]);
+        // Proceed to the next round of selection
+        backtrack(state, target - choices[i], choices, i, res);
+        // Retract: undo the choice, restore to the previous state
+        state.pop_back();
+    }
+}
+
+/* Solve Subset Sum I */
+vector<vector<int>> subsetSumI(vector<int> &nums, int target) {
+    vector<int> state;              // State (subset)
+    sort(nums.begin(), nums.end()); // Sort nums
+    int start = 0;                  // Start point for traversal
+    vector<vector<int>> res;        // Result list (subset list)
+    backtrack(state, target, nums, start, res);
+    return res;
+}
+
+/* Driver Code */
+int main() {
+    vector<int> nums = {3, 4, 5};
+    int target = 9;
+
+    vector<vector<int>> res = subsetSumI(nums, target);
+
+    cout << "Input array nums = ";
+    printVector(nums);
+    cout << "target = " << target << endl;
+    cout << "All subsets summing to " << target << "is" << endl;
+    printVectorMatrix(res);
+
+    return 0;
+}

en/codes/cpp/chapter_backtracking/subset_sum_i_naive.cpp

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+/**
+ * File: subset_sum_i_naive.cpp
+ * Created Time: 2023-06-21
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Backtracking algorithm: Subset Sum I */
+void backtrack(vector<int> &state, int target, int total, vector<int> &choices, vector<vector<int>> &res) {
+    // When the subset sum equals target, record the solution
+    if (total == target) {
+        res.push_back(state);
+        return;
+    }
+    // Traverse all choices
+    for (size_t i = 0; i < choices.size(); i++) {
+        // Pruning: if the subset sum exceeds target, skip that choice
+        if (total + choices[i] > target) {
+            continue;
+        }
+        // Attempt: make a choice, update elements and total
+        state.push_back(choices[i]);
+        // Proceed to the next round of selection
+        backtrack(state, target, total + choices[i], choices, res);
+        // Retract: undo the choice, restore to the previous state
+        state.pop_back();
+    }
+}
+
+/* Solve Subset Sum I (including duplicate subsets) */
+vector<vector<int>> subsetSumINaive(vector<int> &nums, int target) {
+    vector<int> state;       // State (subset)
+    int total = 0;           // Subset sum
+    vector<vector<int>> res; // Result list (subset list)
+    backtrack(state, target, total, nums, res);
+    return res;
+}
+
+/* Driver Code */
+int main() {
+    vector<int> nums = {3, 4, 5};
+    int target = 9;
+
+    vector<vector<int>> res = subsetSumINaive(nums, target);
+
+    cout << "Input array nums = ";
+    printVector(nums);
+    cout << "target = " << target << endl;
+    cout << "All subsets summing to " << target << "is" << endl;
+    printVectorMatrix(res);
+
+    return 0;
+}

en/codes/cpp/chapter_backtracking/subset_sum_ii.cpp

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+/**
+ * File: subset_sum_ii.cpp
+ * Created Time: 2023-06-21
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Backtracking algorithm: Subset Sum II */
+void backtrack(vector<int> &state, int target, vector<int> &choices, int start, vector<vector<int>> &res) {
+    // When the subset sum equals target, record the solution
+    if (target == 0) {
+        res.push_back(state);
+        return;
+    }
+    // Traverse all choices
+    // Pruning two: start traversing from start to avoid generating duplicate subsets
+    // Pruning three: start traversing from start to avoid repeatedly selecting the same element
+    for (int i = start; i < choices.size(); i++) {
+        // Pruning one: if the subset sum exceeds target, end the loop immediately
+        // This is because the array is sorted, and later elements are larger, so the subset sum will definitely exceed target
+        if (target - choices[i] < 0) {
+            break;
+        }
+        // Pruning four: if the element equals the left element, it indicates that the search branch is repeated, skip it
+        if (i > start && choices[i] == choices[i - 1]) {
+            continue;
+        }
+        // Attempt: make a choice, update target, start
+        state.push_back(choices[i]);
+        // Proceed to the next round of selection
+        backtrack(state, target - choices[i], choices, i + 1, res);
+        // Retract: undo the choice, restore to the previous state
+        state.pop_back();
+    }
+}
+
+/* Solve Subset Sum II */
+vector<vector<int>> subsetSumII(vector<int> &nums, int target) {
+    vector<int> state;              // State (subset)
+    sort(nums.begin(), nums.end()); // Sort nums
+    int start = 0;                  // Start point for traversal
+    vector<vector<int>> res;        // Result list (subset list)
+    backtrack(state, target, nums, start, res);
+    return res;
+}
+
+/* Driver Code */
+int main() {
+    vector<int> nums = {4, 4, 5};
+    int target = 9;
+
+    vector<vector<int>> res = subsetSumII(nums, target);
+
+    cout << "Input array nums = ";
+    printVector(nums);
+    cout << "target = " << target << endl;
+    cout << "All subsets summing to " << target << "is" << endl;
+    printVectorMatrix(res);
+
+    return 0;
+}