Add the chapter of backtracking. (#459)

codes/java/chapter_backtracking/backtrack_find_constrained_paths.java

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+/**
+ * File: backtrack_find_constrained_paths.java
+ * Created Time: 2023-04-16
+ * Author: Krahets (krahets@163.com)
+ */
+
+import include.*;
+import java.util.*;
+
+public class backtrack_find_constrained_paths {
+    /* 判断当前状态是否为解 */
+    static boolean isSolution(List<TreeNode> state) {
+        return !state.isEmpty() && state.get(state.size() - 1).val == 7;
+    }
+
+    /* 记录解 */
+    static void recordSolution(List<TreeNode> state, List<List<TreeNode>> res) {
+        res.add(new ArrayList<>(state));
+    }
+
+    /* 判断在当前状态下，该选择是否合法 */
+    static boolean isValid(List<TreeNode> state, TreeNode choice) {
+        return choice != null && choice.val != 3;
+    }
+
+    /* 更新状态 */
+    static void makeChoice(List<TreeNode> state, TreeNode choice) {
+        state.add(choice);
+    }
+
+    /* 恢复状态 */
+    static void undoChoice(List<TreeNode> state, TreeNode choice) {
+        state.remove(state.size() - 1);
+    }
+
+    /* 回溯算法 */
+    static void backtrack(List<TreeNode> state, List<TreeNode> choices, List<List<TreeNode>> res) {
+        // 检查是否为解
+        if (isSolution(state)) {
+            // 记录解
+            recordSolution(state, res);
+            return;
+        }
+        // 遍历所有选择
+        for (TreeNode choice : choices) {
+            // 剪枝：检查选择是否合法
+            if (isValid(state, choice)) {
+                // 尝试：做出选择，更新状态
+                makeChoice(state, choice);
+                backtrack(state, Arrays.asList(choice.left, choice.right), res);
+                // 回退：撤销选择，恢复到之前的状态
+                undoChoice(state, choice);
+            }
+        }
+    }
+
+    public static void main(String[] args) {
+        TreeNode root = TreeNode.listToTree(Arrays.asList(1, 7, 3, 4, 5, 6, 7));
+        System.out.println("\n初始化二叉树");
+        PrintUtil.printTree(root);
+
+        // 回溯算法
+        List<List<TreeNode>> res = new ArrayList<>();
+        backtrack(new ArrayList<>(), Arrays.asList(root), res);
+
+        System.out.println("\n输出所有根节点到节点 7 的路径，要求路径中不包含值为 3 的节点");
+        for (List<TreeNode> path : res) {
+            List<Integer> vals = new ArrayList<>();
+            for (TreeNode node : path) {
+                vals.add(node.val);
+            }
+            System.out.println(vals);
+        }
+    }
+}

codes/java/chapter_backtracking/preorder_find_constrained_paths.java

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+/**
+ * File: preorder_find_constrained_paths.java
+ * Created Time: 2023-04-16
+ * Author: Krahets (krahets@163.com)
+ */
+
+import include.*;
+import java.util.*;
+
+public class preorder_find_constrained_paths {
+    static List<TreeNode> path;
+    static List<List<TreeNode>> res;
+
+    /* 前序遍历 */
+    static void preOrder(TreeNode root) {
+        // 剪枝
+        if (root == null || root.val == 3) {
+            return;
+        }
+        // 尝试
+        path.add(root);
+        if (root.val == 7) {
+            // 记录解
+            res.add(new ArrayList<>(path));
+        }
+        preOrder(root.left);
+        preOrder(root.right);
+        // 回退
+        path.remove(path.size() - 1);
+    }
+
+    public static void main(String[] args) {
+        TreeNode root = TreeNode.listToTree(Arrays.asList(1, 7, 3, 4, 5, 6, 7));
+        System.out.println("\n初始化二叉树");
+        PrintUtil.printTree(root);
+
+        // 前序遍历
+        path = new ArrayList<>();
+        res = new ArrayList<>();
+        preOrder(root);
+
+        System.out.println("\n输出所有根节点到节点 7 的路径，且路径中不包含值为 3 的节点");
+        for (List<TreeNode> path : res) {
+            List<Integer> vals = new ArrayList<>();
+            for (TreeNode node : path) {
+                vals.add(node.val);
+            }
+            System.out.println(vals);
+        }
+    }
+}

codes/java/chapter_backtracking/preorder_find_nodes.java

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+/**
+ * File: preorder_find_nodes.java
+ * Created Time: 2023-04-16
+ * Author: Krahets (krahets@163.com)
+ */
+
+import include.*;
+import java.util.*;
+
+public class preorder_find_nodes {
+    static List<TreeNode> res;
+
+    /* 前序遍历 */
+    static void preOrder(TreeNode root) {
+        if (root == null) {
+            return;
+        }
+        // 尝试
+        if (root.val == 7) {
+            // 记录解
+            res.add(root);
+        }
+        preOrder(root.left);
+        preOrder(root.right);
+        // 回退
+        return;
+    }
+
+    public static void main(String[] args) {
+        TreeNode root = TreeNode.listToTree(Arrays.asList(1, 7, 3, 4, 5, 6, 7));
+        System.out.println("\n初始化二叉树");
+        PrintUtil.printTree(root);
+
+        // 前序遍历
+        res = new ArrayList<>();
+        preOrder(root);
+
+        System.out.println("\n输出所有根节点到节点 7 的路径");
+        List<Integer> vals = new ArrayList<>();
+        for (TreeNode node : res) {
+            vals.add(node.val);
+        }
+        System.out.println(vals);
+    }
+}

codes/java/chapter_backtracking/preorder_find_paths.java

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+/**
+ * File: preorder_find_paths.java
+ * Created Time: 2023-04-16
+ * Author: Krahets (krahets@163.com)
+ */
+
+import include.*;
+import java.util.*;
+
+public class preorder_find_paths {
+    static List<TreeNode> path;
+    static List<List<TreeNode>> res;
+
+    /* 前序遍历 */
+    static void preOrder(TreeNode root) {
+        if (root == null) {
+            return;
+        }
+        // 尝试
+        path.add(root);
+        if (root.val == 7) {
+            // 记录解
+            res.add(new ArrayList<>(path));
+        }
+        preOrder(root.left);
+        preOrder(root.right);
+        // 回退
+        path.remove(path.size() - 1);
+    }
+
+    public static void main(String[] args) {
+        TreeNode root = TreeNode.listToTree(Arrays.asList(1, 7, 3, 4, 5, 6, 7));
+        System.out.println("\n初始化二叉树");
+        PrintUtil.printTree(root);
+
+        // 前序遍历
+        path = new ArrayList<>();
+        res = new ArrayList<>();
+        preOrder(root);
+
+        System.out.println("\n输出所有根节点到节点 7 的路径");
+        for (List<TreeNode> path : res) {
+            List<Integer> vals = new ArrayList<>();
+            for (TreeNode node : path) {
+                vals.add(node.val);
+            }
+            System.out.println(vals);
+        }
+    }
+}

codes/python/chapter_backtracking/backtrack_find_constrained_paths.py

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+"""
+File: backtrack_find_constrained_path.py
+Created Time: 2023-04-15
+Author: Krahets (krahets@163.com)
+"""
+
+import sys, os.path as osp
+
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
+from modules import *
+
+
+def is_solution(state: list[TreeNode]) -> bool:
+    """判断当前状态是否为解"""
+    return state and state[-1].val == 7
+
+
+def record_solution(state: list[TreeNode], res: list[list[TreeNode]]):
+    """记录解"""
+    res.append(list(state))
+
+
+def is_valid(state: list[TreeNode], choice: TreeNode) -> bool:
+    """判断在当前状态下，该选择是否合法"""
+    return choice is not None and choice.val != 3
+
+
+def make_choice(state: list[TreeNode], choice: TreeNode):
+    """更新状态"""
+    state.append(choice)
+
+
+def undo_choice(state: list[TreeNode], choice: TreeNode):
+    """恢复状态"""
+    state.pop()
+
+
+def backtrack(state: list[TreeNode], choices: list[TreeNode], res: list[list[TreeNode]]):
+    """回溯算法"""
+    # 检查是否为解
+    if is_solution(state):
+        # 记录解
+        record_solution(state, res)
+        return
+    # 遍历所有选择
+    for choice in choices:
+        # 剪枝：检查选择是否合法
+        if is_valid(state, choice):
+            # 尝试：做出选择，更新状态
+            make_choice(state, choice)
+            backtrack(state, [choice.left, choice.right], res)
+            # 回退：撤销选择，恢复到之前的状态
+            undo_choice(state, choice)
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    root = list_to_tree([1, 7, 3, 4, 5, 6, 7])
+    print("\n初始化二叉树")
+    print_tree(root)
+    
+    # 回溯算法
+    res = []
+    backtrack(state=[], choices=[root], res=res)
+
+    print("\n输出所有根节点到节点 7 的路径，要求路径中不包含值为 3 的节点")
+    for path in res:
+        print([node.val for node in path])

codes/python/chapter_backtracking/preorder_find_constrained_paths.py

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+"""
+File: preorder_find_constrained_path.py
+Created Time: 2023-04-15
+Author: Krahets (krahets@163.com)
+"""
+
+import sys, os.path as osp
+
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
+from modules import *
+
+
+def pre_order(root: TreeNode) -> None:
+    """前序遍历"""
+    # 剪枝
+    if root is None or root.val == 3:
+        return
+    # 尝试
+    path.append(root)
+    if root.val == 7:
+        # 记录解
+        res.append(list(path))
+    pre_order(root.left)
+    pre_order(root.right)
+    # 回退
+    path.pop()
+    return
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    root = list_to_tree([1, 7, 3, 4, 5, 6, 7])
+    print("\n初始化二叉树")
+    print_tree(root)
+
+    # 前序遍历
+    path = list[TreeNode]()
+    res = list[list[TreeNode]]()
+    pre_order(root)
+
+    print("\n输出所有根节点到节点 7 的路径，且路径中不包含值为 3 的节点")
+    for path in res:
+        print([node.val for node in path])

codes/python/chapter_backtracking/preorder_find_nodes.py

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+"""
+File: preorder_find_nodes.py
+Created Time: 2023-04-15
+Author: Krahets (krahets@163.com)
+"""
+
+import sys, os.path as osp
+
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
+from modules import *
+
+
+def pre_order(root: TreeNode) -> None:
+    """前序遍历"""
+    if root is None:
+        return
+    if root.val == 7:
+        # 记录解
+        res.append(root)
+    pre_order(root.left)
+    pre_order(root.right)
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    root = list_to_tree([1, 7, 3, 4, 5, 6, 7])
+    print("\n初始化二叉树")
+    print_tree(root)
+
+    # 前序遍历
+    res = list[TreeNode]()
+    pre_order(root)
+
+    print("\n输出所有值为 7 的节点")
+    print([node.val for node in res])

codes/python/chapter_backtracking/preorder_find_paths.py

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+"""
+File: preorder_find_paths.py
+Created Time: 2023-04-15
+Author: Krahets (krahets@163.com)
+"""
+
+import sys, os.path as osp
+
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
+from modules import *
+
+
+def pre_order(root: TreeNode) -> None:
+    """前序遍历"""
+    if root is None:
+        return
+    # 尝试
+    path.append(root)
+    if root.val == 7:
+        # 记录解
+        res.append(list(path))
+    pre_order(root.left)
+    pre_order(root.right)
+    # 回退
+    path.pop()
+    return
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    root = list_to_tree([1, 7, 3, 4, 5, 6, 7])
+    print("\n初始化二叉树")
+    print_tree(root)
+
+    # 前序遍历
+    path = list[TreeNode]()
+    res = list[list[TreeNode]]()
+    pre_order(root)
+
+    print("\n输出所有根节点到节点 7 的路径")
+    for path in res:
+        print([node.val for node in path])