Add the chapter of backtracking. (#459)

codes/java/chapter_backtracking/backtrack_find_constrained_paths.java

@@ -0,0 +1,75 @@
+/**
+ * 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);
+        }
+    }
+}