add zig codes for Section Binary Tree, Binary Search Tree and AVL Tree (#293)

* add zig codes for Section 'Binary Tree'

* add zig codes for Section 'Binary Tree'

* add zig codes for Section 'Binary Tree'

* add zig codes for Section 'Binary Tree'

* add zig codes for Section 'Binary Tree' and 'Binary Search Tree'

* update zig codes for Section 'Binary Tree' and 'Binary Search Tree'

* update zig codes for Section 'Binary Tree', 'Binary Search Tree' and 'AVL Tree'

codes/zig/build.zig

@@ -281,6 +281,47 @@ pub fn build(b: *std.build.Builder) void {
         const run_step_binary_tree_bfs = b.step("run_binary_tree_bfs", "Run binary_tree_bfs");
         run_step_binary_tree_bfs.dependOn(&run_cmd_binary_tree_bfs.step);
 
+        // Source File: "chapter_tree/binary_tree_dfs.zig"
+        // Run Command: zig build run_binary_tree_dfs
+        const exe_binary_tree_dfs = b.addExecutable("binary_tree_dfs", "chapter_tree/binary_tree_dfs.zig");
+        exe_binary_tree_dfs.addPackagePath("include", "include/include.zig");
+        exe_binary_tree_dfs.setTarget(target);
+        exe_binary_tree_dfs.setBuildMode(mode);
+        exe_binary_tree_dfs.install();
+        const run_cmd_binary_tree_dfs = exe_binary_tree_dfs.run();
+        run_cmd_binary_tree_dfs.step.dependOn(b.getInstallStep());
+        if (b.args) |args| run_cmd_binary_tree_dfs.addArgs(args);
+        const run_step_binary_tree_dfs = b.step("run_binary_tree_dfs", "Run binary_tree_dfs");
+        run_step_binary_tree_dfs.dependOn(&run_cmd_binary_tree_dfs.step);
+
+    // Section: "Binary Search Tree"
+        // Source File: "chapter_tree/binary_search_tree.zig"
+        // Run Command: zig build run_binary_search_tree
+        const exe_binary_search_tree = b.addExecutable("binary_search_tree", "chapter_tree/binary_search_tree.zig");
+        exe_binary_search_tree.addPackagePath("include", "include/include.zig");
+        exe_binary_search_tree.setTarget(target);
+        exe_binary_search_tree.setBuildMode(mode);
+        exe_binary_search_tree.install();
+        const run_cmd_binary_search_tree = exe_binary_search_tree.run();
+        run_cmd_binary_search_tree.step.dependOn(b.getInstallStep());
+        if (b.args) |args| run_cmd_binary_search_tree.addArgs(args);
+        const run_step_binary_search_tree = b.step("run_binary_search_tree", "Run binary_search_tree");
+        run_step_binary_search_tree.dependOn(&run_cmd_binary_search_tree.step);
+
+    // Section: "AVL Tree"
+        // Source File: "chapter_tree/avl_tree.zig"
+        // Run Command: zig build run_avl_tree
+        const exe_avl_tree = b.addExecutable("avl_tree", "chapter_tree/avl_tree.zig");
+        exe_avl_tree.addPackagePath("include", "include/include.zig");
+        exe_avl_tree.setTarget(target);
+        exe_avl_tree.setBuildMode(mode);
+        exe_avl_tree.install();
+        const run_cmd_avl_tree = exe_avl_tree.run();
+        run_cmd_avl_tree.step.dependOn(b.getInstallStep());
+        if (b.args) |args| run_cmd_avl_tree.addArgs(args);
+        const run_step_avl_tree = b.step("run_avl_tree", "Run avl_tree");
+        run_step_avl_tree.dependOn(&run_cmd_avl_tree.step);
+        
     // Section: "Heap"
         // Source File: "chapter_heap/heap.zig"
         // Run Command: zig build run_heap

codes/zig/chapter_tree/avl_tree.zig

@@ -0,0 +1,260 @@
+// File: avl_tree.zig
+// Created Time: 2023-01-15
+// Author: sjinzh (sjinzh@gmail.com)
+
+const std = @import("std");
+const inc = @import("include");
+
+// 平衡二叉树
+pub fn AVLTree(comptime T: type) type {
+    return struct {
+        const Self = @This();
+
+        root: ?*inc.TreeNode(T) = null,                 // 根节点
+        mem_arena: ?std.heap.ArenaAllocator = null,
+        mem_allocator: std.mem.Allocator = undefined,   // 内存分配器
+
+        // 构造函数
+        pub fn init(self: *Self, allocator: std.mem.Allocator) void {
+            if (self.mem_arena == null) {
+                self.mem_arena = std.heap.ArenaAllocator.init(allocator);
+                self.mem_allocator = self.mem_arena.?.allocator();
+            }
+        }
+
+        // 析构函数
+        pub fn deinit(self: *Self) void {
+            if (self.mem_arena == null) return;
+            self.mem_arena.?.deinit();
+        }
+
+        // 获取结点高度
+        fn height(self: *Self, node: ?*inc.TreeNode(T)) i32 {
+            _ = self;
+            // 空结点高度为 -1 ，叶结点高度为 0
+            return if (node == null) -1 else node.?.height;
+        }
+
+        // 更新结点高度
+        fn updateHeight(self: *Self, node: ?*inc.TreeNode(T)) void {
+            // 结点高度等于最高子树高度 + 1
+            node.?.height = std.math.max(self.height(node.?.left), self.height(node.?.right)) + 1;
+        }
+
+        // 获取平衡因子
+        fn balanceFactor(self: *Self, node: ?*inc.TreeNode(T)) i32 {
+            // 空结点平衡因子为 0
+            if (node == null) return 0;
+            // 结点平衡因子 = 左子树高度 - 右子树高度
+            return self.height(node.?.left) - self.height(node.?.right);
+        }
+
+        // 右旋操作
+        fn rightRotate(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {
+            var child = node.?.left;
+            var grandChild = child.?.right;
+            // 以 child 为原点，将 node 向右旋转
+            child.?.right = node;
+            node.?.left = grandChild;
+            // 更新结点高度
+            self.updateHeight(node);
+            self.updateHeight(child);
+            // 返回旋转后子树的根节点
+            return child;
+        }
+
+        // 左旋操作
+        fn leftRotate(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {
+            var child = node.?.right;
+            var grandChild = child.?.left;
+            // 以 child 为原点，将 node 向左旋转
+            child.?.left = node;
+            node.?.right = grandChild;
+            // 更新结点高度
+            self.updateHeight(node);
+            self.updateHeight(child);
+            // 返回旋转后子树的根节点
+            return child;
+        }
+
+        // 执行旋转操作，使该子树重新恢复平衡
+        fn rotate(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {
+            // 获取结点 node 的平衡因子
+            var balance_factor = self.balanceFactor(node);
+            // 左偏树
+            if (balance_factor > 1) {
+                if (self.balanceFactor(node.?.left) >= 0) {
+                    // 右旋
+                    return self.rightRotate(node);
+                } else {
+                    // 先左旋后右旋
+                    node.?.left = self.leftRotate(node.?.left);
+                    return self.rightRotate(node);
+                }
+            }
+            // 右偏树
+            if (balance_factor < -1) {
+                if (self.balanceFactor(node.?.right) <= 0) {
+                    // 左旋
+                    return self.leftRotate(node);
+                } else {
+                    // 先右旋后左旋
+                    node.?.right = self.rightRotate(node.?.right);
+                    return self.leftRotate(node);
+                }
+            }
+            // 平衡树，无需旋转，直接返回
+            return node;
+        }
+
+        // 插入结点
+        fn insert(self: *Self, val: T) !?*inc.TreeNode(T) {
+            self.root = try self.insertHelper(self.root, val);
+            return self.root;
+        }
+
+        // 递归插入结点（辅助函数）
+        fn insertHelper(self: *Self, node_: ?*inc.TreeNode(T), val: T) !?*inc.TreeNode(T) {
+            var node = node_;
+            if (node == null) {
+                var tmp_node = try self.mem_allocator.create(inc.TreeNode(T));
+                tmp_node.init(val);
+                return tmp_node;
+            }
+            // 1. 查找插入位置，并插入结点
+            if (val < node.?.val) {
+                node.?.left = try self.insertHelper(node.?.left, val);
+            } else if (val > node.?.val) {
+                node.?.right = try self.insertHelper(node.?.right, val);
+            } else {
+                return node;            // 重复结点不插入，直接返回
+            }
+            self.updateHeight(node);    // 更新结点高度
+            // 2. 执行旋转操作，使该子树重新恢复平衡
+            node = self.rotate(node);
+            // 返回子树的根节点
+            return node;
+        }
+
+        // 删除结点
+        fn remove(self: *Self, val: T) ?*inc.TreeNode(T) {
+           self.root = self.removeHelper(self.root, val);
+            return self.root;
+        }
+
+        // 递归删除结点（辅助函数）
+        fn removeHelper(self: *Self, node_: ?*inc.TreeNode(T), val: T) ?*inc.TreeNode(T) {
+            var node = node_;
+            if (node == null) return null;
+            // 1. 查找结点，并删除之
+            if (val < node.?.val) {
+                node.?.left = self.removeHelper(node.?.left, val);
+            } else if (val > node.?.val) {
+                node.?.right = self.removeHelper(node.?.right, val);
+            } else {
+                if (node.?.left == null or node.?.right == null) {
+                    var child = if (node.?.left != null) node.?.left else node.?.right;
+                    // 子结点数量 = 0 ，直接删除 node 并返回
+                    if (child == null) {
+                        return null;
+                    // 子结点数量 = 1 ，直接删除 node
+                    } else {
+                        node = child;
+                    }
+                } else {
+                    // 子结点数量 = 2 ，则将中序遍历的下个结点删除，并用该结点替换当前结点
+                    var temp = self.getInOrderNext(node.?.right);
+                    node.?.right = self.removeHelper(node.?.right, temp.?.val);
+                    node.?.val = temp.?.val;
+                }
+            }
+            self.updateHeight(node);    // 更新结点高度
+            // 2. 执行旋转操作，使该子树重新恢复平衡
+            node = self.rotate(node);
+            // 返回子树的根节点
+            return node;
+        }
+
+        // 获取中序遍历中的下一个结点（仅适用于 root 有左子结点的情况）
+        fn getInOrderNext(self: *Self, node_: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {
+            _ = self;
+            var node = node_;
+            if (node == null) return node;
+            // 循环访问左子结点，直到叶结点时为最小结点，跳出
+            while (node.?.left != null) {
+                node = node.?.left;
+            }
+            return node;
+        }
+
+        // 查找结点
+        fn search(self: *Self, val: T) ?*inc.TreeNode(T) {
+            var cur = self.root;
+            // 循环查找，越过叶结点后跳出
+            while (cur != null) {
+                // 目标结点在 cur 的右子树中
+                if (cur.?.val < val) {
+                    cur = cur.?.right;
+                // 目标结点在 cur 的左子树中
+                } else if (cur.?.val > val) {
+                    cur = cur.?.left;
+                // 找到目标结点，跳出循环
+                } else {
+                    break;
+                }
+            }
+            // 返回目标结点
+            return cur;
+        }
+    };   
+}
+
+pub fn testInsert(comptime T: type, tree_: *AVLTree(T), val: T) !void {
+    var tree = tree_;
+    _ = try tree.insert(val);
+    std.debug.print("\n插入结点 {} 后，AVL 树为\n", .{val});
+    try inc.PrintUtil.printTree(tree.root, null, false);
+}
+
+pub fn testRemove(comptime T: type, tree_: *AVLTree(T), val: T) void {
+    var tree = tree_;
+    _ = tree.remove(val);
+    std.debug.print("\n删除结点 {} 后，AVL 树为\n", .{val});
+    try inc.PrintUtil.printTree(tree.root, null, false);
+}
+
+// Driver Code
+pub fn main() !void {
+    // 初始化空 AVL 树
+    var avl_tree = AVLTree(i32){};
+    avl_tree.init(std.heap.page_allocator);
+    defer avl_tree.deinit();
+
+    // 插入结点
+    // 请关注插入结点后，AVL 树是如何保持平衡的
+    try testInsert(i32, &avl_tree, 1);
+    try testInsert(i32, &avl_tree, 2);
+    try testInsert(i32, &avl_tree, 3);
+    try testInsert(i32, &avl_tree, 4);
+    try testInsert(i32, &avl_tree, 5);
+    try testInsert(i32, &avl_tree, 8);
+    try testInsert(i32, &avl_tree, 7);
+    try testInsert(i32, &avl_tree, 9);
+    try testInsert(i32, &avl_tree, 10);
+    try testInsert(i32, &avl_tree, 6);
+
+    // 插入重复结点
+    try testInsert(i32, &avl_tree, 7);
+
+    // 删除结点
+    // 请关注删除结点后，AVL 树是如何保持平衡的
+    testRemove(i32, &avl_tree, 8); // 删除度为 0 的结点
+    testRemove(i32, &avl_tree, 5); // 删除度为 1 的结点
+    testRemove(i32, &avl_tree, 4); // 删除度为 2 的结点    
+
+    // 查找结点
+    var node = avl_tree.search(7).?;
+    std.debug.print("\n查找到的结点对象为 {any}，结点值 = {}\n", .{node, node.val});
+
+    _ = try std.io.getStdIn().reader().readByte();
+}

codes/zig/chapter_tree/binary_search_tree.zig

@@ -0,0 +1,190 @@
+// File: binary_search_tree.zig
+// Created Time: 2023-01-15
+// Author: sjinzh (sjinzh@gmail.com)
+
+const std = @import("std");
+const inc = @import("include");
+
+// 二叉搜索树
+pub fn BinarySearchTree(comptime T: type) type {
+    return struct {
+        const Self = @This();
+
+        root: ?*inc.TreeNode(T) = null,
+        mem_arena: ?std.heap.ArenaAllocator = null,
+        mem_allocator: std.mem.Allocator = undefined,   // 内存分配器
+
+        // 构造函数
+        pub fn init(self: *Self, allocator: std.mem.Allocator, nums: []T) !void {
+            if (self.mem_arena == null) {
+                self.mem_arena = std.heap.ArenaAllocator.init(allocator);
+                self.mem_allocator = self.mem_arena.?.allocator();
+            }
+            std.sort.sort(T, nums, {}, comptime std.sort.asc(T));   // 排序数组
+            self.root = try self.buildTree(nums, 0, nums.len - 1);  // 构建二叉搜索树
+        }
+
+        // 析构函数
+        pub fn deinit(self: *Self) void {
+            if (self.mem_arena == null) return;
+            self.mem_arena.?.deinit();
+        }
+
+        // 构建二叉搜索树
+        fn buildTree(self: *Self, nums: []T, i: usize, j: usize) !?*inc.TreeNode(T) {
+            if (i > j) return null;
+            // 将数组中间结点作为根结点
+            var mid = (i + j) / 2;
+            var node = try self.mem_allocator.create(inc.TreeNode(T));
+            node.init(nums[mid]);
+            // 递归建立左子树和右子树
+            if (mid >= 1) node.left = try self.buildTree(nums, i, mid - 1);
+            node.right = try self.buildTree(nums, mid + 1, j);
+            return node;
+        }
+
+        // 获取二叉树根结点
+        fn getRoot(self: *Self) ?*inc.TreeNode(T) {
+            return self.root;
+        }
+
+        // 查找结点
+        fn search(self: *Self, num: T) ?*inc.TreeNode(T) {
+            var cur = self.root;
+            // 循环查找，越过叶结点后跳出
+            while (cur != null) {
+                // 目标结点在 cur 的右子树中
+                if (cur.?.val < num) {
+                    cur = cur.?.right;
+                // 目标结点在 cur 的左子树中
+                } else if (cur.?.val > num) {
+                    cur = cur.?.left;
+                // 找到目标结点，跳出循环
+                } else {
+                    break;
+                }
+            }
+            // 返回目标结点
+            return cur;
+        }
+
+        // 插入结点
+        fn insert(self: *Self, num: T) !?*inc.TreeNode(T) {
+            // 若树为空，直接提前返回
+            if (self.root == null) return null;
+            var cur = self.root;
+            var pre: ?*inc.TreeNode(T) = null;
+            // 循环查找，越过叶结点后跳出
+            while (cur != null) {
+                // 找到重复结点，直接返回
+                if (cur.?.val == num) return null;
+                pre = cur;
+                // 插入位置在 cur 的右子树中
+                if (cur.?.val < num) {
+                    cur = cur.?.right;
+                // 插入位置在 cur 的左子树中
+                } else {
+                    cur = cur.?.left;
+                }
+            }
+            // 插入结点 val
+            var node = try self.mem_allocator.create(inc.TreeNode(T));
+            node.init(num);
+            if (pre.?.val < num) {
+                pre.?.right = node;
+            } else {
+                pre.?.left = node;
+            }
+            return node;
+        }
+
+        // 删除结点
+        fn remove(self: *Self, num: T) ?*inc.TreeNode(T) {
+            // 若树为空，直接提前返回
+            if (self.root == null) return null;
+            var cur = self.root;
+            var pre: ?*inc.TreeNode(T) = null;
+            // 循环查找，越过叶结点后跳出
+            while (cur != null) {
+                // 找到待删除结点，跳出循环
+                if (cur.?.val == num) break;
+                pre = cur;
+                // 待删除结点在 cur 的右子树中
+                if (cur.?.val < num) {
+                    cur = cur.?.right;
+                // 待删除结点在 cur 的左子树中
+                } else {
+                    cur = cur.?.left;
+                }
+            }
+            // 若无待删除结点，则直接返回
+            if (cur == null) return null;
+            // 子结点数量 = 0 or 1
+            if (cur.?.left == null or cur.?.right == null) {
+                // 当子结点数量 = 0 / 1 时， child = null / 该子结点
+                var child = if (cur.?.left != null) cur.?.left else cur.?.right;
+                // 删除结点 cur
+                if (pre.?.left == cur) {
+                    pre.?.left = child;
+                } else {
+                    pre.?.right = child;
+                }
+            // 子结点数量 = 2
+            } else {
+                // 获取中序遍历中 cur 的下一个结点
+                var nex = self.getInOrderNext(cur.?.right);
+                var tmp = nex.?.val;
+                // 递归删除结点 nex
+                _ = self.remove(nex.?.val);
+                // 将 nex 的值复制给 cur
+                cur.?.val = tmp;
+            }
+            return cur;
+        }
+
+        // 获取中序遍历中的下一个结点（仅适用于 root 有左子结点的情况）
+        fn getInOrderNext(self: *Self, node: ?*inc.TreeNode(T)) ?*inc.TreeNode(T) {
+            _ = self;
+            var node_tmp = node;
+            if (node_tmp == null) return null;
+            // 循环访问左子结点，直到叶结点时为最小结点，跳出
+            while (node_tmp.?.left != null) {
+                node_tmp = node_tmp.?.left;
+            }
+            return node_tmp;
+        }
+    };   
+}
+
+// Driver Code
+pub fn main() !void {
+    // 初始化二叉树
+    var nums = [_]i32{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 };
+    var bst = BinarySearchTree(i32){};
+    try bst.init(std.heap.page_allocator, &nums);
+    defer bst.deinit();
+    std.debug.print("初始化的二叉树为\n", .{});
+    try inc.PrintUtil.printTree(bst.getRoot(), null, false);
+
+    // 查找结点
+    var node = bst.search(7);
+    std.debug.print("\n查找到的结点对象为 {any}，结点值 = {}\n", .{node, node.?.val});
+
+    // 插入结点
+    node = try bst.insert(16);
+    std.debug.print("\n插入结点 16 后，二叉树为\n", .{});
+    try inc.PrintUtil.printTree(bst.getRoot(), null, false);
+
+    // 删除结点
+    _ = bst.remove(1);
+    std.debug.print("\n删除结点 1 后，二叉树为\n", .{});
+    try inc.PrintUtil.printTree(bst.getRoot(), null, false);
+    _ = bst.remove(2);
+    std.debug.print("\n删除结点 2 后，二叉树为\n", .{});
+    try inc.PrintUtil.printTree(bst.getRoot(), null, false);
+    _ = bst.remove(4);
+    std.debug.print("\n删除结点 4 后，二叉树为\n", .{});
+    try inc.PrintUtil.printTree(bst.getRoot(), null, false);
+
+    _ = try std.io.getStdIn().reader().readByte();
+}

codes/zig/chapter_tree/binary_tree_dfs.zig

@@ -0,0 +1,70 @@
+// File: binary_tree_dfs.zig
+// Created Time: 2023-01-15
+// Author: sjinzh (sjinzh@gmail.com)
+
+const std = @import("std");
+const inc = @import("include");
+
+var list = std.ArrayList(i32).init(std.heap.page_allocator);
+
+// 前序遍历
+fn preOrder(comptime T: type, root: ?*inc.TreeNode(T)) !void {
+    if (root == null) return;
+    // 访问优先级：根结点 -> 左子树 -> 右子树
+    try list.append(root.?.val);
+    try preOrder(T, root.?.left);
+    try preOrder(T, root.?.right);
+}
+
+// 中序遍历
+fn inOrder(comptime T: type, root: ?*inc.TreeNode(T)) !void {
+    if (root == null) return;
+    // 访问优先级：左子树 -> 根结点 -> 右子树
+    try inOrder(T, root.?.left);
+    try list.append(root.?.val);
+    try inOrder(T, root.?.right);
+}
+
+// 后序遍历
+fn postOrder(comptime T: type, root: ?*inc.TreeNode(T)) !void {
+    if (root == null) return;
+    // 访问优先级：左子树 -> 右子树 -> 根结点
+    try postOrder(T, root.?.left);
+    try postOrder(T, root.?.right);
+    try list.append(root.?.val);
+}
+
+// Driver Code
+pub fn main() !void {
+    // 初始化内存分配器
+    var mem_arena = std.heap.ArenaAllocator.init(std.heap.page_allocator);
+    defer mem_arena.deinit();
+    const mem_allocator = mem_arena.allocator();
+
+    // 初始化二叉树
+    // 这里借助了一个从数组直接生成二叉树的函数
+    var nums = [_]i32{1, 2, 3, 4, 5, 6, 7};
+    var root = try inc.TreeUtil.arrToTree(i32, mem_allocator, &nums);
+    std.debug.print("初始化二叉树\n", .{});
+    try inc.PrintUtil.printTree(root, null, false);
+
+    // 前序遍历
+    list.clearRetainingCapacity();
+    try preOrder(i32, root);
+    std.debug.print("\n前序遍历的结点打印序列 = ", .{});
+    inc.PrintUtil.printList(i32, list);
+
+    // 中序遍历
+    list.clearRetainingCapacity();
+    try inOrder(i32, root);
+    std.debug.print("\n中序遍历的结点打印序列 = ", .{});
+    inc.PrintUtil.printList(i32, list);
+
+    // 后序遍历
+    list.clearRetainingCapacity();
+    try postOrder(i32, root);
+    std.debug.print("\n后续遍历的结点打印序列 = ", .{});
+    inc.PrintUtil.printList(i32, list);
+
+    _ = try std.io.getStdIn().reader().readByte();
+}

codes/zig/include/TreeNode.zig

@@ -10,13 +10,15 @@ pub fn TreeNode(comptime T: type) type {
     return struct {
         const Self = @This();
 
-        val: T = undefined,
-        left: ?*Self = null,
-        right: ?*Self = null,
+        val: T = undefined,         // 结点值
+        height: i32 = undefined,    // 结点高度
+        left: ?*Self = null,        // 左子结点指针
+        right: ?*Self = null,       // 右子结点指针
 
         // Initialize a tree node with specific value
         pub fn init(self: *Self, x: i32) void {
             self.val = x;
+            self.height = 0;
             self.left = null;
             self.right = null;
         }