From 1cc743e97ad0447d4578dfdfb1ccbb377c9506d5 Mon Sep 17 00:00:00 2001
From: sjinzh <99076655+sjinzh@users.noreply.github.com>
Date: Thu, 19 Jan 2023 23:27:14 +0800
Subject: [PATCH] add zig codes for Section Quick Sort, Merge Sort, Radix Sort
 (#282)

* add zig codes for Section 'Quick Sort' (quick_sort.zig), 'Merge Sort' (merge_sort.zig)

* add zig codes for Section 'Quick Sort' (quick_sort.zig), 'Merge Sort' (merge_sort.zig)

* add zig codes for Section 'Quick Sort' (quick_sort.zig), 'Merge Sort' (merge_sort.zig), 'Radix Sort' (radix_sort.zig)

* add zig codes for Section 'Quick Sort' (quick_sort.zig), 'Merge Sort' (merge_sort.zig), 'Radix Sort' (radix_sort.zig)
---
 codes/zig/build.zig                      |  42 ++++++
 codes/zig/chapter_sorting/merge_sort.zig |  67 ++++++++++
 codes/zig/chapter_sorting/quick_sort.zig | 160 +++++++++++++++++++++++
 codes/zig/chapter_sorting/radix_sort.zig |  78 +++++++++++
 4 files changed, 347 insertions(+)
 create mode 100644 codes/zig/chapter_sorting/merge_sort.zig
 create mode 100644 codes/zig/chapter_sorting/quick_sort.zig
 create mode 100644 codes/zig/chapter_sorting/radix_sort.zig

diff --git a/codes/zig/build.zig b/codes/zig/build.zig
index 52d2103c7..ee77bd022 100644
--- a/codes/zig/build.zig
+++ b/codes/zig/build.zig
@@ -297,4 +297,46 @@ pub fn build(b: *std.build.Builder) void {
         if (b.args) |args| run_cmd_insertion_sort.addArgs(args);
         const run_step_insertion_sort = b.step("run_insertion_sort", "Run insertion_sort");
         run_step_insertion_sort.dependOn(&run_cmd_insertion_sort.step);
+
+    // Section: "Quick Sort"
+        // Source File: "chapter_sorting/quick_sort.zig"
+        // Run Command: zig build run_quick_sort
+        const exe_quick_sort = b.addExecutable("quick_sort", "chapter_sorting/quick_sort.zig");
+        exe_quick_sort.addPackagePath("include", "include/include.zig");
+        exe_quick_sort.setTarget(target);
+        exe_quick_sort.setBuildMode(mode);
+        exe_quick_sort.install();
+        const run_cmd_quick_sort = exe_quick_sort.run();
+        run_cmd_quick_sort.step.dependOn(b.getInstallStep());
+        if (b.args) |args| run_cmd_quick_sort.addArgs(args);
+        const run_step_quick_sort = b.step("run_quick_sort", "Run quick_sort");
+        run_step_quick_sort.dependOn(&run_cmd_quick_sort.step);
+
+    // Section: "Merge Sort"
+        // Source File: "chapter_sorting/merge_sort.zig"
+        // Run Command: zig build run_merge_sort
+        const exe_merge_sort = b.addExecutable("merge_sort", "chapter_sorting/merge_sort.zig");
+        exe_merge_sort.addPackagePath("include", "include/include.zig");
+        exe_merge_sort.setTarget(target);
+        exe_merge_sort.setBuildMode(mode);
+        exe_merge_sort.install();
+        const run_cmd_merge_sort = exe_merge_sort.run();
+        run_cmd_merge_sort.step.dependOn(b.getInstallStep());
+        if (b.args) |args| run_cmd_merge_sort.addArgs(args);
+        const run_step_merge_sort = b.step("run_merge_sort", "Run merge_sort");
+        run_step_merge_sort.dependOn(&run_cmd_merge_sort.step);
+
+    // Section: "Radix Sort"
+        // Source File: "chapter_sorting/radix_sort.zig"
+        // Run Command: zig build run_radix_sort
+        const exe_radix_sort = b.addExecutable("radix_sort", "chapter_sorting/radix_sort.zig");
+        exe_radix_sort.addPackagePath("include", "include/include.zig");
+        exe_radix_sort.setTarget(target);
+        exe_radix_sort.setBuildMode(mode);
+        exe_radix_sort.install();
+        const run_cmd_radix_sort = exe_radix_sort.run();
+        run_cmd_radix_sort.step.dependOn(b.getInstallStep());
+        if (b.args) |args| run_cmd_radix_sort.addArgs(args);
+        const run_step_radix_sort = b.step("run_radix_sort", "Run radix_sort");
+        run_step_radix_sort.dependOn(&run_cmd_radix_sort.step);
 }
diff --git a/codes/zig/chapter_sorting/merge_sort.zig b/codes/zig/chapter_sorting/merge_sort.zig
new file mode 100644
index 000000000..85e1e3754
--- /dev/null
+++ b/codes/zig/chapter_sorting/merge_sort.zig
@@ -0,0 +1,67 @@
+// File: merge_sort.zig
+// Created Time: 2023-01-15
+// Author: sjinzh (sjinzh@gmail.com)
+
+const std = @import("std");
+const inc = @import("include");
+
+// 合并左子数组和右子数组
+// 左子数组区间 [left, mid]
+// 右子数组区间 [mid + 1, right]
+fn merge(nums: []i32, left: usize, mid: usize, right: usize) !void {
+    // 初始化辅助数组
+    var mem_arena = std.heap.ArenaAllocator.init(std.heap.page_allocator);
+    defer mem_arena.deinit();
+    const mem_allocator = mem_arena.allocator();
+    var tmp = try mem_allocator.alloc(i32, right + 1 - left);
+    std.mem.copy(i32, tmp, nums[left..right+1]);
+    // 左子数组的起始索引和结束索引  
+    var leftStart = left - left;
+    var leftEnd = mid - left;
+    // 右子数组的起始索引和结束索引       
+    var rightStart = mid + 1 - left;
+    var rightEnd = right - left;
+    // i, j 分别指向左子数组、右子数组的首元素
+    var i = leftStart;
+    var j = rightStart;
+    // 通过覆盖原数组 nums 来合并左子数组和右子数组
+    var k = left;
+    while (k <= right) : (k += 1) {
+        // 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++
+        if (i > leftEnd) {
+            nums[k] = tmp[j];
+            j += 1;
+        // 否则，若“右子数组已全部合并完”或“左子数组元素 <= 右子数组元素”，则选取左子数组元素，并且 i++
+        } else if  (j > rightEnd or tmp[i] <= tmp[j]) {
+            nums[k] = tmp[i];
+            i += 1;
+        // 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++
+        } else {
+            nums[k] = tmp[j];
+            j += 1;
+        }
+    }
+}
+
+// 归并排序
+fn mergeSort(nums: []i32, left: usize, right: usize) !void {
+    // 终止条件
+    if (left >= right) return;              // 当子数组长度为 1 时终止递归
+    // 划分阶段
+    var mid = (left + right) / 2;           // 计算中点
+    try mergeSort(nums, left, mid);         // 递归左子数组
+    try mergeSort(nums, mid + 1, right);    // 递归右子数组
+    // 合并阶段
+    try merge(nums, left, mid, right);
+}
+
+// Driver Code
+pub fn main() !void {
+    // 归并排序
+    var nums = [_]i32{ 7, 3, 2, 6, 0, 1, 5, 4 };
+    try mergeSort(&nums, 0, nums.len - 1);
+    std.debug.print("归并排序完成后 nums = ", .{});
+    inc.PrintUtil.printArray(i32, &nums);
+
+    _ = try std.io.getStdIn().reader().readByte();
+}
\ No newline at end of file
diff --git a/codes/zig/chapter_sorting/quick_sort.zig b/codes/zig/chapter_sorting/quick_sort.zig
new file mode 100644
index 000000000..1a62e3879
--- /dev/null
+++ b/codes/zig/chapter_sorting/quick_sort.zig
@@ -0,0 +1,160 @@
+// File: quick_sort.zig
+// Created Time: 2023-01-15
+// Author: sjinzh (sjinzh@gmail.com)
+
+const std = @import("std");
+const inc = @import("include");
+
+// 快速排序类
+const QuickSort = struct {
+    // 元素交换
+    pub fn swap(nums: []i32, i: usize, j: usize) void {
+        var tmp = nums[i];
+        nums[i] = nums[j];
+        nums[j] = tmp;
+    }
+
+    // 哨兵划分
+    pub fn partition(nums: []i32, left: usize, right: usize) usize {
+        // 以 nums[left] 作为基准数
+        var i = left;
+        var j = right;
+        while (i < j) {
+            while (i < j and nums[j] >= nums[left]) j -= 1; // 从右向左找首个小于基准数的元素
+            while (i < j and nums[i] <= nums[left]) i += 1; // 从左向右找首个大于基准数的元素
+            swap(nums, i, j);   // 交换这两个元素
+        }
+        swap(nums, i, left);    // 将基准数交换至两子数组的分界线
+        return i;               // 返回基准数的索引
+    }
+
+    // 快速排序
+    pub fn quickSort(nums: []i32, left: usize, right: usize) void {
+        // 子数组长度为 1 时终止递归
+        if (left >= right) return;
+        // 哨兵划分
+        var pivot = partition(nums, left, right);
+        // 递归左子数组、右子数组
+        quickSort(nums, left, pivot - 1);
+        quickSort(nums, pivot + 1, right);
+    }
+};
+
+// 快速排序类（中位基准数优化）
+const QuickSortMedian = struct {
+    // 元素交换
+    pub fn swap(nums: []i32, i: usize, j: usize) void {
+        var tmp = nums[i];
+        nums[i] = nums[j];
+        nums[j] = tmp;
+    }
+
+    // 选取三个元素的中位数
+    pub fn medianThree(nums: []i32, left: usize, mid: usize, right: usize) usize {
+        // 使用了异或操作来简化代码
+        // 异或规则为 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1
+        if ((nums[left] < nums[mid]) != (nums[left] < nums[right])) {
+            return left;
+        } else if ((nums[mid] < nums[left]) != (nums[mid] < nums[right])) {
+            return mid;
+        } else {
+            return right;
+        }
+    }
+
+    // 哨兵划分（三数取中值）
+    pub fn partition(nums: []i32, left: usize, right: usize) usize {
+        // 选取三个候选元素的中位数
+        var med = medianThree(nums, left, (left + right) / 2, right);
+        // 将中位数交换至数组最左端
+        swap(nums, left, med);
+        // 以 nums[left] 作为基准数
+        var i = left;
+        var j = right;
+        while (i < j) {
+            while (i < j and nums[j] >= nums[left]) j -= 1; // 从右向左找首个小于基准数的元素
+            while (i < j and nums[i] <= nums[left]) i += 1; // 从左向右找首个大于基准数的元素
+            swap(nums, i, j);   // 交换这两个元素
+        }
+        swap(nums, i, left);    // 将基准数交换至两子数组的分界线
+        return i;               // 返回基准数的索引
+    }
+
+    // 快速排序
+    pub fn quickSort(nums: []i32, left: usize, right: usize) void {
+        // 子数组长度为 1 时终止递归
+        if (left >= right) return;
+        // 哨兵划分
+        var pivot = partition(nums, left, right);
+        if (pivot == 0) return;
+        // 递归左子数组、右子数组
+        quickSort(nums, left, pivot - 1);
+        quickSort(nums, pivot + 1, right);
+    }
+};
+
+// 快速排序类（尾递归优化）
+const QuickSortTailCall = struct {
+    // 元素交换
+    pub fn swap(nums: []i32, i: usize, j: usize) void {
+        var tmp = nums[i];
+        nums[i] = nums[j];
+        nums[j] = tmp;
+    }
+
+    // 哨兵划分
+    pub fn partition(nums: []i32, left: usize, right: usize) usize {
+        // 以 nums[left] 作为基准数
+        var i = left;
+        var j = right;
+        while (i < j) {
+            while (i < j and nums[j] >= nums[left]) j -= 1; // 从右向左找首个小于基准数的元素
+            while (i < j and nums[i] <= nums[left]) i += 1; // 从左向右找首个大于基准数的元素
+            swap(nums, i, j);   // 交换这两个元素
+        }
+        swap(nums, i, left);    // 将基准数交换至两子数组的分界线
+        return i;               // 返回基准数的索引
+    }
+
+    // 快速排序（尾递归优化）
+    pub fn quickSort(nums: []i32, left_: usize, right_: usize) void {
+        var left = left_;
+        var right = right_;
+        // 子数组长度为 1 时终止递归
+        while (left < right) {
+            // 哨兵划分操作
+            var pivot = partition(nums, left, right);
+            // 对两个子数组中较短的那个执行快排
+            if (pivot - left < right - pivot) {
+                quickSort(nums, left, pivot - 1);   // 递归排序左子数组
+                left = pivot + 1;                   // 剩余待排序区间为 [pivot + 1, right]
+            } else {
+                quickSort(nums, pivot + 1, right);  // 递归排序右子数组
+                right = pivot - 1;                  // 剩余待排序区间为 [left, pivot - 1]
+            }
+        }
+    }
+};
+
+// Driver Code
+pub fn main() !void {
+    // 快速排序
+    var nums = [_]i32{ 2, 4, 1, 0, 3, 5 };
+    QuickSort.quickSort(&nums, 0, nums.len - 1);
+    std.debug.print("快速排序完成后 nums = ", .{});
+    inc.PrintUtil.printArray(i32, &nums);
+
+    // 快速排序（中位基准数优化）
+    var nums1 = [_]i32{ 2, 4, 1, 0, 3, 5 };
+    QuickSortMedian.quickSort(&nums1, 0, nums1.len - 1);
+    std.debug.print("\n快速排序（中位基准数优化）完成后 nums = ", .{});
+    inc.PrintUtil.printArray(i32, &nums1);
+
+    // 快速排序（尾递归优化）
+    var nums2 = [_]i32{ 2, 4, 1, 0, 3, 5 };
+    QuickSortTailCall.quickSort(&nums2, 0, nums2.len - 1);
+    std.debug.print("\n快速排序（尾递归优化）完成后 nums = ", .{});
+    inc.PrintUtil.printArray(i32, &nums2);
+    
+    _ = try std.io.getStdIn().reader().readByte();
+}
diff --git a/codes/zig/chapter_sorting/radix_sort.zig b/codes/zig/chapter_sorting/radix_sort.zig
new file mode 100644
index 000000000..c9fc2cc9b
--- /dev/null
+++ b/codes/zig/chapter_sorting/radix_sort.zig
@@ -0,0 +1,78 @@
+// File: radix_sort.zig
+// Created Time: 2023-01-15
+// Author: sjinzh (sjinzh@gmail.com)
+
+const std = @import("std");
+const inc = @import("include");
+
+// 获取元素 num 的第 k 位，其中 exp = 10^(k-1)
+fn digit(num: i32, exp: i32) i32 {
+    // 传入 exp 而非 k 可以避免在此重复执行昂贵的次方计算
+    return @mod(@divFloor(num, exp), 10);
+}
+
+// 计数排序（根据 nums 第 k 位排序）
+fn countSort(nums: []i32, exp: i32) !void {
+    // 十进制的各位数字范围为 0~9 ，因此需要长度为 10 的桶
+    var mem_arena = std.heap.ArenaAllocator.init(std.heap.page_allocator);
+    // defer mem_arena.deinit();
+    const mem_allocator = mem_arena.allocator();
+    var bucket = try mem_allocator.alloc(usize, 10);
+    std.mem.set(usize, bucket, 0);
+    var n = nums.len;
+    // 借助桶来统计 0~9 各数字的出现次数
+    for (nums) |num| {
+        var d = @bitCast(u32, digit(num, exp));    // 获取 nums[i] 第 k 位，记为 d
+        bucket[d] += 1;             // 统计数字 d 的出现次数
+    }
+    // 求前缀和，将“出现个数”转换为“数组索引”
+    var i: usize = 1;
+    while (i < 10) : (i += 1) {
+        bucket[i] += bucket[i - 1];
+    }
+    // 倒序遍历，根据桶内统计结果，将各元素填入暂存数组 tmp
+    var tmp = try mem_allocator.alloc(i32, n);
+    i = n - 1;
+    while (i >= 0) : (i -= 1) {
+        var d = @bitCast(u32, digit(nums[i], exp));
+        var j = bucket[d] - 1;  // 获取 d 在数组中的索引 j
+        tmp[j] = nums[i];       // 将当前元素填入索引 j
+        bucket[d] -= 1;         // 将 d 的数量减 1
+        if (i == 0) break;
+    }
+    // 将 tmp 复制到 nums
+    i = 0;
+    while (i < n) : (i += 1) {
+        nums[i] = tmp[i];
+    }
+}
+
+// 基数排序
+fn radixSort(nums: []i32) !void {
+    // 获取数组的最大元素，用于判断最大位数
+    var ma: i32 = std.math.minInt(i32);
+    for (nums) |num| {
+        if (num > ma) ma = num;
+    }
+    // 按照从低位到高位的顺序遍历
+    var exp: i32 = 1;
+    while (ma >= exp) : (exp *= 10) {
+        // 对数组元素的第 k 位执行「计数排序」
+        // k = 1 -> exp = 1
+        // k = 2 -> exp = 10
+        // k = 3 -> exp = 100
+        // 即 exp = 10^(k-1)
+        try countSort(nums, exp);    
+    }
+} 
+
+// Driver Code
+pub fn main() !void {
+    // 基数排序
+    var nums = [_]i32{ 23, 12, 3, 4, 788, 192 };
+    try radixSort(&nums);
+    std.debug.print("基数排序完成后 nums = ", .{});
+    inc.PrintUtil.printArray(i32, &nums);
+    
+    _ = try std.io.getStdIn().reader().readByte();
+}
\ No newline at end of file