diff --git a/codes/zig/chapter_computational_complexity/time_complexity.zig b/codes/zig/chapter_computational_complexity/time_complexity.zig new file mode 100644 index 00000000..dab17034 --- /dev/null +++ b/codes/zig/chapter_computational_complexity/time_complexity.zig @@ -0,0 +1,179 @@ +// File: time_complexity.zig +// Created Time: 2022-12-28 +// Author: sjinzh (sjinzh@gmail.com) + +const std = @import("std"); + +// 常数阶 +fn constant(n: i32) i32 { + _ = n; + var count: i32 = 0; + const size: i32 = 100_000; + var i: i32 = 0; + while(i 0) : (i -= 1) { + var j: usize = 0; + // 内循环:冒泡操作 + while (j < i) : (j += 1) { + // 交换 nums[j] 与 nums[j + 1] + var tmp = nums[j]; + nums[j] = nums[j + 1]; + nums[j + 1] = tmp; + count += 3; // 元素交换包含 3 个单元操作 + } + } + return count; +} + +// 指数阶(循环实现) +fn exponential(n: i32) i32{ + var count: i32 = 0; + var bas: i32 = 1; + var i: i32 = 0; + // cell 每轮一分为二,形成数列 1, 2, 4, 8, ..., 2^(n-1) + while (i < n) : (i += 1) { + var j: i32 = 0; + while (j < bas) : (j += 1) { + count += 1; + } + bas *= 2; + } + // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1 + return count; +} + +// 指数阶(递归实现) +fn expRecur(n: i32) i32{ + if (n == 1) return 1; + return expRecur(n - 1) + expRecur(n - 1) + 1; +} + +// 对数阶(循环实现) +fn logarithmic(n: f32) i32 +{ + var count: i32 = 0; + var n_var = n; + while (n_var > 1) + { + n_var = n_var / 2; + count +=1; + } + return count; +} + +// 对数阶(递归实现) +fn logRecur(n: f32) i32 +{ + if (n <= 1) return 0; + return logRecur(n / 2) + 1; +} + +// 线性对数阶 +fn linearLogRecur(n: f32) i32 +{ + if (n <= 1) return 1; + var count: i32 = linearLogRecur(n / 2) + + linearLogRecur(n / 2); + var i: f32 = 0; + while (i < n) : (i += 1) { + count += 1; + } + return count; +} + +// 阶乘阶(递归实现) +fn factorialRecur(n: i32) i32 { + if (n == 0) return 1; + var count: i32 = 0; + var i: i32 = 0; + // 从 1 个分裂出 n 个 + while (i < n) : (i += 1) { + count += factorialRecur(n - 1); + } + return count; +} + +// Driver Code +pub fn main() void { + // 可以修改 n 运行,体会一下各种复杂度的操作数量变化趋势 + const n: i32 = 8; + std.debug.print("输入数据大小 n = {}\n", .{n}); + + var count = constant(n); + std.debug.print("常数阶的计算操作数量 = {}\n", .{count}); + + count = linear(n); + std.debug.print("线性阶的计算操作数量 = {}\n", .{count}); + var nums = [_]i32{0}**n; + count = arrayTraversal(&nums); + std.debug.print("线性阶(遍历数组)的计算操作数量 = {}\n", .{count}); + + count = quadratic(n); + std.debug.print("平方阶的计算操作数量 = {}\n", .{count}); + for (nums) |*num, i| { + num.* = n - @intCast(i32, i); // [n,n-1,...,2,1] + } + count = bubbleSort(&nums); + std.debug.print("平方阶(冒泡排序)的计算操作数量 = {}\n", .{count}); + + count = exponential(n); + std.debug.print("指数阶(循环实现)的计算操作数量 = {}\n", .{count}); + count = expRecur(n); + std.debug.print("指数阶(递归实现)的计算操作数量 = {}\n", .{count}); + + count = logarithmic(@as(f32, n)); + std.debug.print("对数阶(循环实现)的计算操作数量 = {}\n", .{count}); + count = logRecur(@as(f32, n)); + std.debug.print("对数阶(递归实现)的计算操作数量 = {}\n", .{count}); + + count = linearLogRecur(@as(f32, n)); + std.debug.print("线性对数阶(递归实现)的计算操作数量 = {}\n", .{count}); + + count = factorialRecur(n); + std.debug.print("阶乘阶(递归实现)的计算操作数量 = {}\n", .{count}); +} + diff --git a/codes/zig/chapter_computational_complexity/worst_best_time_complexity.zig b/codes/zig/chapter_computational_complexity/worst_best_time_complexity.zig new file mode 100644 index 00000000..dacf4595 --- /dev/null +++ b/codes/zig/chapter_computational_complexity/worst_best_time_complexity.zig @@ -0,0 +1,42 @@ +// File: worst_best_time_complexity.zig +// Created Time: 2022-12-28 +// Author: sjinzh (sjinzh@gmail.com) + +const std = @import("std"); + +// 生成一个数组,元素为 { 1, 2, ..., n },顺序被打乱 +pub fn randomNumbers(comptime n: usize) [n]i32 { + var nums: [n]i32 = undefined; + // 生成数组 nums = { 1, 2, 3, ..., n } + for (nums) |*num, i| { + num.* = @intCast(i32, i) + 1; + } + // 随机打乱数组元素 + const rand = std.crypto.random; + rand.shuffle(i32, &nums); + return nums; +} + +// 查找数组 nums 中数字 1 所在索引 +pub fn findOne(nums: []i32) i32 { + for (nums) |num, i| { + if (num == 1) return @intCast(i32, i); + } + return -1; +} + +// Driver Code +pub fn main() !void { + var i: i32 = 0; + while (i < 10) : (i += 1) { + const n: usize = 100; + var nums = randomNumbers(n); + var index = findOne(&nums); + std.debug.print("\n数组 [ 1, 2, ..., n ] 被打乱后 = ", .{}); + for (nums) |num, j| { + std.debug.print("{}{s}", .{num, if (j == nums.len-1) "" else "," }); + } + std.debug.print("\n数字 1 的索引为 {}\n", .{index}); + } +} +