hello-algo/codes/zig/chapter_computational_complexity/time_complexity.zig
2023-01-10 19:44:04 +08:00

185 lines
4.8 KiB
Zig

// 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<size) : (i += 1) {
count += 1;
}
return count;
}
// 线性阶
fn linear(n: i32) i32 {
var count: i32 = 0;
var i: i32 = 0;
while (i < n) : (i += 1) {
count += 1;
}
return count;
}
// 线性阶(遍历数组)
fn arrayTraversal(nums: []i32) i32 {
var count: i32 = 0;
// 循环次数与数组长度成正比
for (nums) |_| {
count += 1;
}
return count;
}
// 平方阶
fn quadratic(n: i32) i32 {
var count: i32 = 0;
var i: i32 = 0;
// 循环次数与数组长度成平方关系
while (i < n) : (i += 1) {
var j: i32 = 0;
while (j < n) : (j += 1) {
count += 1;
}
}
return count;
}
// 平方阶(冒泡排序)
fn bubbleSort(nums: []i32) i32 {
var count: i32 = 0; // 计数器
// 外循环:待排序元素数量为 n-1, n-2, ..., 1
var i: i32 = @intCast(i32, nums.len ) - 1;
while (i > 0) : (i -= 1) {
var j: usize = 0;
// 内循环:冒泡操作
while (j < i) : (j += 1) {
if (nums[j] > nums[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 {
// 查看本地CPU架构和操作系统信息
var native_target_info = try std.zig.system.NativeTargetInfo.detect(std.zig.CrossTarget{});
std.debug.print("Native Info: CPU Arch = {}, OS = {}\n", .{native_target_info.target.cpu.arch, native_target_info.target.os.tag});
// 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});
}