hello-algo/codes/csharp/chapter_computational_complexity/time_complexity.cs
krahets 932d14644d Polish the content
Polish the chapter preface, introduction and complexity anlysis
2023-08-08 23:16:33 +08:00

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/**
* File: time_complexity.cs
* Created Time: 2022-12-23
* Author: haptear (haptear@hotmail.com)
*/
namespace hello_algo.chapter_computational_complexity;
public class time_complexity {
void algorithm(int n) {
int a = 1; // +0技巧 1
a = a + n; // +0技巧 1
// +n技巧 2
for (int i = 0; i < 5 * n + 1; i++) {
Console.WriteLine(0);
}
// +n*n技巧 3
for (int i = 0; i < 2 * n; i++) {
for (int j = 0; j < n + 1; j++) {
Console.WriteLine(0);
}
}
}
// 算法 A 时间复杂度:常数阶
void algorithm_A(int n) {
Console.WriteLine(0);
}
// 算法 B 时间复杂度:线性阶
void algorithm_B(int n) {
for (int i = 0; i < n; i++) {
Console.WriteLine(0);
}
}
// 算法 C 时间复杂度:常数阶
void algorithm_C(int n) {
for (int i = 0; i < 1000000; i++) {
Console.WriteLine(0);
}
}
/* 常数阶 */
static int constant(int n) {
int count = 0;
int size = 100000;
for (int i = 0; i < size; i++)
count++;
return count;
}
/* 线性阶 */
static int linear(int n) {
int count = 0;
for (int i = 0; i < n; i++)
count++;
return count;
}
/* 线性阶(遍历数组) */
static int arrayTraversal(int[] nums) {
int count = 0;
// 循环次数与数组长度成正比
foreach (int num in nums) {
count++;
}
return count;
}
/* 平方阶 */
static int quadratic(int n) {
int count = 0;
// 循环次数与数组长度成平方关系
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
count++;
}
}
return count;
}
/* 平方阶(冒泡排序) */
static int bubbleSort(int[] nums) {
int count = 0; // 计数器
// 外循环:未排序区间为 [0, i]
for (int i = nums.Length - 1; i > 0; i--) {
// 内循环:将未排序区间 [0, i] 中的最大元素交换至该区间的最右端
for (int j = 0; j < i; j++) {
if (nums[j] > nums[j + 1]) {
// 交换 nums[j] 与 nums[j + 1]
(nums[j + 1], nums[j]) = (nums[j], nums[j + 1]);
count += 3; // 元素交换包含 3 个单元操作
}
}
}
return count;
}
/* 指数阶(循环实现) */
static int exponential(int n) {
int count = 0, bas = 1;
// 细胞每轮一分为二,形成数列 1, 2, 4, 8, ..., 2^(n-1)
for (int i = 0; i < n; i++) {
for (int j = 0; j < bas; j++) {
count++;
}
bas *= 2;
}
// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
return count;
}
/* 指数阶(递归实现) */
static int expRecur(int n) {
if (n == 1) return 1;
return expRecur(n - 1) + expRecur(n - 1) + 1;
}
/* 对数阶(循环实现) */
static int logarithmic(float n) {
int count = 0;
while (n > 1) {
n = n / 2;
count++;
}
return count;
}
/* 对数阶(递归实现) */
static int logRecur(float n) {
if (n <= 1) return 0;
return logRecur(n / 2) + 1;
}
/* 线性对数阶 */
static int linearLogRecur(float n) {
if (n <= 1) return 1;
int count = linearLogRecur(n / 2) +
linearLogRecur(n / 2);
for (int i = 0; i < n; i++) {
count++;
}
return count;
}
/* 阶乘阶(递归实现) */
static int factorialRecur(int n) {
if (n == 0) return 1;
int count = 0;
// 从 1 个分裂出 n 个
for (int i = 0; i < n; i++) {
count += factorialRecur(n - 1);
}
return count;
}
[Test]
public void Test() {
// 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
int n = 8;
Console.WriteLine("输入数据大小 n = " + n);
int count = constant(n);
Console.WriteLine("常数阶的计算操作数量 = " + count);
count = linear(n);
Console.WriteLine("线性阶的计算操作数量 = " + count);
count = arrayTraversal(new int[n]);
Console.WriteLine("线性阶(遍历数组)的计算操作数量 = " + count);
count = quadratic(n);
Console.WriteLine("平方阶的计算操作数量 = " + count);
int[] nums = new int[n];
for (int i = 0; i < n; i++)
nums[i] = n - i; // [n,n-1,...,2,1]
count = bubbleSort(nums);
Console.WriteLine("平方阶(冒泡排序)的计算操作数量 = " + count);
count = exponential(n);
Console.WriteLine("指数阶(循环实现)的计算操作数量 = " + count);
count = expRecur(n);
Console.WriteLine("指数阶(递归实现)的计算操作数量 = " + count);
count = logarithmic((float)n);
Console.WriteLine("对数阶(循环实现)的计算操作数量 = " + count);
count = logRecur((float)n);
Console.WriteLine("对数阶(递归实现)的计算操作数量 = " + count);
count = linearLogRecur((float)n);
Console.WriteLine("线性对数阶(递归实现)的计算操作数量 = " + count);
count = factorialRecur(n);
Console.WriteLine("阶乘阶(递归实现)的计算操作数量 = " + count);
}
}