mirror of
https://github.com/krahets/hello-algo.git
synced 2026-04-24 02:21:30 +08:00
Translate all code to English (#1836)
* Review the EN heading format. * Fix pythontutor headings. * Fix pythontutor headings. * bug fixes * Fix headings in **/summary.md * Revisit the CN-to-EN translation for Python code using Claude-4.5 * Revisit the CN-to-EN translation for Java code using Claude-4.5 * Revisit the CN-to-EN translation for Cpp code using Claude-4.5. * Fix the dictionary. * Fix cpp code translation for the multipart strings. * Translate Go code to English. * Update workflows to test EN code. * Add EN translation for C. * Add EN translation for CSharp. * Add EN translation for Swift. * Trigger the CI check. * Revert. * Update en/hash_map.md * Add the EN version of Dart code. * Add the EN version of Kotlin code. * Add missing code files. * Add the EN version of JavaScript code. * Add the EN version of TypeScript code. * Fix the workflows. * Add the EN version of Ruby code. * Add the EN version of Rust code. * Update the CI check for the English version code. * Update Python CI check. * Fix cmakelists for en/C code. * Fix Ruby comments
This commit is contained in:
Yudong Jin
@@ -0,0 +1,195 @@
|
||||
/**
|
||||
* 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 (technique 1)
|
||||
a += n; // +0 (technique 1)
|
||||
// +n (technique 2)
|
||||
for (int i = 0; i < 5 * n + 1; i++) {
|
||||
Console.WriteLine(0);
|
||||
}
|
||||
// +n*n (technique 3)
|
||||
for (int i = 0; i < 2 * n; i++) {
|
||||
for (int j = 0; j < n + 1; j++) {
|
||||
Console.WriteLine(0);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Algorithm A time complexity: constant
|
||||
void AlgorithmA(int n) {
|
||||
Console.WriteLine(0);
|
||||
}
|
||||
|
||||
// Algorithm B time complexity: linear
|
||||
void AlgorithmB(int n) {
|
||||
for (int i = 0; i < n; i++) {
|
||||
Console.WriteLine(0);
|
||||
}
|
||||
}
|
||||
|
||||
// Algorithm C time complexity: constant
|
||||
void AlgorithmC(int n) {
|
||||
for (int i = 0; i < 1000000; i++) {
|
||||
Console.WriteLine(0);
|
||||
}
|
||||
}
|
||||
|
||||
/* Constant order */
|
||||
int Constant(int n) {
|
||||
int count = 0;
|
||||
int size = 100000;
|
||||
for (int i = 0; i < size; i++)
|
||||
count++;
|
||||
return count;
|
||||
}
|
||||
|
||||
/* Linear order */
|
||||
int Linear(int n) {
|
||||
int count = 0;
|
||||
for (int i = 0; i < n; i++)
|
||||
count++;
|
||||
return count;
|
||||
}
|
||||
|
||||
/* Linear order (traversing array) */
|
||||
int ArrayTraversal(int[] nums) {
|
||||
int count = 0;
|
||||
// Number of iterations is proportional to the array length
|
||||
foreach (int num in nums) {
|
||||
count++;
|
||||
}
|
||||
return count;
|
||||
}
|
||||
|
||||
/* Exponential order */
|
||||
int Quadratic(int n) {
|
||||
int count = 0;
|
||||
// Number of iterations is quadratically related to the data size n
|
||||
for (int i = 0; i < n; i++) {
|
||||
for (int j = 0; j < n; j++) {
|
||||
count++;
|
||||
}
|
||||
}
|
||||
return count;
|
||||
}
|
||||
|
||||
/* Quadratic order (bubble sort) */
|
||||
int BubbleSort(int[] nums) {
|
||||
int count = 0; // Counter
|
||||
// Outer loop: unsorted range is [0, i]
|
||||
for (int i = nums.Length - 1; i > 0; i--) {
|
||||
// Inner loop: swap the largest element in the unsorted range [0, i] to the rightmost end of that range
|
||||
for (int j = 0; j < i; j++) {
|
||||
if (nums[j] > nums[j + 1]) {
|
||||
// Swap nums[j] and nums[j + 1]
|
||||
(nums[j + 1], nums[j]) = (nums[j], nums[j + 1]);
|
||||
count += 3; // Element swap includes 3 unit operations
|
||||
}
|
||||
}
|
||||
}
|
||||
return count;
|
||||
}
|
||||
|
||||
/* Exponential order (loop implementation) */
|
||||
int Exponential(int n) {
|
||||
int count = 0, bas = 1;
|
||||
// Cells divide into two every round, forming sequence 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;
|
||||
}
|
||||
|
||||
/* Exponential order (recursive implementation) */
|
||||
int ExpRecur(int n) {
|
||||
if (n == 1) return 1;
|
||||
return ExpRecur(n - 1) + ExpRecur(n - 1) + 1;
|
||||
}
|
||||
|
||||
/* Logarithmic order (loop implementation) */
|
||||
int Logarithmic(int n) {
|
||||
int count = 0;
|
||||
while (n > 1) {
|
||||
n /= 2;
|
||||
count++;
|
||||
}
|
||||
return count;
|
||||
}
|
||||
|
||||
/* Logarithmic order (recursive implementation) */
|
||||
int LogRecur(int n) {
|
||||
if (n <= 1) return 0;
|
||||
return LogRecur(n / 2) + 1;
|
||||
}
|
||||
|
||||
/* Linearithmic order */
|
||||
int LinearLogRecur(int n) {
|
||||
if (n <= 1) return 1;
|
||||
int count = LinearLogRecur(n / 2) + LinearLogRecur(n / 2);
|
||||
for (int i = 0; i < n; i++) {
|
||||
count++;
|
||||
}
|
||||
return count;
|
||||
}
|
||||
|
||||
/* Factorial order (recursive implementation) */
|
||||
int FactorialRecur(int n) {
|
||||
if (n == 0) return 1;
|
||||
int count = 0;
|
||||
// Split from 1 into n
|
||||
for (int i = 0; i < n; i++) {
|
||||
count += FactorialRecur(n - 1);
|
||||
}
|
||||
return count;
|
||||
}
|
||||
|
||||
[Test]
|
||||
public void Test() {
|
||||
// You can modify n to run and observe the trend of the number of operations for various complexities
|
||||
int n = 8;
|
||||
Console.WriteLine("Input data size n = " + n);
|
||||
|
||||
int count = Constant(n);
|
||||
Console.WriteLine("Constant order operation count = " + count);
|
||||
|
||||
count = Linear(n);
|
||||
Console.WriteLine("Linear order operation count = " + count);
|
||||
count = ArrayTraversal(new int[n]);
|
||||
Console.WriteLine("Linear order (array traversal) operation count = " + count);
|
||||
|
||||
count = Quadratic(n);
|
||||
Console.WriteLine("Quadratic order operation count = " + 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("Quadratic order (bubble sort) operation count = " + count);
|
||||
|
||||
count = Exponential(n);
|
||||
Console.WriteLine("Exponential order (loop implementation) operation count = " + count);
|
||||
count = ExpRecur(n);
|
||||
Console.WriteLine("Exponential order (recursive implementation) operation count = " + count);
|
||||
|
||||
count = Logarithmic(n);
|
||||
Console.WriteLine("Logarithmic order (loop implementation) operation count = " + count);
|
||||
count = LogRecur(n);
|
||||
Console.WriteLine("Logarithmic order (recursive implementation) operation count = " + count);
|
||||
|
||||
count = LinearLogRecur(n);
|
||||
Console.WriteLine("Linearithmic order (recursive implementation) operation count = " + count);
|
||||
|
||||
count = FactorialRecur(n);
|
||||
Console.WriteLine("Factorial order (recursive implementation) operation count = " + count);
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user