时间复杂度分析

#include<iostream>
#include<string>
#include<cassert>

using namespace std;

//O(1)
void swapTwoInts(int &a, int &b) {
int temp = a;
a = b;
b = temp;
return;
}

//O(n)
int sum(int n) {
assert(n >= 0);

int ret = 0;
for (int i = 0; i <= n; i++)
ret += i;
return ret;
}

void reverse(string &s) {
int n = s.size();
for (int i = 0; i < n / 2; i++)
swap(s[i], s[n - 1 - i]);
return;
}

//O(n^2) Time Complexity
void selectionSort(int arr[], int n) {

for (int i = 0; i < n; i++) {
int minIndex = i;
for (int j = i + 1; j < n; j++) {
if (arr[j] < arr[minIndex])
minIndex = j;
}
swap(arr[i], arr[minIndex]);
}
}

//O(n) Time Complexity
void printInfomation(int n) {

for (int i = 1; i <= n; i++)
for (int j = 1; j <= 30; j++)
cout << "Class " << i << " - " << "No. " << j << endl;
return;
}

//O(logn) Time Complexity
int binarySearch(int arr[], int n, int target) {

int l = 0, r = n - 1;
while (l <= r) {
int mid = l + (r - l) / 2;
if (arr[mid] == target) return mid;
if (arr[mid] > target) r = mid - 1;
else l = mid + 1;
}
return -1;
}

string intTostring(int num) {

string s = "";
string sign = "+";
if (num < 0) {
num = -num;
sign = "-";
}

while (num) {
s += '0' + num % 10;
num /= 10;
}

if (s == "")
s = "0";

reverse(s);
if (sign == "-")
return sign + s;
else
return s;
}

//O(nlogn)
void hello(int n) {
for (int sz = 1; sz < n; sz += sz)
for (int i = 1; i < n; i++)
cout << "Hello, Algorithm" << endl;
}

//O(sqrt(n)) Time Complexity
bool isPrime(int num) {
for (int x = 2; x*x <= num; x++)
if (num % x == 0)
return false;
return true;
}

bool isPrime2(int num) {
if (num <= 1)  return false;
if (num == 2)   return true;
if (num % 2 == 0)  return false;

for (int x = 3; x*x <= num; x += 2)
if (num%x == 0)
return false;
return true;
}

int main() {
cout << intTostring(123) << endl;
cout << intTostring(0) << endl;
cout << intTostring(-123) << endl;

cout << endl;

if (isPrime2(137))  cout << "137 is a prime" << endl;
else  cout << "137 is not a prime" << endl;

if (isPrime(121))  cout << "121 is a prime" << endl;
else  cout << "121 is not a prime" << endl;

return 0;
}