Latex and Code Examples

2020-03-23

Latex and Code Examples

2020-03-23

This blog supports some simple code syntax highlighting and the usage of LaTeX\LaTeX.

Be weary, Katex, the library used to display Latex, will crash your development environment if it encounters a symbol it is unfamiliar with. Be sure to test your posts on the development environment before publishing the site to a production server.

LaTeX\LaTeX Examples

Consider the following list of k a's and l b's:

{a,…,a⏞k a′s,b,…,b⏞l b′s⏟k+l elements}\{\underbrace{% \overbrace{a,\ldots, a}^{k\ a's}, \overbrace{b,\ldots, b}^{l\ b's}} _{k+l\ \mathrm{elements}} \}

Look further at this wild equation:

±∣x1−x2y1−y2l1m1∣∣l1m1l2m2∣2+∣m1n1n1l1∣2\frac{\pm \left|\begin{array}{ccc} x_1-x_2 & y_1-y_2 \\ l_1 & m_1 \end{array}\right|} {\sqrt{\left|\begin{array}{cc}l_1&m_1\\ l_2&m_2\end{array}\right|^2 + \left|\begin{array}{cc}m_1&n_1\\ n_1&l_1\end{array}\right|^2}}

Code Examples

Program in c++ to get the quotient and remainder of a pair of numbers.

#include <iostream>
using namespace std;

int main()
{
  int divisor, dividend, quotient, remainder;

  cout << "Enter dividend: ";
  cin >> dividend;

  cout << "Enter divisor: ";
  cin >> divisor;

  quotient = dividend / divisor;
  remainder = dividend % divisor;

  cout << "Quotient = " << quotient << endl;
  cout << "Remainder = " << remainder;

  return 0;
}

Program in python using the Sieve of Eratosthenes to count primes

def countPrimes_sieve_of_eratosthenes(self, n: int) -> int:
  if n < 2:
      return 0

  marked = set()
  seive = [i for i in range(1, n)]
  skip = 2
  while skip * skip < n:
      if skip not in marked:
          marked.update(seive[2 * skip - 1 :: skip])
      skip += 1

  return len(seive) - len(marked) - 1

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