/* * Author : Yerucham * Bugs : None known(Works well for 0 <= n <= 29 later optimized to 0 <= n <= 49) * Date Created : 3 Jan 2018 */ /* 🔴CHALLENGE 🔴Binomial Expansion First of all, I would like to wish a fantastic new year for everyone in Milky Way Galaxy and wish you health and happiness in your entire life! Now, let's code the following little programming challenge: Your task is to compute and print the expansion of the binomial (X+Y)^N. Here X and Y are variables of the binomial and N is the power of the binomial and you have to receive N from the user. Example: For given N=2, the output must be X^2+2XY+Y^2 (here "^" is short for "to the power of"). For N>2, you can see the required output in my following code. Please google "binomial expansion", for the general formula. */ using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Threading.Tasks; namespace SoloLearn { class BinomialExpansion { static Dictionary factorialValues = new Dictionary(); static void Main(string[] args) { int power = Convert.ToInt32(Console.ReadLine()); Console.Write("(X + Y)^" + power + " = " + (power == 0 ? 1 + "" : "")); for (int i = 0;i <= power;i++) { long coefficient = Combination(power, i); Console.Write((coefficient > 1 ? coefficient + "" : "") + (i < power ? "X" : "") + (i < power - 1 ? "^" + (power - i) + " " : " ") + (i > 0 ? "Y" : "") + (i > 1 ? "^" + i : "") + (i < power ? " + " : "\n")); } } /** * Method to find nCr * @param n * @param r * @return nCr * @throws Exception if n < r */ static long Combination(int n, int r) { if (n < r) throw new Exception("n cannot be less than r"); long num = 1; long denominator; if(n - r > r) { denominator = Factorial(r); for (int i = n;i > n - r;i--) { if (denominator % i == 0) { denominator /= i; continue; } num *= i; } } else { denominator = Factorial(n - r); for (int i = n;i > r;i--) { if (denominator % i == 0) { denominator /= i; continue; } num *= i; } } return num / denominator; } /** * Method to find the factorial of a number * @param x The number whose factorial is to be found * @return x! * @throws Exception if x < 0 */ static long Factorial(int x) { long fact = 0; if (x < 0) throw new Exception("Cannot find factorial of negative numbers"); if (x == 0 || x == 1) return 1; if (factorialValues.ContainsKey(x)) fact = factorialValues[x]; else { fact = x * Factorial(x - 1); factorialValues.Add(x, fact); } return fact; } } }

Binomial Expansion Challenge(Codasan.com)