feat(c++): binomial expansion

-

languages/c++/CMakeLists.txt

@@ -10,3 +10,4 @@ add_executable(pascal code/pascal.cc)
 add_executable(babylonian code/babylonian.cc)
 add_executable(karatsuba code/karatsuba.cc)
 add_executable(dice code/dice.cc)
+add_executable(binomialExpansion code/binomialExpansion.cc)

languages/c++/code/binomialExpansion.cc

@@ -0,0 +1,72 @@
+#include <iostream>
+
+std::string superscript[10] = {"⁰", "¹", "²", "³", "⁴", "⁵", "⁶", "⁷", "⁸", "⁹"};
+
+int factorial(int number) {
+	int out = 1;
+
+	for (int i = 2; i <= number; i++) {
+		out *= i;
+	}
+
+	return out;
+}
+
+int nCr(int n, int r) {
+	return factorial(n) / (factorial(r) * factorial(n - r));
+}
+
+std::string formatNomial(int value, std::string nomial) {
+	std::string term = nomial;
+
+	if (value != 1) {
+		std::string power = "";
+
+		for (char & digit : std::to_string(value)) {
+			power += superscript[digit - '0'];
+		}
+
+		term += power;
+	}
+
+	return term;
+}
+
+std::string binomialExpansion(int power) {
+	std::string output = "";
+
+	for (int r = 0; r <= power; r++) {
+		int a = power - r;
+		int c = nCr(power, r);
+		std::string term = "";
+
+		if (c != 1) {
+			term += std::to_string(c);
+		}
+
+		if (a != 0) {
+			term += formatNomial(a, "a");
+		}
+
+		if (r != 0) {
+			term += formatNomial(r, "b");
+		}
+
+		if (r != 0) {
+			output += " + " + term;
+		} else {
+			output += term;
+		}
+	}
+
+	return output;
+}
+
+int main() {
+	std::cout << "(a + b)ⁿ\nPlease input a value for n! ";
+
+	int n;
+	std::cin >> n;
+
+	std::cout << binomialExpansion(n);
+}