feat(c++): karatsuba algorithm

-

languages/c++/CMakeLists.txt

@@ -8,3 +8,4 @@ set(CMAKE_RUNTIME_OUTPUT_DIRECTORY ${CMAKE_BINARY_DIR}/bin)
 
 add_executable(pascal code/pascal.cc)
 add_executable(babylonian code/babylonian.cc)
+add_executable(karatsuba code/karatsuba.cc)

languages/c++/code/karatsuba.cc

@@ -0,0 +1,45 @@
+#include <iostream>
+#include <math.h>
+using namespace std;
+
+double karatsuba(double num1, double num2) {
+	int num1Length = to_string((int)num1).size();
+	int num2Length = to_string((int)num2).size();
+
+	// Fallback to traditional multiplication
+	if (num1Length == 1 || num2Length == 1) {
+		return num1 * num2;
+	} else {
+		double n = floor(max(num1Length, num2Length) / 2);
+
+		double lowNum1 = fmod(num1, pow(10, n));
+		double lowNum2 = fmod(num2, pow(10, n));
+
+		double highNum1 = floor(num1 / pow(10, n));
+		double highNum2 = floor(num2 / pow(10, n));
+
+		double z0 = karatsuba(lowNum1, lowNum2);
+		double z1 = karatsuba(lowNum1 + highNum1, lowNum2 + highNum2);
+		double z2 = karatsuba(highNum1, highNum2);
+
+		return (z2 * pow(10, n * 2)) + ((z1 - z2 - z0) * pow(10, n)) + z0;
+	}
+}
+
+int main() {
+	cout << "Give me a number! ";
+
+	double num1;
+	cin >> num1;
+
+	cout << "Give me a number to multiply " + to_string(num1) + " by! ";
+
+	double num2;
+	cin >> num2;
+
+	double karatsubaResult = karatsuba(num1, num2);
+	double quadraticResult = num1 * num2;
+
+	cout << endl << "Quadratic Result: " + to_string(quadraticResult) << endl;
+	cout << "Karatsuba Result: " + to_string(karatsubaResult);
+}