Euclid.cpp

Author: lxylxy123456

Euclid.cpp

@@ -0,0 +1,71 @@
+//  
+//  algorithm - some algorithms in "Introduction to Algorithms", third edition
+//  Copyright (C) 2018  lxylxy123456
+//  
+//  This program is free software: you can redistribute it and/or modify
+//  it under the terms of the GNU Affero General Public License as
+//  published by the Free Software Foundation, either version 3 of the
+//  License, or (at your option) any later version.
+//  
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU Affero General Public License for more details.
+//  
+//  You should have received a copy of the GNU Affero General Public License
+//  along with this program.  If not, see <https://www.gnu.org/licenses/>.
+//  
+
+#ifndef MAIN
+#define MAIN
+#define MAIN_Euclid
+#endif
+
+#ifndef FUNC_Euclid
+#define FUNC_Euclid
+
+#include <cassert>
+#include "utils.h"
+
+template <typename T>
+T Euclid(T a, T b) {
+	if (b == 0)
+		return a; 
+	else
+		return Euclid(b, a % b); 
+}
+
+template <typename T>
+T ExtendedEuclid(T a, T b, T& x, T& y) {
+	if (b == 0) {
+		x = 1; 
+		y = 0; 
+		return a; 
+	} else {
+		T xx, yy; 
+		T dd = ExtendedEuclid(b, a % b, xx, yy); 
+		x = yy; 
+		y = xx - (a / b) * yy; 
+		return dd; 
+	}
+}
+#endif
+
+#ifdef MAIN_Euclid
+int main(int argc, char *argv[]) {
+	const size_t n = get_argv(argc, argv, 1, 16); 
+	using T = long long int; 
+    std::random_device rd; 
+    std::uniform_int_distribution<T> dis(0, 1 << n); 
+	T a = get_argv(argc, argv, 2, dis(rd)); 
+	T b = get_argv(argc, argv, 3, dis(rd)); 
+	T x, y; 
+	T d = ExtendedEuclid(a, b, x, y); 
+	assert(d == Euclid(a, b)); 
+	assert(d == a * x + b * y); 
+	std::cout << d << " = gcd(" << a << ", " << b << ") = "
+			 << a << " * " << x << " + " << b << " * " << y << std::endl; 
+	return 0; 
+}
+#endif
+

README.md

@@ -197,6 +197,8 @@
 | 30 | RecursiveFFT.cpp				| Polynomial Multiply					|  914 |
 | 30 | IterativeFFT.cpp				| Iterative FFT							|  917 |
 | 30 | IterativeFFT.cpp				| Bit Reversal Copy						|  918 |
+| 31 | Euclid.cpp					| Euclid								|  935 |
+| 31 | Euclid.cpp					| Extended Euclid						|  937 |
 
 # Supplementary Files
 * `utils.h`: Utils