ModLinEquationSolver.cpp

Author: lxylxy123456

ModLinEquationSolver.cpp

@@ -0,0 +1,65 @@
+//  
+//  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_ModLinEquationSolver
+#endif
+
+#ifndef FUNC_ModLinEquationSolver
+#define FUNC_ModLinEquationSolver
+
+#include "utils.h"
+
+#include "Euclid.cpp"
+
+template <typename T>
+void ModularLinearEquationSolver(T a, T b, T n, std::vector<T>& ans) {
+	T x, y; 
+	T d = ExtendedEuclid(a, n, x, y); 
+	if (b % d == 0) {
+		T x0 = x * (b / d) % n; 
+		ans.reserve(d); 
+		for (T i = 0; i < d; i++)
+			ans.push_back(((x0 + i * (n / d)) % n + n) % n); 
+	}
+}
+
+#endif
+
+#ifdef MAIN_ModLinEquationSolver
+int main(int argc, char *argv[]) {
+	const size_t nn = get_argv(argc, argv, 1, 4); 
+	using T = long long int; 
+    std::random_device rd; 
+    std::uniform_int_distribution<T> dis(0, 1 << nn); 
+	T a = get_argv(argc, argv, 2, dis(rd)); 
+	T b = get_argv(argc, argv, 3, dis(rd)); 
+	T n = get_argv(argc, argv, 4, dis(rd)); 
+	std::vector<T> ans; 
+	ModularLinearEquationSolver(a, b, n, ans); 
+	std::cout << a << " * x === " << b << " (mod " << n << ")" << std::endl; 
+	if (ans.size()) {
+		std::cout << "x = "; 
+		output_integers(ans); 
+	} else
+		std::cout << "no solutions" << std::endl; 
+	return 0; 
+}
+#endif
+

README.md

@@ -199,6 +199,7 @@
 | 30 | IterativeFFT.cpp				| Bit Reversal Copy						|  918 |
 | 31 | Euclid.cpp					| Euclid								|  935 |
 | 31 | Euclid.cpp					| Extended Euclid						|  937 |
+| 31 | ModLinEquationSolver.cpp		| Modular Linear Equation Solver		|  949 |
 
 # Supplementary Files
 * `utils.h`: Utils