From 7858187d59c7189c05b5833162fda8a2c64b5bb4 Mon Sep 17 00:00:00 2001
From: Rahul Chhabra <rahul29112002@gmail.com>
Date: Thu, 28 Oct 2021 22:35:44 +0530
Subject: [PATCH] Add Solver For Linear Diophantine Equations (#2744)

---
 Maths/LinearDiophantineEquationsSolver.java | 143 ++++++++++++++++++++
 1 file changed, 143 insertions(+)
 create mode 100644 Maths/LinearDiophantineEquationsSolver.java

diff --git a/Maths/LinearDiophantineEquationsSolver.java b/Maths/LinearDiophantineEquationsSolver.java
new file mode 100644
index 00000000..09837cc9
--- /dev/null
+++ b/Maths/LinearDiophantineEquationsSolver.java
@@ -0,0 +1,143 @@
+package Maths;
+
+import java.util.Objects;
+
+public final class LinearDiophantineEquationsSolver {
+
+    public static void main(String[] args) {
+        // 3x + 4y = 7
+        final var toSolve = new Equation(3, 4, 7);
+        System.out.println(findAnySolution(toSolve));
+    }
+
+    public static Solution findAnySolution(final Equation equation) {
+        if (equation.a() == 0 && equation.b() == 0 && equation.c() == 0) {
+            return Solution.INFINITE_SOLUTIONS;
+        }
+        final var stub = new GcdSolutionWrapper(0, new Solution(0, 0));
+        final var gcdSolution = gcd(equation.a(), equation.b(), stub);
+        if (equation.c() % gcdSolution.getGcd() != 0) {
+            return Solution.NO_SOLUTION;
+        }
+        final var toReturn = new Solution(0, 0);
+        var xToSet = stub.getSolution().getX() * (equation.c() / stub.getGcd());
+        var yToSet = stub.getSolution().getY() * (equation.c() / stub.getGcd());
+        toReturn.setX(xToSet);
+        toReturn.setY(yToSet);
+        return toReturn;
+    }
+
+    private static GcdSolutionWrapper gcd(final int a, final int b, final GcdSolutionWrapper previous) {
+        if (b == 0) {
+            return new GcdSolutionWrapper(a, new Solution(1, 0));
+        }
+        // stub wrapper becomes the `previous` of the next recursive call
+        final var stubWrapper = new GcdSolutionWrapper(0, new Solution(0, 0));
+        final var next = /* recursive call */ gcd(b, a % b, stubWrapper);
+        previous.getSolution().setX(next.getSolution().getY());
+        previous.getSolution().setY(next.getSolution().getX() - (a / b) * (next.getSolution().getY()));
+        previous.setGcd(next.getGcd());
+        return new GcdSolutionWrapper(next.getGcd(), previous.getSolution());
+    }
+
+    public static final class Solution {
+        public static final Solution NO_SOLUTION = new Solution(Integer.MAX_VALUE, Integer.MAX_VALUE);
+        public static final Solution INFINITE_SOLUTIONS = new Solution(Integer.MIN_VALUE, Integer.MIN_VALUE);
+        private int x;
+        private int y;
+
+        public Solution(int x, int y) {
+            this.x = x;
+            this.y = y;
+        }
+
+        public int getX() {
+            return x;
+        }
+
+        public int getY() {
+            return y;
+        }
+
+        public void setX(int x) {
+            this.x = x;
+        }
+
+        public void setY(int y) {
+            this.y = y;
+        }
+
+        @Override
+        public boolean equals(Object obj) {
+            if (obj == this) return true;
+            if (obj == null || obj.getClass() != this.getClass()) return false;
+            var that = (Solution) obj;
+            return this.x == that.x &&
+                    this.y == that.y;
+        }
+
+        @Override
+        public int hashCode() {
+            return Objects.hash(x, y);
+        }
+
+        @Override
+        public String toString() {
+            return "Solution[" +
+                    "x=" + x + ", " +
+                    "y=" + y + ']';
+        }
+
+    }
+
+    public record Equation(int a, int b, int c) {
+    }
+
+    public static final class GcdSolutionWrapper {
+        private int gcd;
+        private Solution solution;
+
+        public GcdSolutionWrapper(int gcd, Solution solution) {
+            this.gcd = gcd;
+            this.solution = solution;
+        }
+
+        @Override
+        public boolean equals(Object obj) {
+            if (obj == this) return true;
+            if (obj == null || obj.getClass() != this.getClass()) return false;
+            var that = (GcdSolutionWrapper) obj;
+            return this.gcd == that.gcd &&
+                    Objects.equals(this.solution, that.solution);
+        }
+
+        public int getGcd() {
+            return gcd;
+        }
+
+        public void setGcd(int gcd) {
+            this.gcd = gcd;
+        }
+
+        public Solution getSolution() {
+            return solution;
+        }
+
+        public void setSolution(Solution solution) {
+            this.solution = solution;
+        }
+
+        @Override
+        public int hashCode() {
+            return Objects.hash(gcd, solution);
+        }
+
+        @Override
+        public String toString() {
+            return "GcdSolutionWrapper[" +
+                    "gcd=" + gcd + ", " +
+                    "solution=" + solution + ']';
+        }
+
+    }
+}