Implementation of Chinese Remainder Theorem with Extended Euclidean Algorithm

src/main/java/com/thealgorithms/maths/ChineseRemainderTheorem.java

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+//this program is to implement Chinese Remainder Theorem
+public class ChineseRemainderTheorem
+{
+
+    //function to find the greatest common divisor (GCD) of two numbers using the Extended Euclidean Algorithm
+    private static long gcd(long a, long b)
+    {
+        if(b == 0)
+            return a; //base case: if b is 0, a is the GCD
+
+        return gcd(b, a%b);//calling recursively
+    }
+
+    //function to find the modular inverse of 'a' under modulo 'm' using the Extended Euclidean Algorithm
+    private static long extendedGCD(long a, long b)
+    {
+        long originalB = b; //keeping original 'b' for later use
+        long x1 = 1, x2 = 0; //x1 and x2 are coefficients for 'a'
+        long y1 = 0, y2 = 1; //y1 and y2 are coefficients for 'b'
+
+        while(b != 0)
+		{
+            long q = a/b; //quotient
+            long temp = b; //temporary variable to hold value of 'b'
+            b = a % b; //remainder
+            a = temp; //updating 'a' with previous value of 'b'
+
+            //updating coefficients x1, x2, y1, y2
+            temp = x2;
+            x2 = x1 - q*x2; //updating x2 with the quotient
+            x1 = temp;
+
+            temp = y2;
+            y2 = y1 - q*y2; //updating y2 with the quotient
+            y1 = temp;
+        }
+        //ensuring the result is positive
+        return (x1 < 0)? (x1+originalB) : x1;
+    }
+
+    //function to implement the Chinese Remainder Theorem
+    public static long chineseRemainder(int[] n, int[] a)
+    {
+        long N = 1; //variable to hold the product of all moduli
+        for(int ni : n)
+            N *= ni; //calculating the product of all moduli
+
+        long result = 0; //variable to accumulate the final result
+        for (int i = 0; i < n.length; i++)
+		{
+            long Ni = N/n[i]; //calculating Ni (the product of all moduli except n[i])
+            long modularInverse = extendedGCD(Ni, n[i]); //finding the modular inverse of Ni modulo n[i]
+            //updating the result
+            result += a[i]*Ni*modularInverse; 
+        }
+
+        return result%N; //returning final answer
+    }
+
+    public static void main(String[] args)
+    {
+        //example test case
+        int[] moduli = {3, 5, 7};
+        int[] remainder = {2, 3, 2};
+
+        //calculating the solution using the Chinese Remainder Theorem
+        long solution = chineseRemainder(moduli, remainder);
+        //output
+        System.out.println("The solution is: " + solution); //expected output: 23
+    }
+}