Added Shor Algorithm

Author: joelkurien

src/main/java/com/thealgorithms/others/ShorAlgorithm.java

@@ -0,0 +1,51 @@
+package com.thealgorithms.others;
+
+import java.math.BigInteger;
+import java.util.Random;
+
+public class ShorAlgorithm {
+    //trying to find the order of exponent given the base and the number
+    private int exponent(BigInteger base, BigInteger number){
+        BigInteger result = BigInteger.ONE;
+        int increment = 0;
+        while (!result.equals(BigInteger.ONE) || increment == 0){
+            result = result.multiply(base).mod(number);
+            increment++;
+        }
+        return increment;
+    }
+
+    //implementing the shor algorithm
+    public void shorAlgorithm(BigInteger number){
+        if(number.mod(new BigInteger("2")).equals(BigInteger.ZERO)){
+            BigInteger p = number.divide(new BigInteger("2"));
+            BigInteger q = new BigInteger("2");
+            System.out.println("p: "+ p + " q: " + q);
+            return;
+        }
+
+        Random random = new Random();
+        BigInteger base = BigInteger.ZERO;
+        do{
+            base = new BigInteger(number.bitLength(), random);
+        } while (base.compareTo(BigInteger.ZERO) <= 0 || base.compareTo(number) >= 0);
+
+        BigInteger hcf = base.gcd(number);
+        if(hcf.compareTo(BigInteger.ONE) > 0){
+            System.out.println("p: "+ hcf + " q: " + number.divide(hcf));
+            return;
+        }
+
+        int result = exponent(base, number);
+        if(result % 2 != 0) return;
+
+        BigInteger congruentResult = base.modPow(BigInteger.valueOf(result/2), number);
+        if(congruentResult.equals(number.subtract(BigInteger.ONE))) return;
+
+        BigInteger p = congruentResult.add(BigInteger.ONE).gcd(number);
+        BigInteger q = congruentResult.subtract(BigInteger.ONE).gcd(number);
+
+        if(!p.equals(BigInteger.ONE) && !q.equals(BigInteger.ONE))
+            System.out.println("p: "+ p + " q: " + q);
+    }
+}