zad1/Ring.java

@@ -0,0 +1,43 @@
+import java.util.Arrays;
+import java.util.HashSet;
+import java.util.Set;
+import java.util.stream.IntStream;
+
+public class Ring {
+    private int n;
+
+    Ring(int n) {
+        this.n = n;
+    }
+
+    public String findRingDetails() {
+        int[] reversibleElements = getReversibleElements();
+        int[] zeroDivisors = getZeroDivisors();
+        Set nilpotentElements = getNilpotentElements(zeroDivisors);
+        int[] idempotentElements = getIdempotentElements();
+        return "[" + Arrays.toString(reversibleElements) + ", " + Arrays.toString(zeroDivisors) + ", " + nilpotentElements + ", " + Arrays.toString(idempotentElements) + "]";
+    }
+
+    private int[] getReversibleElements() {
+        return IntStream.rangeClosed(0, n - 1).filter(k -> NWDCalculator.findNWD(k, n) == 1).toArray();
+    }
+
+    private int[] getZeroDivisors() {
+        return IntStream.rangeClosed(0, n - 1).filter(k -> NWDCalculator.findNWD(k, n) > 1).toArray();
+    }
+
+    private Set getNilpotentElements(int[] zeroDivisors) {
+        Set<Integer> nilpotentElements = new HashSet<>();
+        for (int i = 0; i < n; i++) {
+            for (int i1 : zeroDivisors) {
+                if (Math.pow(i1, i) % n == 0)
+                    nilpotentElements.add(i1);
+            }
+        }
+        return nilpotentElements;
+    }
+
+    private int[] getIdempotentElements() {
+        return IntStream.rangeClosed(0, n - 1).filter(k -> k * k % n == k).toArray();
+    }
+}