readme

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+ZAD1
+Program można uruchomić za pomocą polecenia: java Main 6
+ZAD2
+Program można uruchomić za pomocą polecenia: java Main "6" "[1,2,3,0,1]" "[2,4,0,0,2]"

zad1/Main.java

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+import java.util.Scanner;
+
+public class Main {
+
+    public static void main(String[] args) {
+        int n;
+        if(args.length == 0) {
+            System.out.println("Proszę podać n ");
+            Scanner scan = new Scanner(System.in);
+            n = scan.nextInt();
+        }
+        else{
+            n = Integer.parseInt(args[0]);
+        }
+        Ring ring = new Ring(n);
+        System.out.println(ring.findRingDetails());
+    }
+}

zad1/NWDCalculator.java

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+public class NWDCalculator {
+    public static int findNWD(int a, int b) {
+        if (b == 0)
+            return a;
+        else {
+            return findNWD(b, a % b);
+        }
+    }
+}

zad1/Ring.java

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+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();
+    }
+}

zad2/Main.java

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+import java.util.Arrays;
+
+
+public class Main {
+
+    public static void main(String[] args) {
+        if (args.length == 0) {
+            System.out.println("Proszę podać parametry np. java Main \"6\" \"[1,2,3,0,1]\" \"[2,4,0,0,2]\"");
+            return;
+        }
+        int modulo = Integer.parseInt(args[0]);
+        int[] polyF = stringToArray(args[1]);
+        int[] polyG = stringToArray(args[2]);
+        String multiple = Arrays.toString(PolynomialOperations.multiple(polyF, polyG, modulo));
+        int[] divisionArray = PolynomialOperations.divide(polyF, polyG, modulo);
+        String division;
+        if(divisionArray == null)
+            division = "DivisionError";
+        else if (divisionArray.length == 0)
+            division = "[0]";
+        else
+            division = Arrays.toString(divisionArray);
+        String nwd = Arrays.toString(PolynomialOperations.NWD(polyF, polyG, modulo));
+        if (nwd.equals("null"))
+            nwd = "DivisionError";
+
+        String outputString = "[" + multiple + ", " + division + ", " + nwd + "]";
+        System.out.println(outputString);
+    }
+
+    private static int[] stringToArray(String str) {
+        return Arrays.stream(str.substring(1, str.length() - 1).split(","))
+                .map(String::trim).mapToInt(Integer::parseInt).toArray();
+    }
+}

zad2/PolynomialOperations.java

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+import java.util.Arrays;
+
+public class PolynomialOperations {
+
+    public static int[] multiple(int[] f, int[] g, int n) {
+        int[] result = new int[f.length + g.length - 1];
+        for (int i = 0; i < f.length; i++)
+            for (int j = 0; j < g.length; j++)
+                result[i + j] += f[i] * g[j];
+
+        for (int i = 0; i < result.length; i++)
+            result[i] = result[i] % n;
+        return result;
+    }
+
+    private static int findFactor(int a, int b, int mod) {
+        for (int i = 0; i < mod; i++)
+            if (a == (b * i) % mod)
+                return i;
+        return Integer.MIN_VALUE;
+    }
+
+    private static int[] shr(int[] p, int shift) {
+        if (shift <= 0)
+            return p;
+        int[] shiftedPoly = new int[p.length];
+        for (int i = 0; i < p.length - shift; i++)
+            shiftedPoly[i] = p[i + shift];
+        return shiftedPoly;
+    }
+
+    private static void polyMultiply(int[] p, int n) {
+        Arrays.stream(p).forEach(value -> value = value * n);
+    }
+
+    private static int[] polySubtract(int[] p, int[] s) {
+        int result[] = Arrays.copyOf(p, p.length);
+        for (int i = 0; i < p.length; ++i) {
+            result[i] = p[i] - s[i];
+        }
+        return result;
+    }
+
+    private static int[] createNewPoly(int[] p, int size) {
+        int[] tmpTab = new int[size];
+        for (int j = 0; j < p.length; j++) {
+            tmpTab[tmpTab.length - 1 - j] = p[p.length - 1 - j];
+        }
+        return tmpTab;
+    }
+
+    private static void applyModuloToTab(int p[], int mod) {
+        Arrays.stream(p).forEach(value -> value = value % mod);
+    }
+
+    public static int[] divide(int[] n, int[] d, int mod) {
+        if (n.length < d.length) {
+            return null;
+        }
+        int nd = n.length - 1;
+        int dd = d.length - 1;
+        int index = 0;
+        int[] tmpTab = createNewPoly(d, n.length);
+        while (nd >= dd) {
+            int factor = findFactor(n[nd], d[dd], mod);
+            tmpTab = shr(tmpTab, index);
+            polyMultiply(tmpTab, factor);
+
+            applyModuloToTab(tmpTab, mod);
+            tmpTab = polySubtract(n, tmpTab);
+            nd--;
+            index++;
+        }
+        return Arrays.copyOf(n, index - 1);
+    }
+
+    public static int[] NWD(int[] a, int[] b, int mod) {
+        if (a.length <= 0 || b.length <= 0)
+            return null;
+
+        while (b.length != 0) {
+            int[] c;
+            if (a.length >= b.length)
+                c = divide(a, b, mod);
+            else
+                c = divide(b, a, mod);
+            a = b;
+            b = c;
+        }
+        return a;
+    }
+}