Prześlij pliki do 'zad2'

Main.java

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+import java.util.Arrays;
+import java.util.Scanner;
+
+public class Main {
+
+    public static void main(String[] args) {
+        int n;
+        if (args.length < 1) {
+            n = -1;
+            Scanner scanner = new Scanner(System.in);
+            while (n < 2) {
+                System.out.print("n = ");
+                n = scanner.nextInt();
+            }
+        } else { n = Integer.parseInt(args[0]); }
+
+        Ring r = new Ring(n);
+
+        r.wyznaczOdwracalne();
+        r.wyznaczDzielniki();
+        r.wyznaczNil();
+        r.wyznaczId();
+
+        System.out.println("elementy odwracalne (" + r.odwracalne.size() + "):");
+        for (int i: r.odwracalne) {
+            System.out.print(i + ", ");
+        }
+        System.out.println();
+        System.out.println("dzielniki zera (" + r.dzielniki.size() + "):");
+        for (int i: r.dzielniki) {
+            System.out.print(i + ", ");
+        }
+        System.out.println();
+        System.out.println("elementy nilpotentne (" + r.nilpotentne.size() + "):");
+        for (int i: r.nilpotentne) {
+            System.out.print(i + ", ");
+        }
+        System.out.println();
+        System.out.println("elementy idempotentne (" + r.idempotentne.size() + "):");
+        for (int i: r.idempotentne) {
+            System.out.print(i + ", ");
+        }
+    }
+}

Ring.java

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+import java.util.ArrayList;
+
+public class Ring {
+    int n;
+    ArrayList<Integer> odwracalne;
+    ArrayList<Integer> dzielniki;
+    ArrayList<Integer> nilpotentne;
+    ArrayList<Integer> idempotentne;
+
+    public Ring(int n) {
+        this.n = n;
+        odwracalne = new ArrayList<>();
+        dzielniki = new ArrayList<>();
+        nilpotentne = new ArrayList<>();
+        idempotentne = new ArrayList<>();
+    }
+    private int nwd(int a, int b){
+        while (a != b){
+            if (a > b) a -=b;
+            else b -= a;
+        }
+        return a;
+    }
+
+    private int phi(int a){
+        float result = a;
+        for (int p = 2; p * p <= a; ++p) {
+            if (a % p == 0) {
+                while (a % p == 0)
+                    a /= p;
+                result *= (1.0 - (1.0 / (float)p));
+            }
+        }
+        if (a > 1)
+            result *= (1.0 - (1.0 / (float)a));
+
+        return (int)result;
+    }
+
+    static int modularPower(int x, int y, int p){
+        int res = 1;
+        x = x % p;
+
+        while (y > 0){
+            if((y & 1)==1) res = (res * x) % p;
+            y = y >> 1;
+            x = (x * x) % p;
+        }
+        return res;
+    }
+
+    void wyznaczOdwracalne(){
+        for (int i = 1; i < n; ++i){
+            if (nwd(i, n) == 1) odwracalne.add(i);
+        }
+    }
+
+    void wyznaczDzielniki(){
+        for (int i = 1; i < n; ++i){
+            for (int j = 1; j < n; ++j){
+                if(((i * j) % n) == 0){
+                    dzielniki.add(i);
+                    break;
+                }
+            }
+        }
+    }
+
+    void wyznaczNil(){
+        for (int i = 1; i < n; ++i){
+            for (int j = 1; j <= phi(n); ++j){
+                if (modularPower(i, j, n) == 0){
+                    nilpotentne.add(i);
+                    break;
+                }
+            }
+        }
+    }
+
+    void wyznaczId(){
+        int pow;
+        for (int i = 0; i < n; ++i){
+            pow = (i * i) % n;
+            if (pow == i){
+                idempotentne.add(i);
+            }
+        }
+    }
+}

zad2/Main.java

@@ -0,0 +1,54 @@
+import java.util.ArrayList;
+import java.util.Scanner;
+
+public class Main {
+    public static void main(String[] args) {
+        ArrayList<Integer> f = new ArrayList<>();
+        ArrayList<Integer> g = new ArrayList<>();
+        int n;
+        Scanner scanner = new Scanner(System.in);
+        Polynomial polynomial;
+
+        System.out.print("Podaj n: ");
+        n = scanner.nextInt();
+        polynomial = new Polynomial(n);
+        System.out.print("Najwyższa potęga współczynników f: ");
+        n = scanner.nextInt();
+        for (int i = 0; i <= n; ++i){
+            System.out.print("x^" + i + " = ");
+            f.add(scanner.nextInt());
+        }
+        System.out.print("Najwyższa potęga współczynników g: ");
+        n = scanner.nextInt();
+        for (int i = 0; i <= n; ++i){
+            System.out.print("g^" + i + " = ");
+            g.add(scanner.nextInt());
+        }
+
+//        polynomial = new Polynomial(2);
+//        f.add(1);
+//        f.add(1);
+//        f.add(1);
+//        f.add(0);
+//        f.add(1);
+//
+//        g.add(0);
+//        g.add(1);
+//        g.add(1);
+
+        ArrayList<Integer> result = polynomial.multiply(f, g);
+        for (Integer i : result){
+            System.out.print(i + " ");
+        }
+        System.out.println();
+        result = polynomial.divide(f, g);
+        for (Integer i : result){
+            System.out.print(i + " ");
+        }
+//        System.out.println();
+//        result = polynomial.nwd(f, g);
+//        for (Integer i : result){
+//            System.out.print(i + " ");
+//        }
+    }
+}

zad2/Polynomial.java

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+import java.util.ArrayList;
+
+public class Polynomial {
+    private int n;
+
+    public Polynomial(int n) {
+        this.n = n;
+    }
+
+    public ArrayList<Integer> normalize(ArrayList<Integer> w){
+        for (int i = w.size()-1; i >= 0; --i){
+            if (w.get(i).equals(0)) {
+                w.remove(i);
+            }else {
+                return w;
+            }
+        }
+        return w;
+    }
+
+    public ArrayList<Integer> multiply(ArrayList<Integer> f, ArrayList<Integer> g){
+        ArrayList<Integer> result = new ArrayList<>();
+        int tmp;
+
+        for (int i = 0; i < f.size(); ++i){
+            for (int j = 0; j < g.size(); ++j){
+                tmp = f.get(i) * g.get(j);
+                if (i + j < result.size()){
+                    tmp += result.get(i+j);
+                    result.set(i + j, tmp % n);
+                } else {
+                    while ((i + j) >= (result.size())){
+                        result.add(0);
+                    }
+                    result.set(i + j, tmp % n);
+                }
+            }
+        }
+        return normalize(result);
+    }
+
+    public ArrayList<Integer> multiplyByConst(ArrayList<Integer> f, Integer a){
+        ArrayList<Integer> result = new ArrayList<>();
+        for (Integer i : f){
+            result.add((i * a) % n);
+        }
+        return result;
+    }
+
+    public ArrayList<Integer> subtract(ArrayList<Integer> f, ArrayList<Integer> g){
+        ArrayList<Integer> result = new ArrayList<>();
+        for (int i = 0; i < f.size(); ++i){
+            if (i < g.size()){
+                result.add(Math.floorMod(f.get(i) - g.get(i), n));
+            } else{
+                result.add(f.get(i));
+            }
+        }
+        return result;
+    }
+
+    private int getZero(int a, int b){
+        int i = 0;
+        while (true){
+            if ((a + (-(b * i))) == 0){
+                return i;
+            }
+            ++i;
+        }
+    }
+
+    public ArrayList<Integer> divide(ArrayList<Integer> f, ArrayList<Integer> g){
+        ArrayList<Integer> quotient = new ArrayList<>();
+        ArrayList<Integer> remainder = new ArrayList<>(f);
+        ArrayList<Integer> tmpList;
+        int a = f.size() - 1;
+        int b = g.size() - 1;
+
+        for (int i = 0; i < a - b + 1; ++i){
+            quotient.add(0);
+        }
+
+        int q = quotient.size()-1;
+        int tmp;
+        while (a >= b) {
+            tmp = getZero(remainder.get(a), g.get(b));
+            quotient.set(q--, tmp);
+            tmpList = multiplyByConst(g, tmp);
+            while(tmpList.size() <= a) tmpList.add(0,0);
+            remainder = subtract(remainder, tmpList);
+            --a;
+        }
+        return normalize(remainder);
+    }
+
+    public ArrayList<Integer> nwd(ArrayList<Integer> f, ArrayList<Integer> g){
+        if (g.size() == 0) return f;
+        return nwd(g, divide(f, g));
+    }
+}