Vaja 02 Fakulteta

src/Vaja02Fakulteta.java

@@ -0,0 +1,94 @@
+public class Vaja02Fakulteta {
+    public static void main(String[] args) {
+        // izpisL();
+        // izpisD();
+//        izpisPiNilakantha();
+        System.out.println(izracunajPi(5));
+    }
+
+
+    static long fakultetaL(int n) {
+        long x = 1;
+        while (n > 1) {
+            x *= n;
+            n--;
+        }
+        return x;
+    }
+
+    static long stirlingL(int n) {
+        return Math.round(Math.sqrt(2 * Math.PI * n) * Math.pow(n / Math.E, n));
+    }
+
+    static void izpisL() {
+        System.out.println(
+                "  n              n!            Stirling(n)      napaka (%)\n" +
+                        "----------------------------------------------------------"
+        );
+        for (int i = 1; i <= 20; i++) {
+            long fakulteta = fakultetaL(i);
+            long stirling = stirlingL(i);
+            float napaka = (1 - (float) stirling / fakulteta) * 100;
+
+            System.out.printf("%3d %20d %20d %10.7f\n", i, fakulteta, stirling, napaka);
+        }
+    }
+
+    static double fakultetaD(int n) {
+        double x = 1;
+        while (n > 1) {
+            x *= n;
+            n--;
+        }
+        return x;
+    }
+
+    static double stirlingD(int n) {
+        return Math.sqrt(2 * Math.PI * n) * Math.pow(n / Math.E, n);
+    }
+
+    static void izpisD() {
+        System.out.println(
+                "  n         n!            Stirling(n)     napaka (%)\n" +
+                        "----------------------------------------------------"
+        );
+
+        for (int i = 1; i <= 100; i++) {
+            double fakulteta = fakultetaD(i);
+            double stirling = stirlingD(i);
+            double napaka = (1 - stirling / fakulteta) * 100;
+
+            System.out.printf("%3d %17.9E %17.9E %11.7f\n", i, fakulteta, stirling, napaka);
+        }
+    }
+
+    static double izracunajPiNilakantha(int k) {
+        double x = 3;
+        for (int i = 0; i < k; i++) {
+            double a = 4.0 / ((2 + 2 * i) * (3 + 2 * i) * (4 + 2 * i));
+            if (i % 2 == 0) {
+                x += a;
+            } else {
+                x -= a;
+            }
+        }
+        return x;
+    }
+
+    static void izpisPiNilakantha() {
+        System.out.println("  k    Math.PI             PI (Nilakantha)     razlika \n" +
+                "-----------------------------------------------------------------");
+        for (int i = 1; i <= 22; i++) {
+            double nilakantha = izracunajPiNilakantha(i);
+            System.out.printf("%3d %19.15f %19.15f %+20.15f\n", i, Math.PI, nilakantha, Math.PI - nilakantha);
+        }
+    }
+
+    static double izracunajPi(int k) {
+        double x = Math.pow(k, 2) / (k * 2 - 1);
+        for (int i = k; i > 1; i--) {
+            x = Math.pow(i - 1, 2) / (((i - 1) * 2 - 1) + x);
+        }
+        return 4 / x;
+    }
+}