ch 22 06

Author: Harry Dulaney

ch_22/Exercise22_06.java

@@ -0,0 +1,100 @@
+package ch_22;
+
+/**
+ * *22.6 (Execution time for GCD) Write a program that obtains the execution time for
+ * finding the GCD of every two consecutive Fibonacci numbers from the index
+ * 40 to index 45 using the algorithms in Listings 22.3 and 22.4. Your program
+ * should print a table like this:
+ * --------------------|   40     41    42    43    44    45
+ * ---------------------------------------------------------------------------------
+ * Listing 22.3 GCD
+ * Listing 22.4 GCDEuclid
+ * <p>
+ * (Hint: You can use the following code template to obtain the execution time.)
+ * long startTime = System.currentTimeMillis();
+ * perform the task;
+ * long endTime = System.currentTimeMillis();
+ * long executionTime = endTime - startTime;
+ */
+public class Exercise22_06 {
+
+    /**
+     * Test Driver
+     */
+    public static void main(String[] args) {
+        /* calculate the Fibonacci numbers from index 40 to index 45 */
+        int[] fibs = calcFibIndexes40to45();
+        System.out.println("\t\t\t\t\t\t40    41    42    43    44    45");
+        System.out.println("---------------------------------------------------------");
+        System.out.print("Listing 22.3 GCD\t\t");
+        for (int i = 0; i < fibs.length - 1; i++) {
+            long startTime = System.currentTimeMillis();
+            int gcd = gcd(fibs[i], fibs[i + 1]);
+            long endTime = System.currentTimeMillis();
+            long executionTime = endTime - startTime;
+            System.out.print("   " + executionTime);
+        }
+        System.out.print("\nListing 22.4 GCDEuclid ");
+        for (int i = 0; i < fibs.length - 1; i++) {
+            long startTime = System.currentTimeMillis();
+            int gcd = gcdEuclid(fibs[i], fibs[i + 1]);
+            long endTime = System.currentTimeMillis();
+            long executionTime = endTime - startTime;
+            System.out.print("     " + executionTime);
+        }
+    }
+
+    /**
+     * Find GCD for integers m and n using Euclid's algorithm
+     */
+    public static int gcdEuclid(int m, int n) {
+        if (m % n == 0)
+            return n;
+        else
+            return gcdEuclid(n, m % n);
+    }
+
+
+    /**
+     * Find GCD for integers m and n
+     */
+    public static int gcd(int m, int n) {
+        int gcd = 1;
+        if (m % n == 0) return n;
+        for (int k = n / 2; k >= 1; k--) {
+            if (m % k == 0 && n % k == 0) {
+                gcd = k;
+                break;
+            }
+        }
+
+        return gcd;
+    }
+
+
+    private static int[] calcFibIndexes40to45() {
+        int[] fibs = new int[6];
+        int i = 2;
+        int f0 = 0;
+        int f1 = 1;
+        int f2 = 0;
+        // Find fib numbers up to 39
+        while (i < 40) {
+            f2 = f0 + f1;
+            f0 = f1;
+            f1 = f2;
+            i++;
+        }
+        // Next fib will be at index 40
+        for (int j = 0; j < fibs.length; j++) {
+            f2 = f0 + f1;
+            fibs[j] = f2;
+            f0 = f1;
+            f1 = f2;
+        }
+
+        return fibs;
+    }
+
+
+}