Write recursive programs for Problems I, II, III, and IV. Problem I. We define the Shaw strings as follows: 1. abb is a Shaw string. 2. bca is a Shaw string. 3. If S is a Shaw string, so is SaS. 4. If U and V are Shaw strings, so is UbV. Here a, b, c are constants and S,U,V are variables. In these rules, the same letter represents the same string. So, if S = abb, rule 3 tells us that abbaabb is a Shaw string. In rule 4, U and V represent Shaw strings, but they may be different. Write the method public static boolean isShaw(String in) that returns true if in is a Shaw string and false otherwise. Problem II. Write the method public static double getLargest(double [] a, int low, int high) that returns the largest number in the array slice a[low:high]. If low > high, it throws an IllegalArgumentException. Otherwise, it checks if the slice has 1 item. If so, it returns that value. If the slice has 2 or more items, it divides the slice into 2 equal subslices, computes the largestvalues of the 2 subslices and returns the largest of the 2 values. Problem III. We define the Raju numbers as Raju(0) = 1 Raju(1) =1 Raju(n) = Raju(n-1) + Raju(n-2) + 3 if n >= 2 Write the method public static long Raju(int n) that returns the n-th Raju number. If n < 0, the method throws an IllegalArgumentException. Problem IV. Write the method public static int binarySearch(double[] arr, int low, int high, double inq) that search the array slice arr[low:high] for an occurrence of inq. If inq occurs in arr, return an index i such that arr[i] == inq. Otherwise, return -1. Assume that arr is sorted in increasing order. Write a recursive version of this method.

Subject | Computer |

Due By (Pacific Time) | 11/20/2015 12:00 am |

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