# Project #94988 - java homework

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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