Java Recursive Problems

                         
Java Recursive Problems (4 problems):

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.

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

public static long Raju(int n)

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.

The Output:
run:
Checking Hw
==============


We check isShaw
isShaw("abbbabb") is true
isShaw("abbbaca") is false
isShaw("abbbabbaabbbabb") is true
isShaw("abbbbcabca") is false
isShaw("abbbbcaaabbaabb") is false
isShaw("abbbbcaabca") is true

We test getLargest
The array is arr = { 6.9, -10.3, 6.7, 2.5, 16.4, -3.1}.
The largest of arr[0:6] is
We got an illegal argument exception.
The largest of arr[2:1] is
We got an illegal argument exception.
The largest of arr[2:2] is 6.7
The largest of arr[0:4] is 16.4

We test the Raju numbers.

We test the Raju numbers.
Raju(-1) is
We got an illegal argument exception.
Raju(2) is 5
Raju(4) is 17
Raju(10) is 353

We test binary search.
The input array is table = { 2, 4, 6, 8, 10, 12, 14 }.
2 was found in table[0:6] at index 0
3 was found in table[0:6] at index -1
4 was found in table[2:6] at index -1
12 was found in table[2:5] at index 5

This is all folks. I hope that your program worked.
BUILD SUCCESSFUL (total time: 2 seconds)