For your sixth lab, you will play around some more with recursion.  You will need to write the following recursive functions

• Implement and test a method that uses tail recursion that takes as input a string and returns a version of the string with all the characters converted to uppercase.  You will likely need to write a "wrapper" function that calls your tail-recursive function with an extra parameter (the solution being created).  Use Character.toUpperCase to convert individual characters.
  
  
• Design and implement a recursive program to produce the following output:
  0
  0 1
  0 1 2
  0 1 2 3
  0 1 2 3 4
  0 1 2 3
  0 1 2
  0 1
  0
  Your program should prompt the user for the total number of rows she wishes to print.  Your program should use no loops at all, only recursion.
  
  Hint 1: You may wish to have two recursive functions ...
  Hint 2: For one of these functions, you may want to count up to n, instead of down to zero ...
  
  
• Design and implement a recursive program to print all permutations of a given string. For instance, given the string "hat" your program should print the strings "hat", "hta", "aht", "ath", "tha", and "tah".   The order that you print out the permuations does not matter.
  
  Hint 1: This is a backtracking problem ...
  Hint 2:  First, print all permutations that start with the first letter, then print all permutations that start with the second letter, and so on
  Hint 3: You may want to have an index that counts up ...
  
  

Grading

This lab is pretty simple, and the grading is as well:

• ToUpperCase  20 points
• printVertical  40 points
• Permutations 40 points
  

Submission

All file(s) required for your project should be in the folder https://www.cs.usfca.edu/svn/<username>/cs112/Lab6/