[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

No Subject

Hi, I am having trouble with Dr scheme and was wondering if You could be of any help by sending me the solutions to 2 questions.
I would be very grateful for any help provided, thank u..


a) Define a Scheme function myMin that takes as input a list of integers and returns the smallest integer in the list. This function is undefined for the case that the given list is empty. You may not use the built-in function min to accomplish this task. Hint define a version with two parameters one for the list and another for the minimal value found so far. The function myMin should call this helper function.

       (myMin (list 5 4 9 2 8 11 17 -3 9)) 
b) Define the Scheme function
splice which given two lists merges the lists together one item from each in turn until the shortest list is empty then finishes with all items remaining, if any, in the longer list.
splice (list 1 2 3 4 5)(list 'a 'b 'c))
          (1 a 2 b 3 c 4 5) 
 c) Write a Scheme function
addLists that takes two lists of integers of equal length and returns a list of integers that is the result of adding element one from both lists together elements 2 together and so on. Hint this is a sort of map function. Note you are not allowed to use the built in function map to accomplish this task.

          (addLists (list 1 2 3 4) (list 10 11 12 13))
(11 13 15 17) 

d) Write a Scheme function nLists that takes a list containing integers and other lists of such integers embedded to any depth and returns a count of the number of embedded lists.
(nLists (list 2 3 (list 4 (list 5))(list 4  1)) )
3 i.e. do not count the outside list. 
e) Write a version of myMin,
myMinLists that like (c) takes as input a of lists of integers and returns the smallest integer found in any of the lists.
(myMinLists (list 2 3 (list 4  (list 5))
                        (list 4  1)) ) returns 1 

    The towers of
Hanoi problem can be extended in an interesting way. Consider the problem where the starting position may be N (N > 3) discs distributed randomly over the three pins. in such a way that larger discs may be on top of smaller discs and vice versa. The only restriction on the starting position is that all discs in the game are on pins, none on the table. Now is it possible to unscramble the discs and build a legal tower of all the discs on any pin that is where a larger disc is not placed on a smaller disc. The rules for moving discs in the new game is that discs may be removed one at a time and immediately placed on to another pin in such a way that the disc placed on a pin is only ever placed on a pin where the top disc is larger than the disc placed on top of it.

First a few definitions
   A legal tower is a tower of discs on a pin where a larger pin is not on top of a smaller pin.
   A good tower, relative to some other disc, is a top segment of a tower such that the top segment forms a legal tower and all the discs are smaller than the given disc.
  A moveable tower is a good tower such that the largest disc in the tower is smaller than the top discs of the towers on any other pin.
  The candidate pin is the pin not containing the moveable tower such that the candidate pin has at its top a disc nearest in size to the bottom disc of the moveable tower.

UnScramble board
    if all discs form a single legal tower
        return empty instruction
        append the results of
          move using hanoiProc the moveable tower excluding
                its bottom disc to the spare (i.e non candidate pin)
          List the instruction to move the bottom disc of the
                best tower to the candidate pin
          UnScramble the resulting board from making the above
                changes to the board

hanoiProc noDiscs board
    if noDiscs = 1
        do move of top disc on pin 1 to pin 2
        append together the instructions for
             moving the tower one smaller than the given tower
                 using hanoiProc to the pin 3
             the list containing the instruction to move the bottom
                  disc of the tower to the pin 2
             moving the tower one smaller than the given tower
                  using hanoiProc from pin 3  to the pin 2

Representation of the hanoi board
    list of three pins
        each pin is a list containing the list of discs on the pin and the name of the pin
    Discs are integers representing their size.

   e.g (list (list (list 1 2 3 4) 'a)(list empty 'b)(list empty 'c))
    has a legal tower on disc a - the other pins have no discs
          (list (list (list 4 2) 'a)(list (list 3 1) 'b) (list empty 'c))
    has disc 4 on top of 2 on pin a has disc 3 on top of disc 1 on pin b and
    has pin c empty

You are to define part of the solution to this problem. You will be given the Scheme code
for the remainder of the problem. The precise elements you must code are described in the supplied program listing. By function name they are: