Reference no: EM132213357

-Write scheme functions for the following making sure they run on Dr Racket "Advanced Student".

-Built-in functions in Dr Racket, with the exception of modulo and quotient, can not be used.

-Do not use other languages such as Java, C, etc..

1) combine3 takes three positive integers and return an integer which is made of the last two digits of the first integer, the first and last digits of the second integer and the first two digits of the last integer. If any of the integers has less than two digits return 0. For example:

( combine 4 124 80534 ) will return 0

( combine3 247939 968634 40348726 ) will return the integer 399440 and

( combine3 5678 456 9264 ) will return 784692.

If any of your numbers has less than two digits, return 0.

Note that you probably need to define several auxiliary functions.

2) inc-by-n takes an integer x and a digit d and returns an integer where each digit in x has been incremented by n. If the result of the incrementation would exceed 9, the result mod 10 will be used. For example:

(inc-by-n 53462 3) will return 86795 and

(inc-by-n 682901 4) will return 026345

Note that if the first digit of the answer is "0" it will not print.

3) countnumber takes a list of integers L (with possible nested sublists) and an integer n and count the number of instances of n in the list. For example:

( countnumber ‘( 5 7 34 28 5 72 ( 5 ) ) 5) returns 3 and

( countnumber ‘( 3 ( 67 34 ( 29 56) 23 ) 56 ( 5 ( 45 34 56 ) 0 ) ) 34 ) returns 2

4) mapeven takes a function and a list and return a list similar to the list argument where the function has been applied to every other element starting with the second one. For example:

( mapevensquare ‘( 3 6 22 9 5 7 10 15 ) ) will return ( 3 36 22 81 5 49 10 225 )

( mapeven even? ‘( 3 6 22 9 5 7 10 15 ) ) will return ( 3 #t 22 #f 5 #f 10 #f )

( mapeven list? ‘( 2 ( 3 4 ) 6 10 ( 88 23 ) ( 5 ) )) will return ( 2 #t 6 #f ( 88 23 ) #t)

Note that the function applied only to the top elements of the list. Make sure that your function works with any relevant function, and that it works with lists of even and odd length.

5) addTheSquares takes a list of integer and returns the sum of all the squares. For example:

( addTheSquares ‘( 6 3 9 2 6 )) will return 166 ( i.e. 36 + 9 + 81 + 4 + 36 )

6) Write a tail recursive version of #5 makeInsertInList takes an argument x and returns a function which will have a list argument and will insert x after each element of the list.