# CSE341 Assignment  1  solution

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Write  the  functions  in  problem  1  –  5  in  a  single  file,  named  “sol1.sml”.   Then  upload  the  file  to  the  uni06.unist.ac.kr  server  (under  your  account),  run  the   following  command  in  the  same  directory  where  you  have  sol1.sml  file.            plsubmit assign1 sol1.sml     You  can  submit  the  file  multiple  times,  and  the  last  one  before  the  deadline  will  be   used  for  grading.  Please  test  submitting  your  solution  a  couple  of  days  before  the   deadline  to  make  sure  the  submission  works  for  you.  If  it  does  not  work,  please   contact  the  TA.     Problems     1. Merge  Lists  (10pt)          Write  merge  function  that  takes  two  sorted  lists  (in  ascending  order)  and  returns   a  sorted  list  that  contains  all  the  elements  in  the  two  lists.  The  signature  of  the   function  is  as  following:     merge: int list * int list – int list For  example,  merge([1,4,5], [2,6,7]) should  return [1,2,4,5,6,7].    You   may  assume  that  each  of  the  input  lists  does  not  have  repeating  elements.  For   example,  [1,1,4,5]  cannot  be  used  as  an  input  to  merge  function  because  1 is   repeated.     2. Reverse  List  (10pt)          Write  reverse  function  that  takes  a  list  and  returns  the  reversed  list.    For  example,   reverse([1,5,4])  returns [4,5,1].  The  signature  of  the  function  is  as   following:     reverse: int list – int list For  problem  2,  you  should  not  use  the  ML’s  built-­‐in  function  rev. 3. Sigma  Function  (10pt)          Write  sigma  function  that  takes  two  integers,  a  and  b,  and  a  function  f  and  returns   the  following:   ?(?) ! !!!  The  signature  of   sigma  is  as  following:   sigma: int * int * (int – int) – int
In  other  words,  sigma(a,b,f)  computes   ?(?) ! !!!     4. Digits  Function  (10pt)          Write  digits  function  that  takes  a  positive  integer  and  returns  the  list  of  digits  of   the  integer.  For  example,  digits(253)  returns [2,5,3]  .  The  function’s   signature  should  be:     digits: int – int list You  may  assume  that  the  input  is  a  positive  number.   5. Digital  Roots  and  Additive  Persistence  (20pt:  10pt  for  each  function)   Consider  the  process  of  taking  a  number,  adding  its  digits,  then  adding  the  digits   of  the  number  derived  from  it,  etc.,  until  the  remaining  number  has  only  one  digit.   The  number  of  additions  required  to  obtain  a  single  digit  from  a  number  n  is  called   the  additive  persistence  of  n,  and  the  digit  obtained  is  called  the  digital  root  of  n.  For   example,  the  sequence  obtained  from  the  starting  number  9876  is  (9876,  30,  3),  so   9876  has  an  additive  persistence  of  2  and  a  digital  root  of  3.  For  the  starting  number   12349,  the  process  produces  (12349,  19,  10,  1),  so  12349  has  an  additive   persistence  of  3  and  a  digital  root  of  1.          Write  two  functions  additivePersistence  and  digitalRoot  that  take  positive  integer   argument  n  and  return  the  additive  persistence  and  the  digital  root  of  n   respectively.  The  signatures  of  the  functions  are  as  following:   additivePersistence: int – int digitalRoot: int – int You  can  use  digits  function  defined  in  the  previous  question.