Saturday, November 12, 2022

HP Prime: Reversing an Integer's Digits

HP Prime:  Reversing an Integer's Digits


(Inspired by the HHC 2022 programming contest)


What Should I Add To Reverse the Digits?


Let A, B, C, D, and E be individual digits (0-9) of an integer.   AB would represent a two digit integer with the value of 10 * A + B.  ABC would represent a three digit integer with the value of 100 * A + 10 * B + C.


Reversing a Two Digit Integer


AB + # = BA

10 * A + B + # = 10 * B + A

# = 9 * (B - A)


Example:  Let AB = 76.

A = 7, B = 6

# = 9 * (6 - 7) = -9

76 - 9 = 67


Reversing a Three Digit Integer


ABC + # = CBA

100 * A + 10* B + C + # = 100 * C + 10 * B + A

# = 99 * (C - A)


Example:  ABC = 469

# = 99 * (9 - 4) = 495

469 + 495 = 964


Reversing a Four Digit Integer


ABCD + # = DCBA

1000 * A + 100 * B + 10 * C + D + # = 1000 * D + 100 * C + 10 * B + A

# = 999 * (D - A) + 90 * (C - B)


Example:  ABCD = 7219

# = 999 * (9 - 7) + 90 * (1 - 2) = 1908

7219 + 1908 = 9127


Reversing a Five Digit Integer


ABCDE + # = EDBCA

10000 * A + 1000 * B + 100 * C + 10 * D + E + # =

10000 * E + 1000 * D + 100 * C + 10 * B + A 

# = 9999 * (E - A) + 990 * (D - B)


Example: ABCDE = 52693

# = 9999 * (3 - 5) + 990 * (9 - 2) = -13068

52693 - 13068 = 39625


Having the Calculator Do It


The program REVINT reverses the digits of an integer, up to 11 digits.   The program does not allow numbers that have non-zero fractional parts or integers more than 11 digits.  Instead of solving for # (see above), the program splits the integers into a list in reverse order, and uses list processing to get the final answer. 


HP Prime Program:  REVINT


Caution:  Integers that end or begin with zero may not return accurate results.   My suggestion is not use 0s with this program.  See examples below for more details.  


EXPORT REVINT(N)

BEGIN

// 2022-09-18 EWS

// reverse the integer N

// up to 12 digits

LOCAL D,P,A,I,M,L;

L:={};

P:=XPON(N);


// check size 

  IF P>11 THEN

  RETURN "TOO BIG";

  KILL;

  END;

 

// check type

  IF FP(N) THEN

  RETURN "NOT AN INTEGER";

  KILL;

  END;

   

D:=N;


// loop

  FOR I FROM P DOWNTO 0 DO

  A:=D/ALOG(I);

  L:=CONCAT({IP(A)},L);

  D:=D-IP(A)*ALOG(I); 

  END;

  

// rebuild 

M:=ΣLIST(MAKELIST(ALOG(X),X,P,0,−1)*L);

RETURN M; 

END;


Examples:


REVINT(4321) returns 1234


REVINT(56765) returns 56765   (56765 is a palindrome, reversing the digits results in the same number)


REVINT(42910) returns 1924 (01924 - be aware about integers ending or beginning with 0)


REVINT(67.28) returns "NOT AN INTEGER" (error)



Eddie


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