Decompose a number into a sum of repdigits

Question

Repdigits are numbers of the form a * (10^n - 1)/9 with a in [-9,9]\{0} (in other words 111, -3333, 66, numbers which are made by repeating only one digit)

Goal: Write a program or function which takes a single positive integer N and prints N = s_1 + s_2 + ... + s_k. There should be one number per line and the numbers need to be right-aligned. No two summands should have the same number of digits and adding zeros is not allowed. The output should be ordered in ascending or descending order (by number of digits)

Examples:

in:
24192
out:
24192 =
22222 +
 2222 -
  222 -
   33 +
    3

in:
24192
out:
    -7
   -22
  +888
 +1111
+22222
=24192

in:
113
out:
113=    NOT  111+  no empty lines  111+
111+          00+                    
  2            2                     2

As you can see there can be multiple solutions and some artistic freedom is allowed. Leading and trailing whitespace in each line is allowed

Shortest byte count wins

Answer 1

perl 5 - 97 92 93 86

$x=$_=pop;{printf"%15s
",$_;$_=$x,s!\d!//,$&!eg,$x-=$_,$i++?s/^\b/+/:s/^/=/;/0/||redo}

Input given as a parameter:

$perl a.pl 2224192
     2224192
    =2222222
       +1111
        +888
         -22
          -7

Answer 2

CJam, 55 50 bytes

'=l:L+Li{_W>"-+"=1$zs(\,)*+:Ii-L,_S*I+\~>\}h;]W%N*

Test it here.

Uses the output format

      -7
     -22
    +888
   +1111
+2222222
=2224192

I might golf this more once I'm beaten.

Explanation:

'=l:L+Li{_W>"-+"=1$zs(\,)*+:Ii-L,_S*I+\~>\}h;]W%N*
'=                                                 "Push = character.";
  l:L                                              "Read STDIN and store in L.";
     +L                                            "Concatenate, push new copy of L.";
       i                                           "Convert to integer.";
        {                                 }h       "Do-while loop. Leaves the condition on the
                                                    stack. I will use the remainder for that.";
         _W>                                       "Duplicate remainder, compare with -1.";
            "-+"=                                  "Select appropriate sign character.";
                 1$                                "Copy remainder again.";
                   zs                              "Take abs() and convert to string.";
                     (                             "Shift off first digit.";
                      \                            "Swap with string.";
                       ,                           "Get length.";
                        )                          "Increment.";
                         *                         "Repeat digit that often.";
                          +                        "Concatenate with sign.";
                           :I                      "Store in I.";
                             i-                    "Convert to integer. Subtract from remainder.";
                                                   "Now we'll right-justify I.";
                               L,                  "Load input, get length.";
                                 _                 "Duplicate.";
                                  S*               "Repeat space that often.";
                                    I+             "Load string and concatenate.";
                                      \~           "Swap with length. Bitwise complement.";
                                        >          "Take that many characters from the right.";
                                         \         "Swap with remainder.";
                                            ;      "Discard final remainder (0).";
                                             ]     "Wrap in array.";
                                              W%   "Reverse.";
                                                N* "Join with line feeds.";

The resulting array is printed automatically at the end of the program.

Answer 3

JavaScript ES6 - 145

i=0;f=n=>{return g=n<0,n=Math.abs(n)+'',l=n.length,r=l-1?n[0].repeat(l):n,(i>0?g?'-':'+':n+'=')+'\n'+' '.repeat(i++)+(l-1?r+f((+n-r)*(g?-1:1)):r)}

Paste into Firefox console. Run as f(24192).

Output for f(24192):

24192=
22222+
 1111+
  888-
   22-
    7

Answer 4

GolfScript 77

~.[{..0>2*(.@*`.,\[0=]*''+~*.@\-.}do;]-1%{[.0>' +'=\`n].1=,2$`,\-' '*\+}%'='@

Online demo links:

• 24192
• 2147483648
• 1 trillionth prime

A slightly more readable version (if GolfScript can be called readable) with unit tests version is available here.