I think if you space out your priorities a bit more, right associative operators could be handled by adding a bonus to their weight: 

As written:
String:  3 ** 2 ** 4
Weights: 2  9 2  9 2

[download]

Now change the algorith as follows: 

String:   3 **  2 **  4
Weights: 20 80 20 81 20

More complex string:
String:   3 **  (   6   -   1   *   4  ) **  2
Weights: 20 80 90 120 140 120 170 120 90 81 20

String:   3 **  (   6   -   4  ) **  2
Weights: 20 80 90 120 140 120 90 81 20

String:   3 **  (   2  ) **  2
Weights: 20 80 90 120 90 81 20

String:   3 **  2 **  2
Weights: 20 80 20 81 20

String:   3 **  4 
Weights: 20 80 20 

String:  81 
Weights: 20

[download]

Obviously, the weakness of this approach is that if you have too many right associative operators at a level, your priorities collide. You can make "too many" arbitrarily large by using a large multiplier for the original priority scheme.

I'll leave actual implementation up to you.


TGI says moo

In reply to Re: a timid approach to parsing arithmetic expressions in perl by TGI
in thread a timid approach to parsing arithmetic expressions in perl by spx2

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.