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I have already explained how to make a TreeMap sort in reverse Integer order. Read the API doc for TreeMap, use the constructor with the Comparator in it and write a Comparator that does what you...

Oh really? I only tested it on the regex test site, so it could be that it works slightly differently for you - although perhaps the test site detects the first zero-length find and stops at that...

A couple of minutes' fiddling at the test site got me this pattern:

\+{0,1}(\-{0,1}[0-9]{0,})x{0,1}(\^[0-9]{0,}){0,1}
which produces one extra match with both groups empty. Remember to double-up...

Seems like you're doing just fine. You're right - a reasonable pattern for something like you're doing could be (not tested by compiling)
Matcher matcher = PATTERN_POLY.matcher(inputString);
if...

Use java.util.regex.Pattern - it takes a while to learn how to use regular expressions properly, but they should be in every programmers' toolbox.

Test your regexes here:
RegEx: online regular...