If you want the best solution, 100 values is not a small list for, at first approximation you need about (n/2)! tries to check all the possible partitions.

You could use a couple of tricks to reduce the range of solutions:

• Say N the sum of all the elements, divided by two, and floored; say S(X) the sum of the elements of a given subset X of your list. Your problem can be reduced to find the subset P with the minimum ABS(S(P)-N) within all the possible subsets. The second set Q is obviously given by the difference between the original list and P.
• Say M the greatest element of the list. You can safely assume that it is part of the solution (all elements are) so you can take it off from the list, decrease N by M and apply the previous point to the shortened list and the reduced N. If your list has a great dispersion, this can lead to a significant reduction of the number of tests required.

---

---

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! —

• How do I compose an effective node title?
• How do I post a question effectively?
• Markup in the Monastery

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:
	&		&
	<		&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.