2007/12/26, Hervé Brönnimann <hervebronnimann@mac.com>:
Regarding the ordering of the sequences for combination counts, your note was very interesting. I don't know which one is more valuable, the (ordered) sequence of combination counts, or the sequence of counts such that the actual combinations are in lexicographical order. Let's make a decision, soon. One important factor (for me): Is there an implementation of your algorithm (sequence of counts such that the actual combinations are in lexicographical order) as a free function, without state? I.e., with the interface that I give in the proposal?
About Repetition Combination Interface The Repetition Combination is useful, even for testing gacap itself. I think that the count versions have some problems: 1. The interfaces are inconsistent with other functions. 2. A transform function is needed for converting the numbers to real values. If we don't provide this, it will be not easy to use. 3. There's two types of the numbers' lexicographic order, the numbers' or the real values'. The count versions are beautiful, but they are not a good choice for this proposal. Users must spend more time to learn those count functions. For consistency, I like this interface: template <typename BidirectionalIterator, typename T, typename Incrementer> bool next_combination (BidirectionalIterator first, BidirectionalIterator last, T first_value, T last_value, Incrementer increment); I use this function for test: const int LEN = 7; int a[LEN]={0}; for (int len = 1; len < LEN; ++len) { fill(a, a + len, 0); do { for (int i = 0; i <= len; ++i) { test_circle_permutation(a, a + i, a + len); test_circle_combination(a, a + i, a + len); } } while (next_combination(a, a + len, 0, len)); } Repetition combination is suitable for those test. As input data for those tests, the elements' positions are not important. And this function's results can simulate all input cases with length of LEN. Herve: I think I lost the steps... Shall you start a new thread for the proposal? This may help the discussion.