combinatorics

I have an unknown number of arrays, each containing an unknown number of words. I want to concatenate the values from each list so that all possible variations of the words are stored to a final array. For example, if array 1 contains: dog cat and array 2 contains: food tooth and array 3 contains: car bike I'd like the output to be: dog food car dog food bike dog tooth car dog tooth bike cat food car cat food bike cat tooth car cat tooth bike There could be more than 3 lists, and each list will most likely have more than 2 words. I'd like to do this in PHP. I know how to do it if I know the

A multi-set is a set in which all the elements may not be unique.How to enumerate all the possible permutations among the set elements? ruggero Generating all the possible permutations and then discarding the repeated ones is highly inefficient. Various algorithms exist to directly generate the permutations of a multiset in lexicographical order or other kind of ordering. Takaoka's algorithm is a good example, but probably that of Aaron Williams is better http://webhome.csc.uvic.ca/~haron/CoolMulti.pdf moreover, it has been implemented in the R package ''multicool''. Btw, if you just want the

I forgot a bit hack to generate all integers with a given number of 1s. Does anybody remember it (and probably can explain it also)? sehe From Bit Twiddling Hacks Update Test program Live On Coliru #include <utility> #include <iostream> #include <bitset> using I = uint8_t; auto dump(I v) { return std::bitset<sizeof(I) * __CHAR_BIT__>(v); } I bit_twiddle_permute(I v) { I t = v | (v - 1); // t gets v's least significant 0 bits set to 1 // Next set to 1 the most significant bit to change, // set to 0 the least significant ones, and add the necessary 1 bits. I w = (t + 1) | (((~t & -~t) - 1) >> (_

I would like to find a clean and clever way (in python) to find all permutations of strings of 1s and 0s x chars long. Ideally this would be fast and not require doing too many iterations... So, for x = 1 I want: ['0','1'] x =2 ['00','01','10','11'] etc.. Right now I have this, which is slow and seems inelegant: self.nbits = n items = [] for x in xrange(n+1): ones = x zeros = n-x item = [] for i in xrange(ones): item.append(1) for i in xrange(zeros): item.append(0) items.append(item) perms = set() for item in items: for perm in itertools.permutations(item): perms.add(perm) perms = list(perms)

I know that there is an algorithm that permits, given a combination of number (no repetitions, no order), calculates the index of the lexicographic order. It would be very useful for my application to speedup things... For example: combination(10, 5) 1 - 1 2 3 4 5 2 - 1 2 3 4 6 3 - 1 2 3 4 7 .... 251 - 5 7 8 9 10 252 - 6 7 8 9 10 I need that the algorithm returns the index of the given combination. es: index( 2, 5, 7, 8, 10 ) --> index EDIT: actually I'm using a java application that generates all combinations C(53, 5) and inserts them into a TreeMap. My idea is to create an array that