combinatorics

We have two lists, A and B: A = ['a','b','c'] B = [1, 2] Is there a pythonic way to build the set of all maps between A and B containing 2^n (here 2^3=8)? That is: [(a,1), (b,1), (c,1)] [(a,1), (b,1), (c,2)] [(a,1), (b,2), (c,1)] [(a,1), (b,2), (c,2)] [(a,2), (b,1), (c,1)] [(a,2), (b,1), (c,2)] [(a,2), (b,2), (c,1)] [(a,2), (b,2), (c,2)] Using itertools.product , it's possible to get all the tuples: import itertools as it P = it.product(A, B) [p for p in P] Which gives: Out[3]: [('a', 1), ('a', 2), ('b', 1), ('b', 2), ('c', 1), ('c', 2)] thefourtheye You can do this with itertools.product and

Possible Duplicate: Given a string and permutation of the string. Find the index of this permuted string in the sorted list of the permutations of the string. This is an interview question. Let there is a list of permutations in lexicographic order. For example, 123 , 132 , 213 , 231 , 312 , 321 . Given a permutation find its index in such a list. For example, the index of permutation 213 is 2 (if we start from 0). Trivially, we can use a next_permutation algorithm to generate a next permutation in lexicographic order, but it leads to O(N!) solution, which is obviously non-feasible. Is there

For example there are 6 chairs in the room and there are 4 girls and 2 boys. There is 15 unique possible ways they can sit on this chairs 6!/(4!*2!)=15 . My problem is to find efficient way to calculate position of possibility they choose to sit. By position I mean following: BBGGGG - possible position #1 BGBGGG - possible position #2 BGGBGG - possible position #3 BGGGBG - possible position #4 BGGGGB - possible position #5 GBBGGG - possible position #6 GBGBGG - possible position #7 GBGGBG - possible position #8 GBGGGB - possible position #9 GGBBGG - possible position #10 GGBGBG - possible

Is there a name for this operation? And: is there a closed-form expression? For a given set of n elements, and value k between 1 and n, Take all subsets (combinations) of k items Find the product of each subset Find the sum of all those products I can express this in Python, and do the calculation pretty easily: from operator import mul from itertools import combinations from functools import reduce def sum_of_product_of_subsets(list1, k): val = 0 for subset in combinations(list1, k): val += reduce(mul, subset) return val I'm just looking for the closed form expression, so as to avoid the loop

i want load in a list the combination of N number without repetition, giving to input the elements and group. For example, with 4 elements [1,2,3,4], i have for: Group 1: [1][2][3][4]; Group 2: [1,2][1,3][1,4][2,3][2,4][3,4]; Group 3: [1,2,3][1,2,4][1,3,4][2,3,4] Group 4: [1,2,3,4] Now, i have solved it using nested loop for, for example with group 2, i write: for x1 := 1 to 3 do for x2 := Succ(x1) to 4 do begin // x1, x2 // end or for group 3, i wrote: for x1 := 1 to 2 do for x2 := Succ(x1) to 3 do for x3 := Succ(x2) to 4 do begin // x1, x2, x3 // end and so for other groups. In general, if i