combinatorics

I need to generate all possible pairings, but with the constraint that a particular pairing only occurs once in the results. So for example: import itertools for perm in itertools.permutations(range(9)): print zip(perm[::2], perm[1::2]) generates all possible two-paired permutations; here's a small subset of the output: ... [(8, 4), (7, 6), (5, 3), (0, 2)] [(8, 4), (7, 6), (5, 3), (1, 0)] [(8, 4), (7, 6), (5, 3), (1, 2)] [(8, 4), (7, 6), (5, 3), (2, 0)] [(8, 4), (7, 6), (5, 3), (2, 1)] [(8, 5), (0, 1), (2, 3), (4, 6)] [(8, 5), (0, 1), (2, 3), (4, 7)] [(8, 5), (0, 1), (2, 3), (6, 4)] [(8, 5),

I'm looking for an algorithm to generate a schedule for a set of teams. For example, imagine a sports season in which each team plays each other, one time as home team and the other as a visitor team on another teams field. To generate a set of all games in the season is easy, if teams is a list of teams the following would do: set((x, y) for x in teams for y in teams if x != y) But I also want to ORDER the games in chronological order in such a way that it satisfies the constraint of a valid game schedule and also looks "naturally random". The constraint is that the game list should be

I'm looking for an efficient algorithm for computing the multiplicative partitions for any given integer. For example, the number of such partitions for 12 is 4, which are 12 = 12 x 1 = 4 x 3 = 2 x 2 x 3 = 2 x 6 I've read the wikipedia article for this, but that doesn't really give me an algorithm for generating the partitions (it only talks about the number of such partitions, and to be honest, even that is not very clear to me!). The problem I'm looking at requires me to compute multiplicative partitions for very large numbers (> 1 billion), so I was trying to come up with a dynamic

Generate a list of lists (or print, I don't mind) a Pascal's Triangle of size N with the least lines of code possible! Here goes my attempt (118 characters in python 2.6 using a trick ): c,z,k=locals,[0],'_[1]' p=lambda n:[len(c()[k])and map(sum,zip(z+c()[k][-1],c()[k][-1]+z))or[1]for _ in range(n)] Explanation: the first element of the list comprehension (when the length is 0) is [1] the next elements are obtained the following way: take the previous list and make two lists, one padded with a 0 at the beginning and the other at the end. e.g. for the 2nd step, we take [1] and make [0,1] and [1

I just saw this question and have no idea how to solve it. can you please provide me with algorithms , C++ codes or ideas? This is a very simple problem. Given the value of N and K, you need to tell us the value of the binomial coefficient C(N,K). You may rest assured that K <= N and the maximum value of N is 1,000,000,000,000,000. Since the value may be very large, you need to compute the result modulo 1009. Input The first line of the input contains the number of test cases T, at most 1000. Each of the next T lines consists of two space separated integers N and K, where 0 <= K <= N and 1 <=