comb.hpp

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#ifndef __COMB_HPP__
#define __COMB_HPP__
 
#include <algorithm>
#include <cstdint>
#include <string>
#include <vector>
 
namespace gpmp {
 
class Comb {
  public:
    int64_t permutation(int n, int r);
 
    int64_t combination(int n, int r);
 
    int64_t binom_coeff(int n, int r);
 
    int64_t factorial(int n);
 
    std::vector<std::vector<int>> partitions(int n);
 
    std::vector<int64_t> bell_num(int n);
 
    int64_t stirling_num(int n, int k);
 
    std::vector<int> gray_code(int n);
 
    int64_t subfactorial(int n);
 
    int64_t subsequences(int n, int k);
 
    std::vector<std::vector<int>> partition_distinct(int n);
 
    std::vector<std::vector<int>> compositions(int n);
 
    int64_t dyck_words(int n);
 
    std::vector<std::string> gen_dyck_words_until(int n);
 
    int64_t necklaces(int n, int k);
 
    int phi(int n);
 
    std::vector<std::vector<int>> generateNecklaces(int n, int k);
 
    int64_t lyndonWords(int n);
 
    std::vector<std::string> generateLyndonWords(int n);
 
    void generatePartitions(int n,
                            int max,
                            std::vector<int> &partition,
                            std::vector<std::vector<int>> &result);
 
    void gen_partition_distinct(int n,
                                int max,
                                std::vector<int> &partition,
                                std::vector<std::vector<int>> &result);
 
    void gen_compositions(int n,
                          int max,
                          std::vector<int> &composition,
                          std::vector<std::vector<int>> &result);
 
    void gen_dyck_words(std::string prefix,
                        int open,
                        int close,
                        std::vector<std::string> &dyck_words);
 
    void gen_necklaces(std::vector<int> &necklace,
                       int index,
                       int n,
                       int k,
                       std::vector<std::vector<int>> &necklaces);
 
    void gen_lyndon_words(std::string prefix,
                          int n,
                          int max,
                          std::vector<std::string> &lyndonWords);
 
    std::vector<int> divisors(int n);
 
    template <typename T>
    std::vector<std::vector<T>> permutations(const std::vector<T> &vec);
 
    template <typename T>
    std::vector<std::vector<T>> combinations(const std::vector<T> &vec, int r);
};
 
} // namespace gpmp
 
#endif