Move combinatorial helpers from power.cpp to utils.h.
[ginac.git] / ginac / power.cpp
index f280316287fc7e4732a40decc6b0ef9e83350084..3c718027bdaa530782d063620fe75b20b440f681 100644 (file)
@@ -889,188 +889,6 @@ ex power::expand(unsigned options) const
 // non-virtual functions in this class
 //////////
 
-namespace {  // anonymous namespace for power::expand_add() helpers
-
-/** Helper class to generate all bounded combinatorial partitions of an integer
- *  n with exactly m parts (including zero parts) in non-decreasing order.
- */
-class partition_generator {
-private:
-       // Partitions n into m parts, not including zero parts.
-       // (Cf. OEIS sequence A008284; implementation adapted from Jörg Arndt's
-       // FXT library)
-       struct mpartition2
-       {
-               // partition: x[1] + x[2] + ... + x[m] = n and sentinel x[0] == 0
-               std::vector<int> x;
-               int n;   // n>0
-               int m;   // 0<m<=n
-               mpartition2(unsigned n_, unsigned m_)
-                 : x(m_+1), n(n_), m(m_)
-               {
-                       for (int k=1; k<m; ++k)
-                               x[k] = 1;
-                       x[m] = n - m + 1;
-               }
-               bool next_partition()
-               {
-                       int u = x[m];  // last element
-                       int k = m;
-                       int s = u;
-                       while (--k) {
-                               s += x[k];
-                               if (x[k] + 2 <= u)
-                                       break;
-                       }
-                       if (k==0)
-                               return false;  // current is last
-                       int f = x[k] + 1;
-                       while (k < m) {
-                               x[k] = f;
-                               s -= f;
-                               ++k;
-                       }
-                       x[m] = s;
-                       return true;
-               }
-       } mpgen;
-       int m;  // number of parts 0<m<=n
-       mutable std::vector<int> partition;  // current partition
-public:
-       partition_generator(unsigned n_, unsigned m_)
-         : mpgen(n_, 1), m(m_), partition(m_)
-       { }
-       // returns current partition in non-decreasing order, padded with zeros
-       const std::vector<int>& current() const
-       {
-               for (int i = 0; i < m - mpgen.m; ++i)
-                       partition[i] = 0;  // pad with zeros
-
-               for (int i = m - mpgen.m; i < m; ++i)
-                       partition[i] = mpgen.x[i - m + mpgen.m + 1];
-
-               return partition;
-       }
-       bool next()
-       {
-               if (!mpgen.next_partition()) {
-                       if (mpgen.m == m || mpgen.m == mpgen.n)
-                               return false;  // current is last
-                       // increment number of parts
-                       mpgen = mpartition2(mpgen.n, mpgen.m + 1);
-               }
-               return true;
-       }
-};
-
-/** Helper class to generate all compositions of a partition of an integer n,
- *  starting with the compositions which has non-decreasing order.
- */
-class composition_generator {
-private:
-       // Generates all distinct permutations of a multiset.
-       // (Based on Aaron Williams' algorithm 1 from "Loopless Generation of
-       // Multiset Permutations using a Constant Number of Variables by Prefix
-       // Shifts." <http://webhome.csc.uvic.ca/~haron/CoolMulti.pdf>)
-       struct coolmulti {
-               // element of singly linked list
-               struct element {
-                       int value;
-                       element* next;
-                       element(int val, element* n)
-                         : value(val), next(n) {}
-                       ~element()
-                       {   // recurses down to the end of the singly linked list
-                               delete next;
-                       }
-               };
-               element *head, *i, *after_i;
-               // NB: Partition must be sorted in non-decreasing order.
-               explicit coolmulti(const std::vector<int>& partition)
-                 : head(nullptr), i(nullptr), after_i(nullptr)
-               {
-                       for (unsigned n = 0; n < partition.size(); ++n) {
-                               head = new element(partition[n], head);
-                               if (n <= 1)
-                                       i = head;
-                       }
-                       after_i = i->next;
-               }
-               ~coolmulti()
-               {   // deletes singly linked list
-                       delete head;
-               }
-               void next_permutation()
-               {
-                       element *before_k;
-                       if (after_i->next != nullptr && i->value >= after_i->next->value)
-                               before_k = after_i;
-                       else
-                               before_k = i;
-                       element *k = before_k->next;
-                       before_k->next = k->next;
-                       k->next = head;
-                       if (k->value < head->value)
-                               i = k;
-                       after_i = i->next;
-                       head = k;
-               }
-               bool finished() const
-               {
-                       return after_i->next == nullptr && after_i->value >= head->value;
-               }
-       } cmgen;
-       bool atend;  // needed for simplifying iteration over permutations
-       bool trivial;  // likewise, true if all elements are equal
-       mutable std::vector<int> composition;  // current compositions
-public:
-       explicit composition_generator(const std::vector<int>& partition)
-         : cmgen(partition), atend(false), trivial(true), composition(partition.size())
-       {
-               for (unsigned i=1; i<partition.size(); ++i)
-                       trivial = trivial && (partition[0] == partition[i]);
-       }
-       const std::vector<int>& current() const
-       {
-               coolmulti::element* it = cmgen.head;
-               size_t i = 0;
-               while (it != nullptr) {
-                       composition[i] = it->value;
-                       it = it->next;
-                       ++i;
-               }
-               return composition;
-       }
-       bool next()
-       {
-               // This ugly contortion is needed because the original coolmulti
-               // algorithm requires code duplication of the payload procedure,
-               // one before the loop and one inside it.
-               if (trivial || atend)
-                       return false;
-               cmgen.next_permutation();
-               atend = cmgen.finished();
-               return true;
-       }
-};
-
-/** Helper function to compute the multinomial coefficient n!/(p1!*p2!*...*pk!)
- *  where n = p1+p2+...+pk, i.e. p is a partition of n.
- */
-const numeric
-multinomial_coefficient(const std::vector<int> & p)
-{
-       numeric n = 0, d = 1;
-       for (auto & it : p) {
-               n += numeric(it);
-               d *= factorial(numeric(it));
-       }
-       return factorial(n) / d;
-}
-
-}  // anonymous namespace
-
-
 /** expand a^n where a is an add and n is a positive integer.
  *  @see power::expand */
 ex power::expand_add(const add & a, long n, unsigned options)