Move combinatorial helpers from power.cpp to utils.h.
authorRichard Kreckel <kreckel@ginac.de>
Wed, 15 Feb 2017 11:42:00 +0000 (12:42 +0100)
committerRichard Kreckel <kreckel@ginac.de>
Wed, 15 Feb 2017 11:42:00 +0000 (12:42 +0100)
This way, these can be used by other modules.

ginac/power.cpp
ginac/utils.cpp
ginac/utils.h

index f280316..3c71802 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)
index 1900e1b..89217a9 100644 (file)
@@ -23,6 +23,7 @@
 
 #include "ex.h"
 #include "numeric.h"
+#include "operators.h"
 #include "utils.h"
 #include "version.h"
 
@@ -53,6 +54,19 @@ unsigned log2(unsigned n)
        return k;
 }
 
+/** 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;
+}
 
 //////////
 // flyweight chest of numbers is initialized here:
index 6462a48..816679d 100644 (file)
@@ -272,6 +272,175 @@ again:
        }
 }
 
+/** 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;
+       }
+};
+
+/** 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;
+       }
+};
+
+/** 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);
+
 
 // Collection of `construct on first use' wrappers for safely avoiding
 // internal object replication without running into the `static