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permutation generators for multiset and with restrictions

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This commit is contained in:
Jiri Pittner 2024-01-11 16:50:19 +01:00
parent 50b2447535
commit 6ea863627d
4 changed files with 195 additions and 6 deletions
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115
permutation.cc
View File

@ -21,6 +21,7 @@
#include <stdio.h>
#include <string.h>
#include <list>
#include "qsort.h"
namespace LA {
@ -246,6 +247,39 @@ end:
return select? sumperm/2:sumperm;
}
//Algorithm L2 from Knuth's volume 4 for multiset permutations
//input must be initialized with (repeated) numbers in any order
template <typename T>
PERM_RANK_TYPE NRPerm<T>::generate_all_multi(void (*callback)(const NRPerm<T>&))
{
PERM_RANK_TYPE sumperm=0;
this->copyonwrite();
myheapsort(this->size(),&(*this)[1],1);
while(1)
{
int j,k,l;
T t;
sumperm++;
(*callback)(*this);
j=this->size()-1;
while(j>0 && (*this)[j]>=(*this)[j+1]) j--;
if(j==0) break; /*finished*/
l=this->size();
while((*this)[j]>=(*this)[l]) l--;
t=(*this)[j];(*this)[j]=(*this)[l];(*this)[l]=t;
k=j+1;
l=this->size();
while(k<l)
{
t=(*this)[k];(*this)[k]=(*this)[l];(*this)[l]=t;
k++;l--;
}
}
return sumperm;
}
template <typename T>
static T _n;
@ -253,13 +287,13 @@ static T _n;
template <typename T>
static void (*_callback)(const NRPerm<T>& );
PERM_RANK_TYPE _sumperm;
static PERM_RANK_TYPE _sumperm;
template <typename T>
NRPerm<T> *_perm;
static NRPerm<T> *_perm;
template <typename T>
void permg(T n)
static void permg(T n)
{
if(n<= _n<T>)
{
@ -307,6 +341,81 @@ do{
return np;
}
template <typename T>
static T _n2;
template <typename T>
static void (*_callback2)(const NRPerm<T>& );
static PERM_RANK_TYPE _sumperm2;
template <typename T>
static NRPerm<T> *_perm2;
template <typename T>
static const T *pclasses2;
template <typename T>
static T *_pperm;
static int sameclass;
template <typename T>
static void permg2(T n) //place number n in a free box in all possible ways and according to restrictions
{
T i;
if(n<=_n2<T>)
{
T c=pclasses2<T>[n];
for(i=1;i<=_n2<T>;i++)
{
if(_pperm<T>[i]>=1) goto skipme; /*place already occupied*/
if (sameclass)
{
if(sameclass==1 && c!=pclasses2<T>[i]) goto skipme;
if(sameclass== -1 && c==pclasses2<T>[i] ) goto skipme;
if(sameclass== -2) /*allow only permutations which leave elements of each class sorted*/
{
T j,k;
for(j=i+1; j<=_n2<T>; j++)
if((k=_pperm<T>[j])>=1)
if(/* automatically fulfilled k<n &&*/ c==pclasses2<T>[k]) goto skipme;
}
}
/*put it there and next number*/
_pperm<T>[i]=n;
permg2(n+1);
_pperm<T>[i]=0;
skipme:;
}
}
else
{
_sumperm2++;
(*_callback2<T>)(*_perm2<T>);
}
}
template <typename T>
PERM_RANK_TYPE NRPerm<T>::generate_restricted(void (*callback)(const NRPerm<T>&), const NRVec_from1<T> &classes, int restriction_type)
{
this->copyonwrite();
this->clear();
_n2<T> = this->size();
_callback2<T> =callback;
_sumperm2=0;
_perm2<T> = this;
_pperm<T> = &(*this)[1]-1;
pclasses2<T> = &classes[1]-1;
sameclass=restriction_type;
permg2<T>(1);
return _sumperm2;
}
template <typename T>
PERM_RANK_TYPE NRPerm<T>::rank() const
{

6
permutation.h
View File

@ -58,12 +58,14 @@ public:
NRPerm operator*(const NRPerm q) const; //q is rhs and applied first, this applied second
NRPerm operator*(const CyclePerm<T> &r) const;
NRPerm conjugate_by(const NRPerm q) const; //q^-1 p q
int parity() const;
int parity() const; //returns +/- 1
void randomize(void); //uniformly random by Fisher-Yates shuffle
bool next(); //generate next permutation in lex order
PERM_RANK_TYPE generate_all(void (*callback)(const NRPerm<T>&), int parity_select=0); //Algorithm from Knuth's vol.4, efficient but not in lex order!
PERM_RANK_TYPE generate_all(void (*callback)(const NRPerm<T>&), int parity_select=0); //Algorithm L from Knuth's vol.4, efficient but not in lex order!
PERM_RANK_TYPE generate_all_multi(void (*callback)(const NRPerm<T>&)); //Algorithm L2 from Knuth's vol.4, for multiset (repeated numbers, not really permutations)
PERM_RANK_TYPE generate_all2(void (*callback)(const NRPerm<T>&)); //recursive method, also not lexicographic
PERM_RANK_TYPE generate_all_lex(void (*callback)(const NRPerm<T>&)); //generate in lex order using next()
PERM_RANK_TYPE generate_restricted(void (*callback)(const NRPerm<T>&), const NRVec_from1<T> &classes, int restriction_type=0);
PERM_RANK_TYPE rank() const; //counted from 0 to n!-1
NRVec_from1<T> inversions(const int type, PERM_RANK_TYPE *prank=NULL) const; //inversion tables
explicit NRPerm(const int type, const NRVec_from1<T> &inversions); //compute permutation from inversions

38
qsort.h
View File

@ -243,5 +243,43 @@ else
return parity;
}
//heapsort
//DATA must have assignmend and comparison operators implemented
template<typename INDEX, typename DATA>
void myheapsort(INDEX n, DATA *ra,int typ=1)
{
INDEX l,j,ir,i;
DATA rra;
ra--; //below indexed from 1
l=(n >> 1)+1;
ir=n;
for (;;) {
if (l > 1) {
rra=ra[--l];
} else {
rra=ra[ir];
ra[ir]=ra[1];
if (--ir == 1) {
ra[1]=rra;
return;
}
}
i=l;
j=l << 1;
while (j <= ir) {
if (j < ir && (typ>0?ra[j] < ra[j+1]:ra[j]>ra[j+1])) ++j;
if (typ>0?rra < ra[j]:rra>ra[j]) {
ra[i]=ra[j];
j += (i=j);
}
else j=ir+1;
}
ra[i]=rra;
}
}
}//namespace
#endif

42
t.cc
View File

@ -75,6 +75,19 @@ for(int i=0; i<4; ++i)
}
}
void printme0(const NRPerm<int> &p)
{
cout<<p;
}
void printme1(const NRPerm<int> &p)
{
cout <<p.parity()<<' ';
cout<<p;
//cout<<p.inverse();
}
static int unitary_n;
static PERM_RANK_TYPE space_dim;
@ -2187,6 +2200,33 @@ int tot=p.generate_all_lex(printme);
cout <<"generated "<<tot<<endl;
}
if(0)
{
int n;
cin >>n;
NRPerm<int> p(n);
int seed;
int f=open("/dev/random",O_RDONLY);
if(sizeof(int)!=read(f,&seed,sizeof(int))) laerror("cannot read /dev/random");
close(f);
srand(seed);
for(int i=1; i<=n; ++i) p[i]=1+RANDINT32()%(n-1);
cout <<"Initial = "<<p<<endl;
int tot=p.generate_all_multi(printme0);
cout <<"generated "<<tot<<endl;
}
if(1)
{
int n; cin >>n;
NRPerm<int> p(n);
NRVec_from1<int> classes; cin>>classes;
if(classes.size()!=p.size()) laerror("sizes do not match");
int tot=p.generate_restricted(printme1,classes,-2);
cout <<"generated "<<tot<<endl;
}
if(0)
{
int n,unitary_n;;
@ -2969,7 +3009,7 @@ cout <<c%ir<<endl;
cout <<cc<<endl;
}
if(1)
if(0)
{
int seed;
int f=open("/dev/random",O_RDONLY);