working on permutations...
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310
permutation.cc
310
permutation.cc
@ -161,6 +161,316 @@ for(int i=n-1; i>=1; --i)
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}
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template <typename T>
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bool NRPerm<T>::next(void)
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{
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this->copyonwrite();
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int n=this->size();
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// Find longest non-increasing suffix and the pivot
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int i = n;
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while (i > 1 && (*this)[i-1] >= (*this)[i]) --i;
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if (i<=1) return false;
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T piv=(*this)[i-1];
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// Find rightmost element greater than the pivot
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int j = n;
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while ((*this)[j] <= piv) --j;
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// Now the value array[j] will become the new pivot, Assertion: j >= i
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// Swap the pivot with j
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(*this)[i - 1] = (*this)[j];
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(*this)[j] = piv;
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// Reverse the suffix
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j = n;
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while (i < j) {
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T temp = (*this)[i];
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(*this)[i] = (*this)[j];
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(*this)[j] = temp;
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i++;
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j--;
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}
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return true;
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}
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//Algorithm L from Knuth's volume 4
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template <typename T>
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PERM_RANK_TYPE NRPerm<T>::generate_all(void (*callback)(const NRPerm<T>&), int select)
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{
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int n=this->size();
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NRVec_from1<T> c(0,n);
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NRVec_from1<T> d(1,n);
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int j,k,s;
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T q;
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T t;
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this->identity();
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PERM_RANK_TYPE sumperm=0;
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p2:
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sumperm++;
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if(!select || (select&1) == (sumperm&1)) (*callback)(*this);
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j=n; s=0;
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p4:
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q=c[j]+d[j];
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if(q<0) goto p7;
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if(q==j) goto p6;
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t=(*this)[j-c[j]+s]; (*this)[j-c[j]+s]=(*this)[j-q+s]; (*this)[j-q+s]=t;
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c[j]=q;
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goto p2;
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p6:
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if(j==1) goto end;
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s++;
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p7:
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d[j]= -d[j];
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j--;
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goto p4;
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end:
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return select? sumperm/2:sumperm;
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}
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template <typename T>
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static T _n;
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template <typename T>
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static void (*_callback)(const NRPerm<T>& );
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PERM_RANK_TYPE _sumperm;
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template <typename T>
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NRPerm<T> *_perm;
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template <typename T>
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void permg(T n)
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{
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if(n<= _n<T>)
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{
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for(T i=1;i<= _n<T>;i++)
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{
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if(!(*_perm<T>)[i]) //place not occupied
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{
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(*_perm<T>)[i]=n;
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permg(n+1);
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(*_perm<T>)[i]=0;
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}
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}
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}
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else
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{
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_sumperm++;
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(*_callback<T>)(*_perm<T>);
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}
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}
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template <typename T>
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PERM_RANK_TYPE NRPerm<T>::generate_all2(void (*callback)(const NRPerm<T>&))
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{
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this->copyonwrite();
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this->clear();
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_n<T> = this->size();
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_callback<T> =callback;
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_sumperm=0;
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_perm<T> = this;
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permg(1);
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return _sumperm;
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}
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template <typename T>
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PERM_RANK_TYPE NRPerm<T>::generate_all_lex(void (*callback)(const NRPerm<T>&))
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{
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PERM_RANK_TYPE np=0;
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this->identity();
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do{
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++np;
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(*callback)(*this);
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}while(this->next());
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return np;
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}
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template <typename T>
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PERM_RANK_TYPE NRPerm<T>::rank() const
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{
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int c,i,k;
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PERM_RANK_TYPE r;
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int n= this->size();
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r=0;
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for (k=1; k<=n; ++k)
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{
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T l=(*this)[k];
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c=0;
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for(i=k+1;i<=n;++i) if((*this)[i]<l) ++c;
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r+= c;
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i=n-k;
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if(i) r*= i;
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}
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return r;
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}
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template <typename T>
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NRVec_from1<T> NRPerm<T>::inversions(const int type, PERM_RANK_TYPE *prank) const
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{
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PERM_RANK_TYPE s=0;
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int n=this->size();
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int j,k;
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T l;
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NRVec_from1<T> i(n);
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i.clear();
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switch(type) {
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case 3: /*number of elements right from p[j] smaller < p[j]*/
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for(j=1;j<n;++j) /*number of elements right from j smaller <j*/
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{
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l=(*this)[j];
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for(k=n;k>j;--k)
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{
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if((*this)[k]<l) ++i[j];
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}
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}
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break;
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case 2: /*number of elements left from p[j] bigger >p[j]*/
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for(j=2;j<=n;++j) /*number of elements left from j bigger >j*/
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{
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l=(*this)[j];
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for(k=1;k<j;++k)
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{
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if((*this)[k]>l) ++i[j];
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}
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}
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break;
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case 1:
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for(j=1;j<=n;++j) /*number of elements right from j smaller <j*/
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{
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for(k=n;k>=1;--k)
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{
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if((*this)[k]==j) break;
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if((*this)[k]<j) ++i[j];
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}
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}
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break;
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case 0:
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for(j=1;j<=n;++j) /*number of elements left from j bigger >j*/
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{
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for(k=1;k<=n;++k)
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{
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if((*this)[k]==j) break;
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if((*this)[k]>j) ++i[j];
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}
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}
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break;
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default: laerror("illegal type in inversions");
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if(prank)
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{
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if(type!=3) laerror("rank can be computed from inversions only for type 3");
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l=1;
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for(j=1;j<n;++j)
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{
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l*= j;
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*prank += l*i[n-j];
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}
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}
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}
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return i;
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}
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template <typename T>
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NRPerm<T>::NRPerm(const int type, const NRVec_from1<T> &i)
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{
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int n=i.size();
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this->resize(n);
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int k,l;
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T j;
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switch(type) {
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case 2:
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case 1:
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for(l=0,j=1; j<=n; ++j,++l)
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{
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/*shift left and place*/
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for(k=n-l+1; k<=n-i[j]; ++k) (*this)[k-1]=(*this)[k];
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(*this)[n-i[j]]=j;
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}
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break;
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case 3:
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case 0:
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for(l=0,j=n; j>0; --j,++l)
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{
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/*shift right and place*/
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for(k=l; k>=i[j]+1; --k) (*this)[k+1]=(*this)[k];
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(*this)[i[j]+1]=j;
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}
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break;
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default: laerror("illegal type in nrperm from inversions");
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}
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if(type>=2) (*this) = this->inverse();
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}
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template <typename T>
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NRPerm<T>::NRPerm(const int n, const PERM_RANK_TYPE rank)
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{
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this->resize(n);
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NRVec_from1<T> inv(n) ;
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#ifdef DEBUG
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if(rank>=factorial(n)) laerror("illegal rank for this n");
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#endif
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inv[n]=0;
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int k;
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PERM_RANK_TYPE r=rank;
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for(k=n-1; k>=0; --k)
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{
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PERM_RANK_TYPE t;
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t=factorial(k);
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inv[n-k]=r/t;
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r=r%t;
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}
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*this = NRPerm(3,inv);
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}
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#define MAXFACT 20
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PERM_RANK_TYPE factorial(const int n)
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{
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static int ntop=20;
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static PERM_RANK_TYPE a[MAXFACT+1]={1,1,2,6,24,120,720,5040,
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40320,
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362880,
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3628800,
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39916800ULL,
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479001600ULL,
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6227020800ULL,
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87178291200ULL,
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1307674368000ULL,
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20922789888000ULL,
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355687428096000ULL,
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6402373705728000ULL,
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121645100408832000ULL,
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2432902008176640000ULL};
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int j;
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if (n < 0) laerror("negative argument of factorial");
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if (n > MAXFACT) laerror("overflow in factorial");
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while (ntop<n) {
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j=ntop++;
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a[ntop]=a[j]*ntop;
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}
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return a[n];
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}
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////////////////////////////////////////////////////////
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template <typename T>
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@ -23,6 +23,8 @@
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#include "la_traits.h"
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#include "vec.h"
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typedef unsigned long long PERM_RANK_TYPE;
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//permutations are always numbered from 1; offset is employed when applied to vectors and matrices
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namespace LA {
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@ -39,7 +41,6 @@ public:
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NRPerm(): NRVec_from1<T>() {};
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NRPerm(const int n) : NRVec_from1<T>(n) {};
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NRPerm(const NRVec_from1<T> &rhs): NRVec_from1<T>(rhs) {};
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NRPerm(const T &a, const int n): NRVec_from1<T>(a, n) {};
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NRPerm(const T *a, const int n): NRVec_from1<T>(a, n) {};
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explicit NRPerm(const CyclePerm<T> &rhs, const int n=0);
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@ -52,15 +53,17 @@ public:
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NRPerm conjugate_by(const NRPerm q) const; //q^-1 p q
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int parity() const;
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void randomize(void); //uniformly random by Fisher-Yates shuffle
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//TODO:
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//@@@permgener
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//@@@next permutation
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//@@@lex rank
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//@@@inversion tables
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bool next(); //generate next permutation in lex order
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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!
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PERM_RANK_TYPE generate_all2(void (*callback)(const NRPerm<T>&)); //recursive method, also not lexicographic
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PERM_RANK_TYPE generate_all_lex(void (*callback)(const NRPerm<T>&)); //generate in lex order using next()
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PERM_RANK_TYPE rank() const; //counted from 0 to n!-1
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NRVec_from1<T> inversions(const int type, PERM_RANK_TYPE *prank=NULL) const; //inversion tables
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explicit NRPerm(const int type, const NRVec_from1<T> &inversions); //compute permutation from inversions
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explicit NRPerm(const int n, const PERM_RANK_TYPE rank); //compute permutation from its rank
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};
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extern PERM_RANK_TYPE factorial(const int n);
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//permutations represented in the cycle format
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template <typename T>
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@ -71,6 +74,7 @@ public:
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bool is_valid() const; //is it really a permutation
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bool is_identity() const; //no cycles of length > 1
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void identity() {this->resize(0);};
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CyclePerm inverse() const; //reverse all cycles
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int parity() const; //negative if having odd number of even-length cycles
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T max() const {T m=0; for(int i=1; i<=this->size(); ++i) {T mm= (*this)[i].max(); if(mm>m) m=mm;} return m;}
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36
t.cc
36
t.cc
@ -53,6 +53,21 @@ inline int randind(const int n)
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complex<double> mycident (const complex<double>&x) {return x;}
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void printme(const NRPerm<int> &p)
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{
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PERM_RANK_TYPE rank=p.rank();
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int n=p.size();
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cout<<p.rank()<<" "<<p;
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NRPerm<int> qq(n,rank);
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if(qq!=p) laerror("error in rank algorithm");
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for(int i=0; i<4; ++i)
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{
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NRVec_from1<int> inv=p.inversions(i);
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NRPerm<int> q(i,inv);
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if(q!=p) laerror("error in inversions algorithm");
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}
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}
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int main()
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{
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@ -2038,7 +2053,7 @@ cout<<vvv;
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cout<<"error "<<(v-vvv).norm()<<endl;
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}
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if(1)
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if(0)
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{
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int seed;
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int f=open("/dev/random",O_RDONLY);
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@ -2057,7 +2072,26 @@ NRVec<double> v4=vv.permuted(p,false);
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cout<<v<<vv;
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cout<<vvv<<v4<<p;
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cout <<"error "<<(vv-vvv).norm() <<" "<<(v-v4).norm()<<endl;
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}
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if(0)
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{
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int n;
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cin >>n;
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NRPerm<int> p(n);
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p.identity();
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do{
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cout <<p;
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}while(p.next());
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}
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if(1)
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{
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int n;
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cin >>n;
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NRPerm<int> p(n);
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int tot=p.generate_all_lex(printme);
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cout <<"generated "<<tot<<endl;
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}
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}
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