286 lines
12 KiB
C++
286 lines
12 KiB
C++
/*
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LA: linear algebra C++ interface library
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Copyright (C) 2008 Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef _QSORT_H
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#define _QSORT_H
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//quicksort, returns parity of the permutation
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//
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namespace LA {
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template<typename INDEX, typename COMPAR>
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int genqsort(INDEX l, INDEX r,COMPAR (*cmp)(const INDEX, const INDEX), void (*swap)(const INDEX,const INDEX))
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{
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INDEX i,j,piv;
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int parity=0;
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if(r<=l) return parity; //1 element
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if(cmp(r,l)<0) {parity^=1; swap(l,r);}
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if(r-l==1) return parity; //2 elements and preparation for median
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piv= l+(r-l)/2; //pivoting by median of 3 - safer
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if(cmp(piv,l)<0) {parity^=1; swap(l,piv);} //and change the pivot element implicitly
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if(cmp(r,piv)<0) {parity^=1; swap(r,piv);} //and change the pivot element implicitly
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if(r-l==2) return parity; //in the case of 3 elements we are finished too
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//general case , l-th r-th already processed
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i=l+1; j=r-1;
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do{
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//important sharp inequality - stops at sentinel element for efficiency
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// this is inefficient if all keys are equal - unnecessary n log n swaps are done, but we assume that it is atypical input
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while(cmp(i++,piv)<0);
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i--;
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while(cmp(j--,piv)>0);
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j++;
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if(i<j)
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{
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// swap and keep track of position of pivoting element
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parity^=1; swap(i,j);
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if(i==piv) piv=j; else if(j==piv) piv=i;
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}
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if(i<=j) {i++; j--;}
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}while(i<=j);
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if(j-l < r-i) //because of the stack in bad case process first the shorter subarray
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{if(l<j) parity ^=genqsort(l,j,cmp,swap); if(i<r) parity ^=genqsort(i,r,cmp,swap);}
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else
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{if(i<r) parity ^=genqsort(i,r,cmp,swap); if(l<j) parity ^=genqsort(l,j,cmp,swap);}
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return parity;
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}
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//for SORTABLE classes which provide LA_sort_traits<SORTABLE,INDEX,type>::compare and swap member functions
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//this allows to use it in general templates also for complex elements, for which comparison falls back to error
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template<int type, typename SORTABLE, typename INDEX, typename PERMINDEX>
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int memqsort(SORTABLE &object, PERMINDEX *perm, INDEX l, INDEX r)
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{
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INDEX i,j,piv;
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int parity=0;
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if(r<=l) return parity; //1 element
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if(LA_sort_traits<SORTABLE,INDEX,type>::compare(object,l,r)) {parity^=1; object.swap(l,r); if(perm) {PERMINDEX tmp=perm[l]; perm[l]=perm[r]; perm[r]=tmp;}}
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if(r-l==1) return parity; //2 elements and preparation for median
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piv= l+(r-l)/2; //pivoting by median of 3 - safer
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if(LA_sort_traits<SORTABLE,INDEX,type>::compare(object,l,piv)) {parity^=1; object.swap(l,piv); if(perm) {PERMINDEX tmp=perm[l]; perm[l]=perm[piv]; perm[piv]=tmp;}} //and change the pivot element implicitly
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if(LA_sort_traits<SORTABLE,INDEX,type>::compare(object,piv,r)) {parity^=1; object.swap(r,piv); if(perm) {PERMINDEX tmp=perm[r]; perm[r]=perm[piv]; perm[piv]=tmp;}} //and change the pivot element implicitly
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if(r-l==2) return parity; //in the case of 3 elements we are finished too
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//general case , l-th r-th already processed
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i=l+1; j=r-1;
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do{
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//important sharp inequality - stops at sentinel element for efficiency
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// this is inefficient if all keys are equal - unnecessary n log n swaps are done, but we assume that it is atypical input
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while(LA_sort_traits<SORTABLE,INDEX,type>::compare(object,piv,i++));
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i--;
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while(LA_sort_traits<SORTABLE,INDEX,type>::compare(object,j--,piv));
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j++;
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if(i<j)
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{
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// swap and keep track of position of pivoting element
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parity^=1; object.swap(i,j); if(perm) {PERMINDEX tmp=perm[i]; perm[i]=perm[j]; perm[j]=tmp;}
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if(i==piv) piv=j; else if(j==piv) piv=i;
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}
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if(i<=j) {i++; j--;}
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}while(i<=j);
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if(j-l < r-i) //because of the stack in bad case process first the shorter subarray
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{if(l<j) parity ^=memqsort<type,SORTABLE,INDEX,PERMINDEX>(object,perm,l,j); if(i<r) parity ^=memqsort<type,SORTABLE,INDEX,PERMINDEX>(object,perm,i,r);}
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else
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{if(i<r) parity ^=memqsort<type,SORTABLE,INDEX,PERMINDEX>(object,perm,i,r); if(l<j) parity ^=memqsort<type,SORTABLE,INDEX,PERMINDEX>(object,perm,l,j);}
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return parity;
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}
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//stabilized version of quicksort employing auxiliary key of the original position
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template<int type, typename SORTABLE, typename INDEX, typename PERMINDEX>
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int memqsortaux(SORTABLE &object, PERMINDEX *perm, INDEX l, INDEX r, INDEX *aux)
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{
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INDEX i,j,piv;
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int parity=0;
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if(r<=l) return parity; //1 element
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if(LA_sort_traits<SORTABLE,INDEX,type>::comparestable(object,l,r,aux)) {parity^=1; object.swap(l,r); {INDEX tmp=aux[l]; aux[l]=aux[r]; aux[r]=tmp;} if(perm) {PERMINDEX tmp=perm[l]; perm[l]=perm[r]; perm[r]=tmp;}}
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if(r-l==1) return parity; //2 elements and preparation for median
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piv= l+(r-l)/2; //pivoting by median of 3 - safer
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if(LA_sort_traits<SORTABLE,INDEX,type>::comparestable(object,l,piv,aux)) {parity^=1; object.swap(l,piv); {INDEX tmp=aux[l]; aux[l]=aux[piv]; aux[piv]=tmp;} if(perm) {PERMINDEX tmp=perm[l]; perm[l]=perm[piv]; perm[piv]=tmp;}} //and change the pivot element implicitly
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if(LA_sort_traits<SORTABLE,INDEX,type>::comparestable(object,piv,r,aux)) {parity^=1; object.swap(r,piv); {INDEX tmp=aux[r]; aux[r]=aux[piv]; aux[piv]=tmp;} if(perm) {PERMINDEX tmp=perm[r]; perm[r]=perm[piv]; perm[piv]=tmp;}} //and change the pivot element implicitly
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if(r-l==2) return parity; //in the case of 3 elements we are finished too
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//general case , l-th r-th already processed
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i=l+1; j=r-1;
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do{
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//important sharp inequality - stops at sentinel element for efficiency
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// this is inefficient if all keys are equal - unnecessary n log n swaps are done, but we assume that it is atypical input
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while(LA_sort_traits<SORTABLE,INDEX,type>::comparestable(object,piv,i++,aux));
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i--;
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while(LA_sort_traits<SORTABLE,INDEX,type>::comparestable(object,j--,piv,aux));
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j++;
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if(i<j)
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{
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// swap and keep track of position of pivoting element
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parity^=1;
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object.swap(i,j);
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{INDEX tmp =aux[i]; aux[i]=aux[j]; aux[j]=tmp;}
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if(perm) {PERMINDEX tmp=perm[i]; perm[i]=perm[j]; perm[j]=tmp;}
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if(i==piv) piv=j; else if(j==piv) piv=i;
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}
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if(i<=j) {i++; j--;}
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}while(i<=j);
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if(j-l < r-i) //because of the stack in bad case process first the shorter subarray
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{if(l<j) parity ^=memqsortaux<type,SORTABLE,INDEX,PERMINDEX>(object,perm,l,j,aux); if(i<r) parity ^=memqsortaux<type,SORTABLE,INDEX,PERMINDEX>(object,perm,i,r,aux);}
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else
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{if(i<r) parity ^=memqsortaux<type,SORTABLE,INDEX,PERMINDEX>(object,perm,i,r,aux); if(l<j) parity ^=memqsortaux<type,SORTABLE,INDEX,PERMINDEX>(object,perm,l,j,aux);}
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return parity;
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}
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template<int type, typename SORTABLE, typename INDEX, typename PERMINDEX>
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int memqsortstable(SORTABLE &object, PERMINDEX *perm, INDEX l, INDEX r)
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{
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if(r<=l) return 0; //1 element
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INDEX *aux= new INDEX[r-l+1];
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if(aux==NULL) laerror("allocation failed in memqsortstable");
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INDEX *auxshifted = aux-l;
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for(INDEX i=l; i<=r; ++i) auxshifted[i]=i;
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int parity=memqsortaux<type,SORTABLE,INDEX,PERMINDEX>(object,perm,l,r,auxshifted);
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delete[] aux;
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return parity;
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}
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template<typename S, typename PERMINDEX>
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int ptrqsortup(S *l, S *r, PERMINDEX *perm=NULL)
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{
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S *i,*j,*piv;
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int parity=0;
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if(r-l<=0) return parity; //1 element
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if(*l > *r) {parity^=1; {S tmp; tmp=*l; *l= *r; *r=tmp;} if(perm) {PERMINDEX tmp=*perm; *perm=perm[r-l]; perm[r-l]=tmp;}}
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if(r-l==1) return parity; //2 elements and preparation for median
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piv= l+(r-l)/2; //pivoting by median of 3 - safer
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if(*l>*piv) {parity^=1; {S tmp; tmp=*l; *l=*piv; *piv=tmp;} if(perm) {PERMINDEX tmp= *perm; *perm=perm[piv-l]; perm[piv-l]=tmp;}} //and change the pivot element implicitly
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if(*piv>*r) {parity^=1; {S tmp; tmp=*r; *r=*piv; *piv=tmp;} if(perm) {PERMINDEX tmp=perm[r-l]; perm[r-l]=perm[piv-l]; perm[piv-l]=tmp;}} //and change the pivot element implicitly
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if(r-l==2) return parity; //in the case of 3 elements we are finished too
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//general case , l-th r-th already processed
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i=l+1; j=r-1;
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do{
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//important sharp inequality - stops at sentinel element for efficiency
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// this is inefficient if all keys are equal - unnecessary n log n swaps are done, but we assume that it is atypical input
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while(*piv > *i++);
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i--;
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while(*j-- > *piv);
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j++;
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if(i<j)
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{
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// swap and keep track of position of pivoting element
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parity^=1; {S tmp; tmp=*i; *i=*j; *j=tmp;} if(perm) {PERMINDEX tmp=perm[i-l]; perm[i-l]=perm[j-l]; perm[j-l]=tmp;}
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if(i==piv) piv=j; else if(j==piv) piv=i;
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}
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if(i<=j) {i++; j--;}
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}while(i<=j);
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if(j-l < r-i) //because of the stack in bad case process first the shorter subarray
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{if(l<j) parity ^=ptrqsortup(l,j,perm); if(i<r) parity ^=ptrqsortup(i,r,perm+(i-l));}
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else
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{if(i<r) parity ^=ptrqsortup(i,r,perm+(i-l)); if(l<j) parity ^=ptrqsortup(l,j,perm);}
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return parity;
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}
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template<typename S, typename PERMINDEX>
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int ptrqsortdown(S *l, S *r, PERMINDEX *perm=NULL)
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{
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S *i,*j,*piv;
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int parity=0;
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if(r-l<=0) return parity; //1 element
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if(*l < *r) {parity^=1; {S tmp; tmp=*l; *l= *r; *r=tmp;} if(perm) {PERMINDEX tmp=*perm; *perm=perm[r-l]; perm[r-l]=tmp;}}
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if(r-l==1) return parity; //2 elements and preparation for median
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piv= l+(r-l)/2; //pivoting by median of 3 - safer
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if(*l<*piv) {parity^=1; {S tmp; tmp=*l; *l=*piv; *piv=tmp;} if(perm) {PERMINDEX tmp= *perm; *perm=perm[piv-l]; perm[piv-l]=tmp;}} //and change the pivot element implicitly
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if(*piv<*r) {parity^=1; {S tmp; tmp=*r; *r=*piv; *piv=tmp;} if(perm) {PERMINDEX tmp=perm[r-l]; perm[r-l]=perm[piv-l]; perm[piv-l]=tmp;}} //and change the pivot element implicitly
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if(r-l==2) return parity; //in the case of 3 elements we are finished too
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//general case , l-th r-th already processed
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i=l+1; j=r-1;
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do{
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//important sharp inequality - stops at sentinel element for efficiency
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// this is inefficient if all keys are equal - unnecessary n log n swaps are done, but we assume that it is atypical input
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while(*piv < *i++);
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i--;
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while(*j-- < *piv);
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j++;
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if(i<j)
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{
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// swap and keep track of position of pivoting element
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parity^=1; {S tmp; tmp=*i; *i=*j; *j=tmp;} if(perm) {PERMINDEX tmp=perm[i-l]; perm[i-l]=perm[j-l]; perm[j-l]=tmp;}
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if(i==piv) piv=j; else if(j==piv) piv=i;
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}
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if(i<=j) {i++; j--;}
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}while(i<=j);
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if(j-l < r-i) //because of the stack in bad case process first the shorter subarray
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{if(l<j) parity ^=ptrqsortdown(l,j,perm); if(i<r) parity ^=ptrqsortdown(i,r,perm+(i-l));}
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else
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{if(i<r) parity ^=ptrqsortdown(i,r,perm+(i-l)); if(l<j) parity ^=ptrqsortdown(l,j,perm);}
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return parity;
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}
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//heapsort
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//DATA must have assignmend and comparison operators implemented
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template<typename INDEX, typename DATA>
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void myheapsort(INDEX n, DATA *ra,int typ=1)
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{
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INDEX l,j,ir,i;
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DATA rra;
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ra--; //below indexed from 1
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l=(n >> 1)+1;
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ir=n;
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for (;;) {
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if (l > 1) {
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rra=ra[--l];
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} else {
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rra=ra[ir];
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ra[ir]=ra[1];
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if (--ir == 1) {
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ra[1]=rra;
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return;
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}
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}
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i=l;
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j=l << 1;
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while (j <= ir) {
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if (j < ir && (typ>0?ra[j] < ra[j+1]:ra[j]>ra[j+1])) ++j;
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if (typ>0?rra < ra[j]:rra>ra[j]) {
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ra[i]=ra[j];
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j += (i=j);
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}
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else j=ir+1;
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}
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ra[i]=rra;
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}
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}
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}//namespace
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#endif
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