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// Copyright (c) 1998-2003 ETH Zurich (Switzerland). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Matrix_search/include/CGAL/sorted_matrix_search.h $ // $Id: include/CGAL/sorted_matrix_search.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Michael Hoffmann #ifndef CGAL_SORTED_MATRIX_SEARCH_H #define CGAL_SORTED_MATRIX_SEARCH_H 1 #include #include #include #include #include #include namespace CGAL { template < class Matrix > class Padded_matrix { public: typedef typename Matrix::Value Value; Padded_matrix( const Matrix& m) : matrix( &m) {} Value operator()( int x, int y) const // padded access operator { return matrix->operator()( x < matrix->number_of_columns() ? x : matrix->number_of_columns() - 1, y < matrix->number_of_rows() ? y : matrix->number_of_rows() - 1); } bool is_sorted() // tests iff this matrix is sorted, i.e. in each column/row // the elements appear in increasing order // time complexity is proportional to the number of elements { for ( int i = 0; i < matrix->number_of_columns(); ++i) for ( int j = 0; j < matrix->number_of_rows(); ++j) { if ( i > 0 && (*matrix)( i - 1, j) > (*matrix)( i, j)) return false; if ( j > 0 && (*matrix)( i, j - 1) > (*matrix)( i, j)) return false; } return true; } private: const Matrix* matrix; }; template < class PaddedMatrix > class Matrix_cell { public: typedef typename PaddedMatrix::Value Value; Matrix_cell(PaddedMatrix m, int xpos = 0, int ypos = 0) : base_matrix(m), x(xpos), y(ypos) {} Value min BOOST_PREVENT_MACRO_SUBSTITUTION () const { return base_matrix(x, y); } Value max BOOST_PREVENT_MACRO_SUBSTITUTION (int offset) const // offset denotes the cell's dimension { return base_matrix(x + offset - 1, y + offset - 1); } int x_min() const { return x; } int y_min() const { return y; } PaddedMatrix matrix() const { return base_matrix; } void output(std::ostream& o, int dim) const { for (int i = 0; i < dim; ++i) { for (int j = 0; j < dim; ++j) o << base_matrix(x + i, y + j) << " "; o << std::endl; } } bool check_for(Value v, int dim) const { for (int i = 0; i < dim; ++i) for (int j = 0; j < dim; ++j) { if (CGAL_NTS abs(base_matrix(x + i, y + j) - v) < Value(1E-10)) std::cerr << "***" << base_matrix(x + i, y + j) << std::endl; if (base_matrix(x + i, y + j) == v) return true; } return false; } private: PaddedMatrix base_matrix; int x; int y; }; template < class Cell > struct Cell_min : public CGAL::cpp98::unary_function< Cell, typename Cell::Value > { typename Cell::Value operator()( const Cell& c) const { return (c.min)(); } }; template < class Cell > struct Cell_max : public CGAL::cpp98::unary_function< Cell, typename Cell::Value > { Cell_max( int offset) : ofs( offset) {} typename Cell::Value operator()( const Cell& c) const { return (c.max)( ofs); } private: int ofs; }; template < class InputIterator, class Traits > typename Traits::Value sorted_matrix_search(InputIterator f, InputIterator l, Traits t) { BOOST_USING_STD_MAX(); using std::iter_swap; using std::find_if; using std::remove_if; using std::logical_or; using std::equal_to; typedef typename Traits::Matrix Matrix; typedef typename Traits::Value Value; typedef Padded_matrix< Matrix > PaddedMatrix; typedef Matrix_cell< PaddedMatrix > Cell; typedef std::vector< Cell > Cell_container; typedef typename Cell_container::iterator Cell_iterator; // typedef typename Cell_container::reverse_iterator Cell_reverse_iterator; Cell_container active_cells; // set of input matrices must not be empty: CGAL_precondition( f != l); // for each input matrix insert a cell into active_cells: InputIterator i( f); int maxdim( -1); while ( i != l) { CGAL_expensive_precondition( PaddedMatrix( *i).is_sorted()); active_cells.push_back( Cell( PaddedMatrix( *i))); maxdim = max BOOST_PREVENT_MACRO_SUBSTITUTION ( max BOOST_PREVENT_MACRO_SUBSTITUTION ( (*i).number_of_columns(), (*i).number_of_rows()), maxdim); ++i; } CGAL_precondition( maxdim > 0); // current cell dimension: int ccd( 1); // set ccd to a power of two >= maxdim: while ( ccd < maxdim) ccd <<= 1; // now start the search: for (;;) { if ( ccd > 1) { // ------------------------------------------------------ // divide cells: ccd >>= 1; // reserve is required here! // otherwise one of the insert operations might cause // a reallocation invalidating j // (should typically result in a segfault) // active_cells.reserve( 4 * active_cells.size()); for ( int j = static_cast(active_cells.size()) - 1 ; j >= 0 ; -- j ) { //for ( Cell_reverse_iterator j( active_cells.rbegin()); // j != active_cells.rend(); // ++j) { Cell lRefCell = active_cells.at(j) ; // upper-left quarter: // Cell( (*j).matrix(), // (*j).x_min(), // (*j).y_min()) remains in active_cells, // since it is implicitly shortened by decreasing ccd // lower-left quarter: active_cells.push_back( Cell( lRefCell.matrix(), lRefCell.x_min(), lRefCell.y_min() + ccd)); // upper-right quarter: active_cells.push_back( Cell( lRefCell.matrix(), lRefCell.x_min() + ccd, lRefCell.y_min())); // lower-right quarter: active_cells.push_back( Cell( lRefCell.matrix(), lRefCell.x_min() + ccd, lRefCell.y_min() + ccd)); } // for all active cells } // if ( ccd > 1) else if ( active_cells.size() <= 1) //!!! maybe handle <= 3 break; // there has to be at least one cell left: CGAL_assertion( active_cells.size() > 0); // ------------------------------------------------------ // compute medians of smallest and largest elements: int lower_median_rank = static_cast((active_cells.size() - 1) >> 1); int upper_median_rank = static_cast(active_cells.size() >> 1); // compute upper median of cell's minima: std::nth_element(active_cells.begin(), active_cells.begin() + upper_median_rank, active_cells.end(), [&t](const Cell& c1, const Cell& c2) { return t.compare_strictly()(Cell_min()(c1), Cell_min()(c2)); }); Cell_iterator lower_median_cell = active_cells.begin() + upper_median_rank; Value lower_median = (lower_median_cell->min)(); // compute lower median of cell's maxima: std::nth_element(active_cells.begin(), active_cells.begin() + lower_median_rank, active_cells.end(), [&t, &ccd](const Cell& c1, const Cell& c2) { return t.compare_strictly()(Cell_max< Cell >(ccd)(c1), Cell_max< Cell >(ccd)(c2)); }); Cell_iterator upper_median_cell = active_cells.begin() + lower_median_rank; Value upper_median = (upper_median_cell->max)(ccd); // restore lower_median_cell, if it has been displaced // by the second search if ((lower_median_cell->min)() != lower_median) lower_median_cell = find_if(active_cells.begin(), active_cells.end(), [&lower_median](const Cell& c) { return equal_to< Value >()(lower_median, Cell_min< Cell >()(c)); }); CGAL_assertion(lower_median_cell != active_cells.end()); // ------------------------------------------------------ // test feasibility of medians and remove cells accordingly: Cell_iterator new_end; if ( t.is_feasible( lower_median)) if ( t.is_feasible( upper_median)) { // lower_median and upper_median are feasible // discard cells with all entries greater than // min( lower_median, upper_median) except for // one cell defining this minimum Cell_iterator min_median_cell; Value min_median; if ( lower_median < upper_median) { min_median_cell = lower_median_cell; min_median = lower_median; } else { min_median_cell = upper_median_cell; min_median = upper_median; } // save min_median_cell: iter_swap( min_median_cell, active_cells.begin()); new_end = remove_if( active_cells.begin() + 1, active_cells.end(), [&t, &min_median](const Cell& c) { return t.compare_non_strictly()(min_median, Cell_min< Cell >()(c)); }); } // lower_median and upper_median are feasible else { // lower_median is feasible, but upper_median is not // discard cells with all entries greater than // lower_median or all entries smaller than // upper_median except for the lower median cell // save lower_median_cell: iter_swap( lower_median_cell, active_cells.begin()); new_end = remove_if( active_cells.begin() + 1, active_cells.end(), [&t, &lower_median, &upper_median, &ccd](const Cell& c) { return t.compare_non_strictly()(lower_median, Cell_min< Cell >()(c)) || t.compare_non_strictly()(Cell_max< Cell >(ccd)(c), upper_median); }); } // lower_median is feasible, but upper_median is not else if ( t.is_feasible( upper_median)) { // upper_median is feasible, but lower_median is not // discard cells with all entries greater than // upper_median or all entries smaller than // lower_median except for the upper median cell // save upper_median_cell: iter_swap( upper_median_cell, active_cells.begin()); new_end = remove_if( active_cells.begin() + 1, active_cells.end(), [&t, &lower_median, &upper_median, &ccd](const Cell& c) { return t.compare_non_strictly()(upper_median, Cell_min()(c)) || t.compare_non_strictly()(Cell_max(ccd)(c),lower_median); }); } // upper_median is feasible, but lower_median is not else { // both upper_median and lower_median are infeasible // discard cells with all entries smaller than // max BOOST_PREVENT_MACRO_SUBSTITUTION ( lower_median, upper_median) new_end = remove_if( active_cells.begin(), active_cells.end(), [&t, &ccd, &lower_median, &upper_median](const Cell& c) { return t.compare_non_strictly()(Cell_max( ccd)(c), max BOOST_PREVENT_MACRO_SUBSTITUTION ( lower_median, upper_median)); }); } // both upper_median and lower_median are infeasible active_cells.erase( new_end, active_cells.end()); } // for (;;) // there must be only one cell left: CGAL_assertion( active_cells.size() == 1); CGAL_assertion( ccd == 1); return ((*active_cells.begin()).min)(); } } //namespace CGAL #endif // ! (CGAL_SORTED_MATRIX_SEARCH_H) // ---------------------------------------------------------------------------- // ** EOF // ----------------------------------------------------------------------------