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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/monotone_matrix_search.h $ // $Id: include/CGAL/monotone_matrix_search.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Michael Hoffmann #ifndef CGAL_MONOTONE_MATRIX_SEARCH_H #define CGAL_MONOTONE_MATRIX_SEARCH_H 1 #include #include #include #include namespace CGAL { template < class Matrix, class RandomAccessIterator > inline void monotone_matrix_search( const Matrix& M, RandomAccessIterator t) { typedef typename Matrix::Value V; monotone_matrix_search( M, t, std::less< V >()); } // monotone_matrix_search( M, t) template < class Matrix, class RandomAccessIterator, class Compare_strictly > void monotone_matrix_search( const Matrix& M, RandomAccessIterator t, const Compare_strictly& compare_strictly) // Matrix has to define: // o operator()( int, int) [access] // o int number_of_columns(), int number_of_rows() // o replace_column( int o, int n) // o shrink_to_quadratic_size() // o Matrix* extract_all_even_rows() // // Precondition: M is totally monotone // M.number_of_rows() > 1 and // RandomAccessIterator has value type int // // writes to t the positions (columns) // of the row maxima of M { // divide // ------ // get even rows of M: Matrix* M_new = M.extract_all_even_rows(); CGAL_assertion( M_new->number_of_columns() == M.number_of_columns()); CGAL_assertion( M_new->number_of_rows() == 0 || M_new->number_of_rows() == ( M.number_of_rows() + 1) >> 1); // reduce M_new to a quadratic matrix: // table to store the reduction permutation: // (incl. sentinel) int* reduction_table = new int[ M_new->number_of_rows() + 1]; if ( M_new->number_of_rows() < M_new->number_of_columns()) { // set sentinel: reduction_table[M_new->number_of_rows()] = M.number_of_columns() - 1; _reduce_matrix( *M_new, reduction_table, compare_strictly); CGAL_assertion( M_new->number_of_columns() == M_new->number_of_rows()); } // if ( M_new->number_of_rows() < M_new->number_of_columns()) else { // no reduction -> reduction_table is identity table: for ( int i1( 0); i1 < M_new->number_of_columns(); ++i1) reduction_table[i1] = i1; // set sentinel: reduction_table[M_new->number_of_columns()] = M_new->number_of_columns() - 1; } // recursion: CGAL_assertion( M_new->number_of_rows() >= M_new->number_of_columns()); // table to store the rmax values of M_new: // (incl. sentinel) int* t_new = new int[M_new->number_of_rows() + 1]; t_new[M_new->number_of_rows()] = M_new->number_of_columns(); if ( M_new->number_of_rows() == 1) // recursion anchor: // we have just one element ==> no choice t_new[0] = 0; else monotone_matrix_search( *M_new, t_new); // and conquer // ----------- int j( 0); // actual index in t int j_new( 0); // actual index in t_new do { // even row ==> we know *(t+j) = reduction_table[t_new[j_new++]]; if ( ++j >= M.number_of_rows()) break; // odd row // search *(t+j) between *(t+j-1) and t_new[j_new]: *(t+j) = reduction_table[t_new[j_new]]; int j_tmp( *(t+j-1)); while ( j_tmp < reduction_table[t_new[j_new]]) { if ( compare_strictly( M( j, t[j]), M( j, j_tmp))) *(t+j) = j_tmp++; else ++j_tmp; } } while ( ++j < M.number_of_rows()); delete M_new; delete[] t_new; delete[] reduction_table; } // monotone_matrix_search( M, t) template < class Matrix, class RandomAccessIterator, class Compare_strictly > void _reduce_matrix( Matrix& M, RandomAccessIterator t, const Compare_strictly& compare_strictly) // Matrix has to define: // o operator()( int, int) [access] // o int number_of_columns(), int number_of_rows() // o replace_column( int o, int n) // o shrink_to_quadratic_size() // o Matrix* extract_all_even_rows() // // Precondition: M is totally monotone // reduces M, i.e. deletes some columns that // do not contain the maximum value of any row // such that M becomes quadratic // and returns for each column of the resulting // matrix its column index in the original matrix { CGAL_precondition( M.number_of_columns() >= M.number_of_rows()); // active columns are 0, ..., j1, j2, ..., M.x_dim()-1 int j1( 0), j2( 1); *t = 0; while ( j2 - j1 < M.number_of_columns() - M.number_of_rows() + 1) { if ( compare_strictly( M( j1, j1), M( j1, j2))) { // delete column j1 if ( j1 > 0) --j1; else { M.replace_column( 0, j2); *t = j2++; } } else { if ( j1 < M.number_of_rows() - 1) { // proceed M.replace_column( ++j1, j2); *(t+j1) = j2; } // else delete column j2 ++j2; } } // while ( j2 - j1 < // M.number_of_columns() - M.number_of_rows() + 1) // M.number_of_columns() - M.number_of_rows() columns // have been deleted, now move columns // j2 .. M.number_of_columns()-1 to the first part while ( j1 < M.number_of_rows() - 1) { CGAL_assertion( j2 < M.number_of_columns()); M.replace_column( ++j1, j2); *(t+j1) = j2++; } M.shrink_to_quadratic_size(); } // _reduce_matrix( M, t) } //namespace CGAL #endif // ! (CGAL_MONOTONE_MATRIX_SEARCH_H) // ---------------------------------------------------------------------------- // ** EOF // ----------------------------------------------------------------------------