pascals_triangle.hpp
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00001 
00008 /*****************************************************************************
00009 ** Ifdefs
00010 *****************************************************************************/
00011 
00012 #ifndef ECL_GEOMETRY_PASCALS_HPP_
00013 #define ECL_GEOMETRY_PASCALS_HPP_
00014 
00015 /*****************************************************************************
00016 ** Includes
00017 *****************************************************************************/
00018 
00019 #include <ecl/config/macros.hpp>
00020 #include <ecl/containers/array.hpp>
00021 #include <ecl/formatters/common.hpp>
00022 #include <ecl/formatters/number.hpp>
00023 
00024 /*****************************************************************************
00025 ** Namespaces
00026 *****************************************************************************/
00027 
00028 namespace ecl {
00029 
00030 /*****************************************************************************
00031 ** Class [PascalsTriangle]
00032 *****************************************************************************/
00033 
00056 template <int N>
00057 class ECL_PUBLIC PascalsTriangle {
00058     public:
00059         /*********************
00060         ** C&D
00061         **********************/
00062         PascalsTriangle();
00063         virtual ~PascalsTriangle() {};
00064 
00065         /*********************
00066         ** Iterators
00067         **********************/
00068         typedef typename Array<int,(N+2)*(N+1)/2>::const_iterator const_iterator;  
00069         const_iterator begin(unsigned int index = 0) const;
00070         const_iterator end(unsigned int index = 0) const;
00071 
00072         /*********************
00073         ** Streaming
00074         **********************/
00075         template <typename OutputStream, int PowerN>
00076         friend OutputStream& operator<<(OutputStream &ostream, const PascalsTriangle<PowerN> &triangle);
00077 
00078     private:
00079         Array<int,(N+2)*(N+1)/2> coefficients;
00080 };
00081 /*****************************************************************************
00082 ** Specialisations [Pascals Triangle][3]
00083 *****************************************************************************/
00094 template <>
00095 class ECL_PUBLIC PascalsTriangle<3> {
00096     public:
00097         /*********************
00098         ** C&D
00099         **********************/
00106         PascalsTriangle();
00107         virtual ~PascalsTriangle() {};
00108 
00109         /*********************
00110         ** Iterators
00111         **********************/
00112         typedef Array<int,10>::const_iterator const_iterator; 
00120         const_iterator begin(unsigned int index = 0) const;
00128         const_iterator end(unsigned int index = 0) const;
00129 
00130         /*********************
00131         ** Streaming
00132         **********************/
00133         template <typename OutputStream>
00134         friend OutputStream& operator<<(OutputStream &ostream, const PascalsTriangle<3> &triangle);
00135 
00136     private:
00137         Array<int,10> coefficients;
00138 };
00139 
00140 /*****************************************************************************
00141 ** Specialisations [Pascals Triangle][5]
00142 *****************************************************************************/
00153 template <>
00154 class ECL_PUBLIC PascalsTriangle<5> {
00155     public:
00156         /*********************
00157         ** C&D
00158         **********************/
00165         PascalsTriangle();
00166         virtual ~PascalsTriangle() {};
00167 
00168         /*********************
00169         ** Iterators
00170         **********************/
00171         typedef Array<int,21>::const_iterator const_iterator; 
00179         const_iterator begin(unsigned int index = 0) const;
00187         const_iterator end(unsigned int index = 0) const;
00188 
00189         /*********************
00190         ** Streaming
00191         **********************/
00192         template <typename OutputStream>
00193         friend OutputStream& operator<<(OutputStream &ostream, const PascalsTriangle<5> &triangle);
00194 
00195     private:
00196         Array<int,21> coefficients;
00197 };
00198 
00199 /*****************************************************************************
00200 ** Implementation [Pascals Triangle]
00201 *****************************************************************************/
00207 template <int N>
00208 PascalsTriangle<N>::PascalsTriangle() {
00209     int counter = 0;
00210     for (int i = N+1; i > 0; --i ) {
00211         for (int j = 0; j < i; ++j ) {
00212             if ( ( i == N+1 ) || ( j == 0 ) ) {
00213                 coefficients[counter] = 1;
00214             } else {
00215                 coefficients[counter] =  coefficients[counter-1] + coefficients[counter-(i+1)];
00216             }
00217             ++counter;
00218         }
00219     }
00220 }
00221 
00229 template <int N>
00230 typename PascalsTriangle<N>::const_iterator PascalsTriangle<N>::begin(unsigned int index) const {
00231     int coeff_index = 0;
00232     for (unsigned int i = 0; i < index; ++i ) {
00233         coeff_index += N+1-i;
00234     }
00235     return const_iterator( &coefficients[coeff_index] );
00236 }
00244 template <int N>
00245 typename PascalsTriangle<N>::const_iterator PascalsTriangle<N>::end(unsigned int index) const {
00246     int coeff_index = 0;
00247     for (unsigned int i = 0; i <= index; ++i ) {
00248         coeff_index += N+1-i;
00249     }
00250     coeff_index -= 1; // dont want to call beyond the array limit.
00251     return const_iterator( (&coefficients[coeff_index])+1);
00252 }
00253 
00254 /*****************************************************************************
00255 ** Streaming
00256 *****************************************************************************/
00257 
00270 template <typename OutputStream, int PowerN>
00271 OutputStream& operator << ( OutputStream &ostream, const PascalsTriangle<PowerN> &triangle)
00272 {
00273     Format<int> format(2+PowerN/5,CentreAlign); // Rough hack to get a good auto-sizing working. Might blow up for large N.
00274     int counter = 0;
00275     for (int i = PowerN+1; i > 0; --i ) {
00276         for (int j = 0; j < i; ++j ) {
00277             ostream << format(triangle.coefficients[counter]) << " ";
00278             ++counter;
00279         }
00280         ostream << "\n";
00281     }
00282     ostream.flush();
00283 
00284     return ostream;
00285 }
00286 
00296 template <typename OutputStream>
00297 OutputStream& operator << ( OutputStream &ostream, const PascalsTriangle<3> &triangle)
00298 {
00299     Format<int> format(2,CentreAlign);
00300     int counter = 0;
00301     for (int i = 4; i > 0; --i ) {
00302         for (int j = 0; j < i; ++j ) {
00303             ostream << format(triangle.coefficients[counter]) << " ";
00304             ++counter;
00305         }
00306         ostream << "\n";
00307     }
00308     ostream.flush();
00309 
00310     return ostream;
00311 }
00312 
00322 template <typename OutputStream>
00323 OutputStream& operator << ( OutputStream &ostream, const PascalsTriangle<5> &triangle)
00324 {
00325     Format<int> format(3,CentreAlign);
00326     int counter = 0;
00327     for (int i = 6; i > 0; --i ) {
00328         for (int j = 0; j < i; ++j ) {
00329             ostream << format(triangle.coefficients[counter]) << " ";
00330             ++counter;
00331         }
00332         ostream << "\n";
00333     }
00334     ostream.flush();
00335 
00336     return ostream;
00337 }
00338 
00339 } // namespace ecl
00340 
00341 
00342 
00343 #endif /* ECL_GEOMETRY_PASCALS_HPP_ */


ecl_geometry
Author(s): Daniel Stonier
autogenerated on Thu Jun 6 2019 21:17:52