DGtal  0.9.4beta
convergents.cpp
1 
34 #include <iostream>
37 #include "DGtal/arithmetic/LighterSternBrocot.h"
39 
41 
42 using namespace DGtal;
43 
45 
46 void usage( int, char** argv )
47 {
48  std::cerr << "Usage: " << argv[ 0 ] << " <p> <q>" << std::endl;
49  std::cerr << "\t - computes the successive convergent of the fraction p / q." << std::endl;
50 }
51 
55 int main( int argc, char** argv )
56 {
57  if ( argc < 3 )
58  {
59  usage( argc, argv );
60  return 1;
61  }
62 
64  typedef LighterSternBrocot<DGtal::int64_t, DGtal::int64_t, StdMapRebinder> SB; // the type of the Stern-Brocot tree
65  typedef SB::Fraction Fraction; // the type for fractions
66  typedef Fraction::ConstIterator ConstIterator; // the iterator type for visiting quotients
67  typedef Fraction::Value Value; // the value of the iterator, a pair (quotient,depth).
69 
71  DGtal::int64_t p = atoll( argv[ 1 ] );
72  DGtal::int64_t q = atoll( argv[ 2 ] );
73  Fraction f( p, q ); // fraction p/q
75 
77  // Visit quotients u_k as pair (u_k,k)
78  std::cout << "z = ";
79  ConstIterator itbegin = f.begin(), itend = f.end();
80  for ( ConstIterator it = itbegin; it != itend; ++it )
81  {
82  Value u = *it;
83  std::cout << ( ( it == itbegin ) ? "[" : "," )
84  << u.first;
85  }
86  std::cout << "]" << std::endl;
88 
90  Fraction g; // fraction null, 0/0, invalid
91  for ( ConstIterator it = itbegin; it != itend; ++it )
92  {
93  Value u = *it;
94  std::cout << "z_" << u.second << " = ";
95  g.push_back( u ); // add (u_i,i) to existing fractions
96  std::cout << g.p() << " / " << g.q() << std::endl;
97  }
99  return 0;
100 }
101 
DGtal is the top-level namespace which contains all DGtal functions and types.
Aim: The Stern-Brocot tree is the tree of irreducible fractions. This class allows to construct it pr...
boost::int64_t int64_t
signed 94-bit integer.
Definition: BasicTypes.h:74