SCIP in C++11 ― 1.3.1節その2

問題1.30はScheme特有の話なのでパス。

問題1.31

aの再帰版のみ示す。反復版はあまり興味ないのでbはパス。

--------

template<typename TermResult, typename TermArgument,

         typename NextResult,typename NextArgument>

const TermResult product

(const function<TermResult(TermArgument)>& term,

 const NextArgument& lower,

 const function<NextResult(NextArgument)>& next,

 const NextArgument& upper)

{

    if(lower>upper){return(1);}

    return(term(lower)*product(term,next(lower),next,upper));

}

const function<int(int)> identity=[](const int x){return(x);};

template<typename ResultType>

const ResultType incrementFun(const ResultType x){return(x+1);}

const int productFactorial(const int upper)

{

    const function<int(int)> increment=incrementFun<int>;

    return(product(identity,1,increment,upper));

}

const double piProduct(const int upper)

{

    const function<double(double)>

        piProductElement=[](const double x){

        return(4.0*x*(x+1.0)/(2.0*x+1.0)/(2.0*x+1.0));

    };

    const function<double(double)> increment=incrementFun<double>;

    return(product(piProductElement,1.0,increment,

                   static_cast<double>(upper))*4.0);

}

int main(int argc, char** argv)

{

    int upper(5);

    cout<<upper<<"!="<<productFactorial(upper)<<endl;

    upper=1000;

    cout<<"pi="<<piProduct(upper)<<endl;

    return(0);

}

------

出力

------

5!=120

pi=3.14238

問題1.32

accumulateと、accumulateを用いたsum,productのみ示す。

------

template<typename TermResult, typename TermArgument,

         typename NextResult,typename NextArgument>

const TermResult accumulate

(const function<TermResult(TermArgument,TermArgument)>& combiner,

 const TermResult& nullValue,

 const function<TermResult(TermArgument)>& term,

 const NextArgument& lower,

 const function<NextResult(NextArgument)>& next,

 const NextArgument& upper)

{

    if(lower>upper){return(nullValue);}

    return(combiner(term(lower),

                    accumulate(combiner,nullValue,term,

                               next(lower),next,upper)));

}

template<typename TermResult, typename TermArgument,

         typename NextResult,typename NextArgument>

const TermResult sum

(const function<TermResult(TermArgument)>& term,

 const NextArgument& lower,

 const function<NextResult(NextArgument)>& next,

 const NextArgument& upper)

{

    const TermResult zero(0);

    const function<TermResult(TermArgument,TermArgument)>

        add=std::plus<TermResult>();

    return(accumulate(add,zero,term,lower,next,upper));

}

template<typename TermResult, typename TermArgument,

         typename NextResult,typename NextArgument>

const TermResult product

(const function<TermResult(TermArgument)>& term,

 const NextArgument& lower,

 const function<NextResult(NextArgument)>& next,

 const NextArgument& upper)

{

    const TermResult one(1);

    const function<TermResult(TermArgument,TermArgument)>

         mul=std::multiplies<TermResult>();

    return(accumulate(mul,one,term,lower,next,upper));

}

------

問題1.33

filter付きaccumulateのみ示す。

a,bは特に実装してないけど・・・。

------

template<typename TermResult, typename TermArgument,

         typename NextResult,typename NextArgument>

const TermResult filteredAccumulate

(const function<TermResult(TermArgument,TermArgument)>& combiner,

 const TermResult& nullValue,

 const function<bool(TermArgument)>& predicate,

 const function<TermResult(TermArgument)>& term,

 const NextArgument& lower,

 const function<NextResult(NextArgument)>& next,

 const NextArgument& upper)

{

    if(lower>upper){return(nullValue);}

    if(predicate(lower)){

        return(combiner(term(lower),

                        filteredAccumulate(combiner,nullValue,predicate,

                                   term,next(lower),next,upper)));

    }

    return(filteredAccumulate(combiner,nullValue,predicate,

                      term,next(lower),next,upper));

}