An answer of http://nabetani.sakura.ne.jp/hena/orde13hextet/

yhpg.cpp

#include <string>
#include <vector>
#include <iostream>

class HexagonalTetromino
{
    public:
        HexagonalTetromino(
                const std::string & name,
                const std::string & src,
                const std::vector<std::vector<int>> & diff)
            :name_(name), src_(src), diff_(diff)
        {}

        bool exist_in(const std::string & field) const
        {
            const auto base = field.find(src_[0]);
            if(base == std::string::npos) {
                return false;
            }

            for(auto && d : diff_) {
                std::vector<int> ps = { 0 };
                for(std::size_t i = 1; i < src_.length(); ++i) {
                    ps.push_back(field.find(src_[i]) - base);
                }
                if(d == ps) {
                    return true;
                }
            }

            return false;
        }

        std::string name() const { return name_; }

    private:
        const std::string name_;
        const std::string src_;
        const std::vector<std::vector<int>> diff_;
};

std::vector<HexagonalTetromino> make_hexagonal_tetrominos(const std::string & src)
{
    std::vector<HexagonalTetromino> hts;

    const std::vector<std::vector<int>> b = {
        { 0, 6, 7, 12 }, { 0, 4, 5, 6 },
        { 0, 5, 6, 12 }, { 0, 5, 10, 11 },
        { 0, 1, 6, 11 }, { 0, 1, 2, 6 }
    };
    hts.push_back(HexagonalTetromino("B", src, b));

    const std::vector<std::vector<int>> d = {
        { 0, 6, 11, 12 }, { 0, 5,  6,  7 },
        { 0, 1,  2, 7  }, { 0, 4,  5, 10 },
        { 0, 1,  6, 12 }, { 0, 5,  6, 10 }
    };
    hts.push_back(HexagonalTetromino("D", src, d));

    const std::vector<std::vector<int>> i = {
        { 0, 5, 10, 15 }, { 0, 1, 2, 3 },
        { 0, 6, 12, 18 }
    };
    hts.push_back(HexagonalTetromino("I", src, i));

    const std::vector<std::vector<int>> j = {
        { 0, 5,  9, 10 }, { 0, 6,  7,  8 },
        { 0, 1,  2,  8 }, { 0, 1,  5, 10 },
        { 0, 5, 11, 17 }, { 0, 6, 12, 17 }
    };
    hts.push_back(HexagonalTetromino("J", src, j));

    const std::vector<std::vector<int>> l = {
        { 0, 6, 12, 13 }, { 0, 1,  7, 13 },
        { 0, 3,  4,  5 }, { 0, 1,  2,  5 },
        { 0, 6, 11, 16 }, { 0, 5, 10, 16 }
    };
    hts.push_back(HexagonalTetromino("L", src, l));

    const std::vector<std::vector<int>> n = {
        { 0, 1,  5,  7 }, { 0, 5, 11, 12 },
        { 0, 6, 10, 11 }, { 0, 1,  7, 12 },
        { 0, 1,  5, 11 }, { 0, 2,  6,  7 }
    };
    hts.push_back(HexagonalTetromino("N", src, n));

    const std::vector<std::vector<int>> o = {
        { 0, 5, 6, 11 }, { 0, 1, 6, 7 },
        { 0, 1, 5,  6 }
    };
    hts.push_back(HexagonalTetromino("O", src, o));

    const std::vector<std::vector<int>> s = {
        { 0, 5, 11, 16 }, { 0, 1, 4, 5 },
        { 0, 6,  7, 13 }
    };
    hts.push_back(HexagonalTetromino("S", src, s));

    const std::vector<std::vector<int>> y = {
        { 0, 6, 7, 11 }, { 0, 4, 5, 11 },
        { 0, 6,  7, 13 }
    };
    hts.push_back(HexagonalTetromino("Y", src, y));

    const std::vector<std::vector<int>> z = {
        { 0, 6, 11, 17 }, { 0, 1, 7, 8 },
        { 0, 4,  5,  9 }
    };
    hts.push_back(HexagonalTetromino("Z", src, z));

    return hts;
}

std::string solve(const std::string & src)
{
    const std::string field = "abcde*fghi*jklmn*opqr*stuvw";
    const auto hts = make_hexagonal_tetrominos(src);

    for(auto && ht : hts) {
        if(ht.exist_in(field)) {
            return ht.name();
        }
    }

    return "-";
}

void test(const std::string & src, const std::string & expected)
{
    const auto actual = solve(src);
    std::cout << (actual == expected ? "ok" : "***NG***") << std::endl;
}

void test()
{
    /*0*/ test( "glmq", "B" );
    /*1*/ test( "fhoq", "-" );
    /*2*/ test( "lmpr", "N" );
    /*3*/ test( "glmp", "Y" );
    /*4*/ test( "dhkl", "J" );
    /*5*/ test( "glpq", "D" );
    /*6*/ test( "hlmq", "O" );
    /*7*/ test( "eimq", "I" );
    /*8*/ test( "cglp", "S" );
    /*9*/ test( "chlq", "Z" );
    /*10*/ test( "glqr", "L" );
    /*11*/ test( "cdef", "-" );
    /*12*/ test( "hijk", "-" );
    /*13*/ test( "kpqu", "B" );
    /*14*/ test( "hklm", "B" );
    /*15*/ test( "mqrw", "B" );
    /*16*/ test( "nrvw", "B" );
    /*17*/ test( "abfj", "B" );
    /*18*/ test( "abcf", "B" );
    /*19*/ test( "mrvw", "D" );
    /*20*/ test( "ptuv", "D" );
    /*21*/ test( "lmnr", "D" );
    /*22*/ test( "hklp", "D" );
    /*23*/ test( "himr", "D" );
    /*24*/ test( "dhil", "D" );
    /*25*/ test( "hlpt", "I" );
    /*26*/ test( "stuv", "I" );
    /*27*/ test( "bglq", "I" );
    /*28*/ test( "glmn", "J" );
    /*29*/ test( "fghm", "J" );
    /*30*/ test( "cdgk", "J" );
    /*31*/ test( "lpst", "J" );
    /*32*/ test( "imrw", "J" );
    /*33*/ test( "dinr", "J" );
    /*34*/ test( "cdin", "L" );
    /*35*/ test( "eghi", "L" );
    /*36*/ test( "cdeg", "L" );
    /*37*/ test( "bgko", "L" );
    /*38*/ test( "eimr", "L" );
    /*39*/ test( "jotu", "L" );
    /*40*/ test( "kotu", "N" );
    /*41*/ test( "lqtu", "N" );
    /*42*/ test( "cdim", "N" );
    /*43*/ test( "klot", "N" );
    /*44*/ test( "kloq", "N" );
    /*45*/ test( "kmpq", "N" );
    /*46*/ test( "qrvw", "O" );
    /*47*/ test( "mnqr", "O" );
    /*48*/ test( "kopt", "O" );
    /*49*/ test( "mnpq", "S" );
    /*50*/ test( "bfko", "S" );
    /*51*/ test( "chin", "S" );
    /*52*/ test( "hmnq", "Y" );
    /*53*/ test( "nqrw", "Y" );
    /*54*/ test( "bchi", "Z" );
    /*55*/ test( "inrw", "Z" );
    /*56*/ test( "cfgj", "Z" );
    /*57*/ test( "jnpv", "-" );
    /*58*/ test( "flmp", "-" );
    /*59*/ test( "adpw", "-" );
    /*60*/ test( "eilr", "-" );
    /*61*/ test( "bejv", "-" );
    /*62*/ test( "enot", "-" );
    /*63*/ test( "fghq", "-" );
    /*64*/ test( "cjms", "-" );
    /*65*/ test( "elov", "-" );
    /*66*/ test( "chlm", "D" );
    /*67*/ test( "acop", "-" );
    /*68*/ test( "finr", "-" );
    /*69*/ test( "qstu", "L" );
    /*70*/ test( "abdq", "-" );
    /*71*/ test( "jkln", "-" );
    /*72*/ test( "fjkn", "-" );
    /*73*/ test( "ijmn", "-" );
    /*74*/ test( "flqr", "-" );
}

int main()
{
    test();
    return 0;
}