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Vowel Ratio Resolution (Posted on 2022-09-17) Difficulty: 3 of 5
The respective number of 'e's and 'a's in any given word is denoted by ε and α.

o (1)(a) Determine the longest common English word/words having the maximum value of ε/α
o   (1)(b) Determine the longest common English word/words having the minimum value of ε/α
o   (1)(c) Determine the longest common English word/words where ε=α

o  (2) Extend (1) to cover the case of esoteric/archaic words.

Notes:
  • The valid word/words must have at least one 'e' and at least one 'a'.
  • No abbreviations/acronyms/slangs and no hyphenated words like A-Bomb, X-Ray etc.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts computer findings | Comment 1 of 3
clearvars,clc
fid=fopen('c:\words\words.txt');
longAval=0; longEval=0; longEqval=0;
longAset={}; longEset={}; longEqset={};
while ~feof(fid)
  l=fgetl(fid);
  alpha=length(strfind(l,'e'));
  eps=length(strfind(l,'a'));
  if alpha>0 && eps>0 && isequal(l,lower(l))
    ratioA=alpha/eps;
    ratioE=eps/alpha;
    if ratioA>longAval
        longAval=ratioA;
        longAset={l};
      else
        if ratioA==longAval
          longAset(length(longAset)+1)={l};
        end
      end
    if ratioE>longEval
        longEval=ratioE;
        longEset={l};
      else
        if ratioE==longEval
          longEset(length(longEset)+1)={l};
        end
    end    
    if alpha==eps
      if length(l)>longEqval
        longEqval=length(l);
        longEqset={l};
      else
        if length(l)==longEqval
          longEqset(length(longEqset)+1)={l};
        end
      end
    end
  end
end
fclose(fid);

disp(longAval)
disp(longAset')
disp(' ')
disp(longEval)
disp(longEset')
disp(' ')
disp(longEqval)
disp(longEqset')

finds

     6                  maximum alpha/eps
    {'degeneratenesses'      }
    {'levelheadednesses'     }
    {'regeneratenesses'      }
    {'representativenesses'  }
    {'tenderheartednesses'   }
    {'unrepresentativenesses'} longest
 
     4    (i.e., 1/4)   maximum eps/alpha (min alpha/eps)
    {'acanthocephalan'     }
    {'acanthocephalans'    }
    {'adenocarcinomata'    }
    {'agammaglobulinemia'  }
    {'agammaglobulinemias' }
    {'amalgamate'          }
    {'amalgamated'         }
    {'amalgamates'         }
    {'anabaena'            }
    {'anabaenas'           }
    {'anagrammatize'       }
    {'anagrammatized'      }
    {'anagrammatizes'      }
    {'analemmata'          }
    {'anathemata'          }
    {'antiegalitarian'     }
    {'armamentaria'        }
    {'caravansaries'       }
    {'caravanserai'        }
    {'caravanserais'       }
    {'extravaganza'        }
    {'extravaganzas'       }
    {'megalomaniacal'      }
    {'megalomaniacally'    }
    {'paralanguage'        }
    {'paralanguages'       }
    {'paramagnetically'    }
    {'paraphernalia'       }
    {'paraphrasable'       }
    {'parliamentarian'     }
    {'parliamentarians'    }
    {'radioimmunoassayable'}  tied for longest
    {'radiopharmaceutical' }
    {'radiopharmaceuticals'}  tied for longest
    {'razzamatazzes'       }
    {'teratocarcinomata'   }
    {'thalassaemia'        }
    {'thalassaemias'       }
 
    22                   alpha = eps
    {'indistinguishabilities'} tied for longest
    {'overcommercializations'} tied for longest
>> 

The ratios of 6 and 4 (i.e., 1/4, as specified in the problem) respectively head sets 1 and 2 and the length 22 heads the last (equality) list.

For more common words we'll try 80kwords.txt instead of words.txt:

     6
    {'levelheadednesses'  }
    {'tenderheartednesses'}
 
     4
    {'amalgamate'      }
    {'amalgamated'     }
    {'amalgamates'     }
    {'caravansaries'   }
    {'caravanserai'    }
    {'caravanserais'   }
    {'extravaganza'    }
    {'extravaganzas'   }
    {'paraphernalia'   }
    {'paraphernalias'  }
    {'parliamentarian' }
    {'parliamentarians'}
 
    21
    {'straightforwardnesses'}  
    {'unconstitutionalities'}    


or, trying the 36Kwords file:

     4
    {'bereavement'     }
    {'bereavement's'   }
    {'bereavements'    }
    {'degenerate's'    }
    {'degenerated'     }
    {'degenerates'     }
    {'perseverance'    }
    {'perseverance's'  }
    {'racketeered'     }
    {'redeemable'      }
    {'regenerate'      }
    {'regenerated'     }
    {'regenerates'     }
    {'reverberate'     }
    {'reverberated'    }
    {'reverberates'    }
    {'unrepresentative'}
 
     4
    {'amalgamate'     }
    {'amalgamated'    }
    {'amalgamates'    }
    {'paraphernalia'  }
    {'paraphernalia's'}
 
    18
    {'oversimplification'}

I think the winners in this case are

unrepresentative (ratio 4:1)

but unrepresentativeness (5:1) would actually be a contender, if considered common enough.

paraphernalia (ratio 1:4)

oversimplification (18 letter word for ratio=1:1)

  Posted by Charlie on 2022-09-17 12:45:06
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