An algorithm used to recursively construct a Set of objects from the smallest possible constituent parts.

Given a Set of Integers (, , ..., ) with
, a greedy
algorithm can be used to find a Vector of coefficients (, , ..., ) such that

(1) |

(2) |

(3) |

(4) |

For example, McNugget Numbers are numbers which are representable using only
. Taking and applying the algorithm iteratively gives the sequence (0, 0, 3), (0, 2, 2), (2, 1, 2), (3,
0, 2), (1, 4, 1), at which point . 62 is therefore a McNugget Number with

(5) |

If *any* Integer can be represented with or 1 using a sequence (, , ...), then this sequence
is called a Complete Sequence.

A greedy algorithm can also be used to break down arbitrary fractions into Unit Fractions in a finite number
of steps. For a Fraction , find the least Integer such that , i.e.,

(6) |

Paul Erdös and E. G. Strays have conjectured that the Diophantine Equation

(7) |

(8) |

© 1996-9

1999-05-25