This one is slightly more complicated but USES a Ruby hash (associative array) to simplify the reduction operation (see Listing 5).

虽然此应用程序稍微有些复杂，但是使用Ruby hash(关联阵列)可简化reduce操作(请参考清单5)。

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Mathematics a set with an associative binary operation under which the set is closed, which contains an identity element and an inverse for every element in the set.

群：二元结合运算为闭合的数学集合，具有单位元素。集合中每一元素都有逆元素。

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