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opnum - that the earliest lexigraphically shall be the...

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Sheet1 Page 1 Optimum Number Representation ------- ------ -------------- The inhabitants of the ancient tribe of Pagong had in- credible numerical dexterity. Their numeral system was not decimal, but reverse-polish-notation based. Each number was represented by a sequence of digits and oper- ations. The `digits' they used were surprisingly simi- lar to those we use today: one two three four five six seven eight nine ten represented our numbers 1 through 10, respectively. To build numbers larger than ten, they composed other num- bers with the operations * or +, respectively, using reverse polish notation, where the operation follows the two operands. Thus, one representation for our number 13 is eight five + Another representation is one two + two * two * one + Because there were so many representations of the same number, `high' Pagong dictates that the canonical representation of a number be the shortest possible representation, and where there were ties in length,
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Unformatted text preview: that the earliest lexigraphically shall be the canonical number. (Their lexigraphical ordering was the same as ASCII, amazingly). The length includes all characters, including a single space that follows each digit or op-eration but the last. Thus, the shortest possible representations of 13 are: r three ten + four nine + six seven + seven six + nine four + ten three + and of these, four nine + is the earliest and thus canonical representation of 13. Your task is to translate numbers from our Arabic repre-sentation to the canonical Pagong representation. Each input number will be on a line by itself, and the output Sheet1 Page 2 should consist of lines each containing just one canon-ical Pagong number. All numbers will be 1000 or less, and there will be fewer than five hundred numbers in the input set. Sample input: 5 101 64 Sample output: five one ten ten * + eight eight *...
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