5-2.1594.pdf - 4723 Ducci Sequence Asia Seoul 2009/2010 A...

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4723 - Ducci Sequence Asia - Seoul - 2009/2010 A Ducci sequence is a sequence of n -tuples of integers. Given an n -tuple of integers ( a 1 , a 2 , ... , a n ), the next n -tuple in the sequence is formed by taking the absolute differences of neighboring integers: ( a 1 , a 2 , ... , a n ) (| a 1 - a 2 |,| a 2 - a 3 |, ... ,| a n - a 1 |) Ducci sequences either reach a tuple of zeros or fall into a periodic loop. For example, the 4-tuple sequence starting with 8,11,2,7 takes 5 steps to reach the zeros tuple: (8, 11, 2, 7) (3, 9, 5, 1) (6, 4, 4, 2) (2, 0, 2, 4) (2, 2, 2, 2) (0, 0, 0, 0). The 5-tuple sequence starting with 4,2,0,2,0 enters a loop after 2 steps: (4, 2, 0, 2, 0) (2, 2, 2, 2, 4) ( 0, 0, 0, 2, 2 ) (0, 0, 2, 0, 2) (0, 2, 2, 2, 2) (2, 0, 0, 0, 2) (2, 0, 0, 2, 0) (2, 0, 2, 2, 2) (2, 2, 0, 0, 0) (0, 2, 0, 0, 2) (2, 2, 0, 2, 2) (0, 2, 2, 0, 0) (2, 0, 2, 0, 0) (2, 2, 2, 0, 2) (0, 0, 2, 2, 0) (0, 2, 0, 2, 0) (2, 2, 2, 2, 0) ( 0, 0, 0, 2, 2 ) ... Given an n -tuple of integers, write a program to decide if the sequence is reaching to a zeros tuple or a periodic loop. Input Your program is to read the input from standard input. The input consists of
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