第五章 - Ducci Sequence - uva1594 - vector,map
A Ducci sequence is a sequence of n-tuples of integers. Given an n-tuple of integers (a1, a2, · · · , an),the next n-tuple in the sequence is formed by taking the absolute differences of neighboring integers:(a1, a2, · · · , an) → (|a1 − a2|, |a2 − a3|, · · · , |an − a1|)Ducci sequences either reach a tuple of zeros or fall into a periodic loop. For example, the 4-tuplesequence 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 tupleor a periodic loop.InputYour program is to read the input from standard input. The input consists of T test cases. The numberof test cases T is given in the first line of the input. Each test case starts with a line containing aninteger n (3 ≤ n ≤ 15), which represents the size of a tuple in the Ducci sequences. In the followingline, n integers are given which represents the n-tuple of integers. The range of integers are from 0 to1,000. You may assume that the maximum number of steps of a Ducci sequence reaching zeros tupleor making a loop does not exceed 1,000.OutputYour program is to write to standard output. Print exactly one line for each test case. Print ‘LOOP’ ifthe Ducci sequence falls into a periodic loop, print ‘ZERO’ if the Ducci sequence reaches to a zeros tuple.Sample Input448 11 2 754 2 0 2 070 0 0 0 0 0 061 2 3 1 2 3Sample OutputZEROLOOPZEROLOOP
分析：
一开始用数组做，然后，每生成一个新的数组就存入，然后判断，结果就是超时……
后来用了map和vector（不用每个都存，每次都重新遍历判断了！）
思路：
用map
如果值大于1就出现了loop的情况！
代码如下：
#include
#include
#include
#include