Ducci序列（Ducci Sequence ，UVa1594)
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-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 T test cases. The number of test cases T is given in the first line of the input. Each test case starts with a line containing an integer n (3 ≤ n ≤ 15), which represents the size of a tuple in the Ducci sequences. In the following line, n integers are given which represents the n-tuple of integers. The range of integers are from 0 to 1,000. You may assume that the maximum number of steps of a Ducci sequence reaching zeros tuple or making a loop does not exceed 1,000.
Output
Your program is to write to standard output. Print exactly one line for each test case. Print ‘LOOP’ if the Ducci sequence falls into a periodic loop, print ‘ZERO’ if the Ducci sequence reaches to a zeros tuple.
Sample Input
4
4
8 11 2 7
5
4 2 0 2 0
7
0 0 0 0 0 0 0
6
1 2 3 1 2 3
Sample Output
ZERO
LOOP
ZERO
LOOP
题意如下：
1、有一个由n个元组（a1,a2,a3,......,an)组成的数组，可以对于每个数求出它和下个数的差的绝对值，得到一个新的由n个元组组成的数组（|a1-a2|,|a2-a3|,...,|an-a1|)。重复这个过程，得到的序列称为Ducci序列。
2、Ducci序列有的最终会循环，也有的最终会变成0。
3、输入保证最多1000步就会变成1000步或者循环。
代码如下：
#include
#include
#include
#include
#include
#include
using namespace std;
int s[1005][16];//创建一个二维数组。
bool k=true;
int main()
{
int T;
cin>>T;
while(T--)
{
int n;
cin>>n;
k=true;
for(int i=0;i>s[0][i];
for(int i=1;i<1001;i++)//1000步循环
{
for(int j=0;j