Ducci Sequence UVA - 1594

[align=center]  Ducci Sequence UVA - 1594 [/align][align=center][/align]              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

#include <iostream>
#include <bits/stdc++.h>

using namespace std;

int main()
{
int a[20];
int t,n,i,flag;
cin>>t;
while(t--)
{
cin>>n;
for(i=0; i<n; i++)
cin>>a[i];
int x=1005;
while(x--)
{
flag=0;
int y=a[0];
for(i=0; i<n; i++)
{
if(i!=n-1)
a[i]=abs(a[i]-a[i+1]);
else
a[i]=abs(a[i]-y);
if(a[i]!=0)
flag=1;
}
if(flag==0)
{
cout<<"ZERO"<<endl;
break;
}
}
if(flag==1)
cout<<"LOOP"<<endl;
}
return 0;
}



[align=center]                        [/align]