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
#include<cstdio>
#include<iostream>
#include<string>
#include<sstream>
using namespace std;
int main(){
int n;
cin>>n;
while(n--){
int m,a[1005];
cin>>m;
int flag=0;
for(int i=0;i<m;i++){
cin>>a[i];
}
for(int j=1;j<=1000;j++){
int d=a[0];
for(int i=0;i<m-1;i++){
a[i]=a[i+1]-a[i];
if(a[i]<0){
a[i]=-a[i];
}
}
a[m-1]=a[m-1]-d;
if(a[m-1]<0){
a[m-1]=-a[m-1];
}
int sum=0;
for(int i=0;i<m;i++){
sum+=a[i];
// cout<<a[i]<<" ";
}
if(sum==0){
flag=1;
break;
}
}
if(flag){
printf("ZERO\n");
}else{
cout<<"LOOP"<<endl;
}
}
return 0;
}