UVA 1594 Ducci Sequence（两极问题）

Ducci Sequence

Time Limit:3000MS Memory Limit:0KB 64bit IO Format:%lld & %llu

Description

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.

The following shows sample input and output for four test cases.

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

题解：给定数组，依次求前一个减后一个的值的绝对值，如果是最后一个则是最后一个减第一个的值的绝对值，

最多循环1000次，如果出现数组的值全部变为0，则为ZERO，否则为LOOP，所以只求全部为0的情况即可。

#include<iostream>
using namespace std;
int main()
{int a[20];
int i,j,t,n,sum;
cin>>t;
while(t--)
{
cin>>n;
for(i=0; i<n; i++)
cin>>a[i];
for(i=0; i<1000; i++)
{  sum=0;
int s=a[0];
for(j=0; j<n-1; j++)
{
if(a[j]>a[j+1])
a[j]=a[j]-a[j+1];
else
a[j]=a[j+1]-a[j];
sum+=a[j];

}

if(a[n-1]>s)
a[n-1]=a[n-1]-s;
else a[n-1]=s-a[n-1];
sum+=a[n-1];
if(sum==0)
break;

}

if(sum==0)
cout<<"ZERO"<<endl;
else
cout<<"LOOP"<<endl;

}
return 0;
}