程式師世界 >> 編程語言 >> C語言 >> C++ >> C++入門知識 >> Ducci Sequence，duccisequence

Ducci Sequence，duccisequence

編輯：C++入門知識

Ducci Sequence，duccisequence

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,^..., a_n), the next n-tuple in the sequence is formed by taking the absolute differences of neighboring integers:

( a₁, a₂, ^..., a_n) $\displaystyle \rightarrow$ (| a₁ - a₂|,| a₂ - a₃|, ^...,| a_n - 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) $\displaystyle \rightarrow$ (3, 9, 5, 1) $\displaystyle \rightarrow$ (6, 4, 4, 2) $\displaystyle \rightarrow$ (2, 0, 2, 4) $\displaystyle \rightarrow$ (2, 2, 2, 2) $\displaystyle \rightarrow$ (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) $\displaystyle \rightarrow$ (2, 2, 2, 2, 4) $\displaystyle \rightarrow$ ( 0, 0, 0, 2, 2) $\displaystyle \rightarrow$ (0, 0, 2, 0, 2) $\displaystyle \rightarrow$ (0, 2, 2, 2, 2) $\displaystyle \rightarrow$ (2, 0, 0, 0, 2) $\displaystyle \rightarrow$ (2, 0, 0, 2, 0) $\displaystyle \rightarrow$ (2, 0, 2, 2, 2) $\displaystyle \rightarrow$ (2, 2, 0, 0, 0) $\displaystyle \rightarrow$ (0, 2, 0, 0, 2) $\displaystyle \rightarrow$ (2, 2, 0, 2, 2) $\displaystyle \rightarrow$ (0, 2, 2, 0, 0) $\displaystyle \rightarrow$ (2, 0, 2, 0, 0) $\displaystyle \rightarrow$ (2, 2, 2, 0, 2) $\displaystyle \rightarrow$ (0, 0, 2, 2, 0) $\displaystyle \rightarrow$ (0, 2, 0, 2, 0) $\displaystyle \rightarrow$ (2, 2, 2, 2, 0) $\displaystyle \rightarrow$ ( 0, 0, 0, 2, 2) $\displaystyle \rightarrow$ ^...

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 $\le$ n $\le$ 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

題解：給定數組，依次求前一個減後一個的值的絕對值，如果是最後一個則是最後一個減第一個的值的絕對值，

最多循環1000次，如果出現數組的值全部變為0，則為ZERO，否則為LOOP，所以只求全部為0的情況即可。

#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];//每循環一次a【0】的值都會變，所以要定義一個變量s
　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