Ducci Sequence解题报告

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)

(| 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)

(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(3n15), 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

题意：给你一个数组，相邻数相加（最后一个数应该加第一个数），然后又可以得到一个新的数组，反复进行这样的步骤，结果会有两种，数组每个成员都是零，或者在这样的过程中出现了周期，即出现了和以前已经出现过的相同的项。
最后要求判断是哪一种情况

思路：
如果按照一般的解题思想，每得到一个新的数组都去判断是zero，还是loop。zero还好说，如果判断loop那就要每次遍历一遍数组，程序肯定会超时。、
所以~~~
反正结果只有两种可能，不是loop，就是zero，只判断zero就好了

代码：

#include <iostream>

#include <cstdio>

using namespace std;

const int maxn=;

int a[][maxn];

int n;

int iszero;

void Init()

{

    cin>>n;

    for(int i=;i<n;i++)

    cin>>a[][i];

}

bool judge()

{

    iszero=;

    int now,form;

    for(int i=;i<=;i++)

    {

        if(i%==) now=,form=;

        else now=,form=;

       for(int j=;j<n;j++)

       {

           if(j==n-)

           {

               a[now][j]=a[form][j]+a[form][];

           }

           else

           a[now][j]=a[form][j]+a[form][j+];

       }

       int flag=;

       for(int k=;k<n;k++)

       if(a[now][k]!=) {flag=;break;}

       if(!flag) {iszero=;break;}

    }

    if(iszero) return true;

    else       return false;

}

int main()

{

    int T;

    cin>>T;

    while(T--)

    {

     Init();

     if(judge()) cout<<"ZERO"<<endl;

     else cout<<"LOOP"<<endl;

    }

    return ;

}

巴特西

Ducci Sequence解题报告

Input

Output

Sample Input

Sample Output

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