Ducci 队列

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-tuplesequence 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 tupleor a periodic loop.InputYour program is to read the input from standard input. The input consists of T test cases. The numberof test cases T is given in the first line of the input. Each test case starts with a line containing aninteger n (3 ≤ n ≤ 15), which represents the size of a tuple in the Ducci sequences. In the followingline, n integers are given which represents the n-tuple of integers. The range of integers are from 0 to1,000. You may assume that the maximum number of steps of a Ducci sequence reaching zeros tupleor making a loop does not exceed 1,000.OutputYour program is to write to standard output. Print exactly one line for each test case. Print ‘LOOP’ ifthe Ducci sequence falls into a periodic loop, print ‘ZERO’ if the Ducci sequence reaches to a zeros tuple.

Sample Input4

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：有一个数组，判断是否可以通过变化变成全0；可以的话输出ZERO，否则输出LOOP

#include <cstdio>#include <string>#include <queue>#include <cmath>using namespace std;int main(){    int t,n;    int a[16];    scanf("%d",&t);    queue<int> Q;    while(t--)    {        while(!Q.empty())            Q.pop();        scanf("%d",&n);        for(int i=0; i<n; i++)        {            scanf("%d",&a[i]);            Q.push(a[i]);        }        int head,first,second,num=0,ok=0;        while(num++<1000&&!Q.empty())        {            if(!ok)            {                head=Q.front();                ok=1;            }            first=Q.front();//            printf("%d\n",head);//            if(num==16)//            break;            Q.pop();            second=Q.front();            if(num%n==0)            {                first=abs(head-first);                ok=0;            }            else                first=abs(second-first);            Q.push(first);        }        int sum=0;        while(!Q.empty())        {            sum+=Q.front();            Q.pop();        }        if(!sum)            printf("ZERO\n");        else            printf("LOOP\n");    }    return 0;}