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 Input448 11 2 754 2 0 2 070 0 0 0 0 0 061 2 3 1 2 3Sample OutputZEROLOOPZEROLOOP
用队列存每此次的结果，用set判断是否只有0.
#include<iostream>
#include<cstdio>
#include<cstring>
#include<queue>
#include<set>
using namespace std;
int main()
{
queue<int>que;
set<int>s2;
set<int>::iterator ii;
int n,m,i,j,t,k,s,s1;
int f=0;
scanf("%d",&n);
while(n--)
{
f=0;
scanf("%d",&m);
for(i=0; i<m; i++)
{
scanf("%d",&t);
que.push(t);
}
for(i=0; i<1000; i++)
{
for(j=0; j<m; j++)
{
if(j==0)
{
t=que.front();
k=que.back();
if(t>k)
s=t-k;
else
s=k-t;
}
t=que.front();
que.pop();
if(j<m-1)
{
k=que.front();
s1=t-k;
if(s1<0)
{
s1=-s1;
}
que.push(s1);
s2.insert(s1);
}
if(j==m-1)
{
que.push(s);
s2.insert(s);
}
}
if(s2.size()==1)
{
f=1;
break;
}
s2.clear();
}
while(!que.empty())
{
que.pop();
}
if(f==0)
{
printf("LOOP\n");
}
else
{
printf("ZERO\n");
}
}
return 0;
}
