Ducci 队列

快来打我* 2022-06-12 04:19 112阅读 0赞

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

8 11 2 7

4 2 0 2 0

0 0 0 0 0 0 0

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;
    }