UVA1594 UVALive4723 Ducci Sequence【vector+set】

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-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 (3 ≤ n ≤ 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.

Sample Input

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

Regionals 2009 >> Asia - Seoul

问题链接：UVA1594 UVALive4723 Ducci Sequence

问题简述：（略）

问题分析：

序列放在STL向量中，出现过的序列放入STL集合中用来判断是否出现循环。

程序说明：（略）

题记：（略）

参考链接：（略）

AC的C++语言程序如下：

/* UVA1594 UVALive4723 Ducci Sequence */#include <bits/stdc++.h>using namespace std;vector<int> v, zero;
set< vector<int>> s;int main()
{int t, n;scanf("%d", &t);while(t--) {v.clear();zero.clear();s.clear();int a;scanf("%d", &n);for(int i=0; i<n; i++) {scanf("%d", &a);v.push_back(a);zero.push_back(0);}s.insert(v);for(;;) {if(v == zero) {puts("ZERO");break;}int a0 = abs(v[0] - v[1]);for(int i=1; i<n; i++)v[i] = abs(v[i] - v[(i + 1) % n]);v[0] = a0;if(s.count(v)) {puts("LOOP");break;} elses.insert(v);}}return 0;
}

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