uva 1594 Ducci Sequence

2024-03-24 08:32

文章标签 ducci sequence uva 1594

本文主要是介绍uva 1594 Ducci Sequence，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！

原题：
A Ducci sequence is a sequence of n-tuples of integers. Given an n-tuple of integers (a 1 ,a 2 ,···,a n ), the
next n-tuple in the sequence is formed by taking the absolute differences of neighboring integers:
(a 1 ,a 2 ,···,a n ) → (|a 1 − a 2 |,|a 2 − a 3 |,···,|a n − a 1 |)
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
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
中文：
紫书上的练习题，给你n个数，这n个数可以分别和下一个数相减，如下(a 1 ,a 2 ,···,a n ) → (|a 1 − a 2 |,|a 2 − a 3 |,···,|a n − a 1 |)。如果，不断进行这样的操作，如果出现全是0输出ZERO，如果出现循环输出LOOP。数据保证出现循环或者0

#include <bits/stdc++.h>
using namespace std;set<vector<int>> sv;
int main()
{ios::sync_with_stdio(false);int t,n;cin>>t;while(t--){cin>>n;vector<int> v,emp(n,0);sv.clear();for(int i=0;i<n;i++){int x;cin>>x;v.push_back(x);}sv.insert(v);int flag=0;vector<int> tmp;while(true){tmp.clear();for(int i=0;i<n-1;i++)tmp.push_back(abs(v[i+1]-v[i]));tmp.push_back(abs(v[n-1]-v[0]));v=tmp;if(sv.find(emp)!=sv.end()){flag=1;break;}if(sv.find(tmp)!=sv.end()){flag=2;break;}sv.insert(tmp);}if(flag==1)cout<<"ZERO"<<endl;elsecout<<"LOOP"<<endl;}return 0;
}