UVA 1594 Ducci Sequence

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Ducci Sequence

Time Limit:3000MS Memory Limit:0KB 64bit IO Format:%lld & %llu

Description

A Ducci sequence is a sequence of n-tuples of integers. Given an n-tuple of integers (a₁, a₂,^..., a_n), the next n-tuple in the sequence is formed by taking the absolute differences of neighboring integers:

( a₁, a₂, ^..., a_n) $\displaystyle \rightarrow$ (| a₁ - a₂|,| a₂ - a₃|, ^...,| a_n - 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) $\displaystyle \rightarrow$ (3, 9, 5, 1) $\displaystyle \rightarrow$ (6, 4, 4, 2) $\displaystyle \rightarrow$ (2, 0, 2, 4) $\displaystyle \rightarrow$ (2, 2, 2, 2) $\displaystyle \rightarrow$ (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) $\displaystyle \rightarrow$ (2, 2, 2, 2, 4) $\displaystyle \rightarrow$ ( 0, 0, 0, 2, 2) $\displaystyle \rightarrow$ (0, 0, 2, 0, 2) $\displaystyle \rightarrow$ (0, 2, 2, 2, 2) $\displaystyle \rightarrow$ (2, 0, 0, 0, 2) $\displaystyle \rightarrow$ (2, 0, 0, 2, 0) $\displaystyle \rightarrow$ (2, 0, 2, 2, 2) $\displaystyle \rightarrow$ (2, 2, 0, 0, 0) $\displaystyle \rightarrow$ (0, 2, 0, 0, 2) $\displaystyle \rightarrow$ (2, 2, 0, 2, 2) $\displaystyle \rightarrow$ (0, 2, 2, 0, 0) $\displaystyle \rightarrow$ (2, 0, 2, 0, 0) $\displaystyle \rightarrow$ (2, 2, 2, 0, 2) $\displaystyle \rightarrow$ (0, 0, 2, 2, 0) $\displaystyle \rightarrow$ (0, 2, 0, 2, 0) $\displaystyle \rightarrow$ (2, 2, 2, 2, 0) $\displaystyle \rightarrow$ ( 0, 0, 0, 2, 2) $\displaystyle \rightarrow$ ^...

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 $\le$ n $\le$ 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.

The following shows sample input and output for four test cases.

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

终于看明白vector是个啥了。。

→ →。。。

#include<iostream>#include<map>#include<string>#include<vector>#include<cmath>#include<cstdio>using namespace std;vector<int>ducci;map<vector<int>,int>cnt;int main(){    int t;    scanf("%d",&t);    while(t--)    {        ducci.clear();        cnt.clear();        int n,x;        cin>>n;        int i;        for(i=0;i<=n-1;i++)        {            cin>>x;            ducci.push_back(x);        }        vector<int>pa;        pa=ducci;        cnt[pa]=0;        vector<int>ducci2;        int j;        for(j=0;cnt[pa]==0&&j<1000;j++)        {            cnt[pa]=1;            pa.clear();            for(i=0;i<=ducci.size()-1;i++)            {                ducci2.push_back(abs(ducci[i]-ducci[(i+1)%ducci.size()]));            }            pa=ducci2;            ducci=ducci2;            ducci2.clear();        }        int out=0;        for(i=0;i<=pa.size()-1;i++)        {            if(pa[i]!=0) out=1;        }        if(out==1) cout<<"LOOP"<<endl;        else cout<<"ZERO"<<endl;    }    return 0;}

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