uvaoj-1594:ducci sequence
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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
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
题解:模拟题,刘汝佳白书135页练习题5-2;看意思是要用map和vector做的,但是毕竟我比较懒,直接循环;
今天不行了,明天把这题用map做一下,今天看一看数据结构;
另外之前因为用来检测的语句忘记删了,wa了好几次,Orz,下次注意;
code:
#include <vector>
#include <algorithm>
#include <cstdlib>
using namespace std;
{
int t;
int n;
cin>>t;
while(t--)
{
vec.clear();
cin>>n;
int x;
for(int i=0; i<n; i++)
{
cin>>x;
vec.push_back(x);
//cout<<x<<endl;
}
int ans;
bool flag=0;
for(int i=0; i<1000; i++)
{
ans=0;
int a0=vec[0];
for(int j=0; j<n; j++)
{
j!=n-1? vec[j]=abs(vec[j]-vec[j+1]): vec[j]=abs(vec[j]-a0);
}
for(int j=0; j<n; j++)
{
if(vec[j]==0) ans++;
}
if(ans==n)
{
flag=1;
break;
}
}
flag==1? cout<<"ZERO"<<endl : cout<<"LOOP"<<endl;
}
return 0;
}
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