UVa 1594 Ducci Sequence

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) $\displaystyle \rightarrow$ (| 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) $\displaystyle \rightarrow$ (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, nintegers 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


这道题比较水啊，注意一点就是an-a1的时候a1有可能已经改变




#include <bits/stdc++.h>
using namespace std;

int main()
{
    int T;
    cin >> T;
    next:
    while(T--)
    {
        int n;
        vector<int> num;
        cin >> n;
        for(int i = 0; i < n; i++)
        {
            int t;
            cin >> t;
            num.push_back(t);
        }

        for(int cnt = 0; cnt < 1024; cnt++)
        {
            bool flag = true;
            int temp = num[0];
            for(int i = 0; i < num.size() - 1; i++)
                num[i] = abs(num[i] - num[i+1]);
            num[num.size()-1] = abs(num[num.size()-1] - temp);
            for(int i = 0; i < num.size(); i++)
                if(num[i]!=0)
                    flag = false;
            if(flag==true)
            {
                cout << "ZERO" << endl;
                goto next;
            }
        }
        cout << "LOOP" << endl;
    }
    return 0;
}




   






            

            
posted @ 
2014-11-22 18:45 
Popco 
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