zoukankan      html  css  js  c++  java
  • UVa 1594 Ducci Sequence

    A Ducci sequence is a sequence of n-tuples of integers. Given an n-tuple of integers (a1a2, ... an), the next n-tuple in the sequence is formed by taking the absolute differences of neighboring integers:

    a1a2... an$displaystyle 
ightarrow$ (| 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) $displaystyle 
ightarrow$ (3, 9, 5, 1) $displaystyle 
ightarrow$ (6, 4, 4, 2) $displaystyle 
ightarrow$ (2, 0, 2, 4) $displaystyle 
ightarrow$ (2, 2, 2, 2) $displaystyle 
ightarrow$ (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) $displaystyle 
ightarrow$ (2, 2, 2, 2, 4) $displaystyle 
ightarrow$ ( 0, 0, 0, 2, 2$displaystyle 
ightarrow$ (0, 0, 2, 0, 2) $displaystyle 
ightarrow$ (0, 2, 2, 2, 2) $displaystyle 
ightarrow$ (2, 0, 0, 0, 2) $displaystyle 
ightarrow$

    (2, 0, 0, 2, 0) $displaystyle 
ightarrow$ (2, 0, 2, 2, 2) $displaystyle 
ightarrow$ (2, 2, 0, 0, 0) $displaystyle 
ightarrow$ (0, 2, 0, 0, 2) $displaystyle 
ightarrow$ (2, 2, 0, 2, 2) $displaystyle 
ightarrow$ (0, 2, 2, 0, 0) $displaystyle 
ightarrow$

    (2, 0, 2, 0, 0) $displaystyle 
ightarrow$ (2, 2, 2, 0, 2) $displaystyle 
ightarrow$ (0, 0, 2, 2, 0) $displaystyle 
ightarrow$ (0, 2, 0, 2, 0) $displaystyle 
ightarrow$ (2, 2, 2, 2, 0) $displaystyle 
ightarrow$ ( 0, 0, 0, 2, 2$displaystyle 
ightarrow$ ...

    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;
    }
    


  • 相关阅读:
    POJ 1953 World Cup Noise
    POJ 1995 Raising Modulo Numbers (快速幂取余)
    poj 1256 Anagram
    POJ 1218 THE DRUNK JAILER
    POJ 1316 Self Numbers
    POJ 1663 Number Steps
    POJ 1664 放苹果
    如何查看DIV被设置什么CSS样式
    独行DIV自适应宽度布局CSS实例与扩大应用范围
    python 从入门到精通教程一:[1]Hello,world!
  • 原文地址:https://www.cnblogs.com/kunsoft/p/5312797.html
Copyright © 2011-2022 走看看