题干
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
————————————————————————————————————————————
题目就不解读了，自行翻译
思路
这道题在网上搜到的代码100%都是c/c++的，而其中绝大部分人的做法是：
直接按照题目所说模拟，也就是循环计算1000次，用map并发多线程
然后就AC了。没错这道题很水，
于是我也用同样的写法，循环加map。不出所料的超时！！
木得办法，Python还是慢呀，而且众所周知，因为GIL锁的问题，python多线程实际是单线程。
上一下代码先，然后再说解决办法：
T = int(input())
list_dc = [[] for _ in range(T)]
for t in range(T):
n = int(input())
list_dc[t] = list(map(int, input().split(' ')))
def Recursion(du):
length = len(du) - 1
for m in range(200):
for k in du:
if k != 0:
break
else:
return 'ZERO'
du_c = [v for v in du]
for j in range(length):
du[j] = abs(du_c[j] - du_c[j + 1])
du[length] = abs(du_c[length] - du_c[0])
for e in du:
if e != 0:
return 'LOOP'
else:
return 'zero'
result = map(Recursion, list_dc)
for i in result:
print(i)
我尝试各种改进，可终究是杯水车薪，时间终究不能有质的飞跃。
正当打算放弃时，偶然看到一个帖子，帖子里说其实只需要计算200次就可以了
我的第一反应是用了什么算法，或者推导出数列本身的性质了
但是稍微一分析，便知道绝对不是数列本身性质，因为按照题目条件，最坏就是数列中的整数全都是1000，这样真的就要循环1000次才能发现是zero。
而对于算法我是无可奈何，于是抱着试一试的心态，我直接把1000改为了200次循环
竟然成功了！！！
这道题的限制时间是3s，所以也是很极限了。
——————————————————————————
由此看来，应该是判题系统的数据水了。。。钻了个空子
至于这位大神是如何发现的，实在不得而知，佩服
在循环1000的代码下，我自己曾拿T = 1100（1100个测试数列）测试过，时间是符合的
所以可见这道题官方的测试数据应该有很多很多组，注重于如何快速处理更多组的数据，于是在数列数字的大小上放松了
