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 → �, �, �, �, � → 0,0,2,0,2 → 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 → �, �, �, �, � → ⋯
Given an n-tuple of integers, write a program to decide if the sequence is reaching to a zeros tuple or a
periodic loop.
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.
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.
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
ZERO LOOP ZERO LOOP
Migrated from old NTUJ.
2009Seoul
| No. | Testdata Range | Score |
|---|