📅  最后修改于: 2023-12-03 15:07:06.634000             🧑  作者: Mango
在本文中,我们将讨论如何找到一个序列中具有相同左右旋转的数字的最长子序列。首先,我们需要对左右旋转进行定义。
对于一个数字,左旋转意味着将最高位移动到最低位,而右旋转意味着将最低位移动到最高位。例如,对于数字1234,左旋转一次变为2341,右旋转一次变为4123。
为了找到具有相同左右旋转的数字的最长子序列,我们需要将每个数字左右旋转,并将其添加到一个哈希表中。在哈希表中,我们可以查找相同的数字,以查找可用于构造子序列的数字对。
以下是实现该算法的基本思路:
下面是一个Python实现,包括详细的注释。
def find_longest_subsequence(sequence):
"""
Finds the longest subsequence of a given sequence that contains numbers with the same left-right rotation.
Args:
sequence: a list of integers representing the sequence to be searched
Returns:
a list of integers representing the longest subsequence with numbers with the same left-right rotation
"""
# initialize a hash table to store each number and its corresponding left-right rotation as key-value pairs
digits = {}
for number in sequence:
number_str = str(number)
# find the left and right rotations of the number
left_rotation = number_str[1:] + number_str[0]
right_rotation = number_str[-1] + number_str[:-1]
# add the number and its rotations to the hash table
digits[number_str] = (left_rotation, right_rotation)
# initialize a dictionary to store each candidate subsequence and its length
candidates = {}
for number in sequence:
# initialize a new candidate subsequence with the current number
new_candidate = [number]
# look for all numbers with the same left-right rotations as the current number
for rotation in digits[number_str]:
if rotation in digits:
# if a matching number is found, add it to the candidate subsequence
matching_number = int(rotation)
new_candidate.append(matching_number)
# update the hash table to mark the matching number as "used"
digits.pop(rotation)
# store the length of the candidate subsequence in the candidates dictionary
candidates[tuple(new_candidate)] = len(new_candidate)
# return the longest candidate subsequence
longest_subsequence = max(candidates, key=candidates.get)
return list(longest_subsequence)
具有相同左右旋转的数字的最长子序列算法可以用于查找给定序列中存在的数字对,这些数字对具有相同左右旋转,可以用于构造一个具有相同左右旋转的数字的最长子序列。该算法的实现需要使用哈希表来存储每个数字及其左右旋转,并使用一个字典来存储可能的候选子序列及其长度。最终,该算法以线性时间复杂度($O(n)$)找到最长的具有相同左右旋转的数字的子序列。