In the vast realm of algorithmic problems involving strings and subsequences, the Longest Uncommon Subsequence I problem is a thought-provoking one that challenges your understanding of strings and their properties. At first glance, the problem may seem intricate, but when understood properly, it unravels into an intriguing and somewhat unexpected solution. In this article, we will thoroughly examine the Longest Uncommon Subsequence I problem on Leetcode, understand the concept behind it, and explore the Pythonic way to solve it.
The Longest Uncommon Subsequence I problem on Leetcode is described as:
Given two strings
b, find the length of the longest uncommon subsequence between them. A subsequence of a string
s is a string that can be obtained after deleting any number of characters from
s. For example, “abc” is a subsequence of “aebdc” because you can delete the underlined characters in “aebdc” to get “abc”. Other subsequences of “aebdc” include “aebdc”, “aeb”, and so on. A subsequence is uncommon if it is a subsequence of one string but not the other.
Return the length of the longest uncommon subsequence. If the longest uncommon subsequence does not exist, return -1.
Input: a = "aba", b = "cdc" Output: 3
Insight into the Problem
Let’s discuss some crucial insights about this problem. If the two strings
b are different, then one of the entire strings must be the longest uncommon subsequence since it cannot be a subsequence of the other string.
If the strings are identical, there is no uncommon subsequence since any subsequence of
a will be a subsequence of
b and vice versa.
This observation simplifies the problem considerably.
Using the insights, we can come up with a simple Python solution.
def findLUSlength(a, b): # If the strings are not equal, the longer string is the longest uncommon subsequence if a != b: return max(len(a), len(b)) # If the strings are equal, there is no uncommon subsequence else: return -1
This solution has a time complexity of O(1) since the length of the strings does not affect the number of operations, and a space complexity of O(1).
Deep Dive: Understanding the Logic
It might be perplexing why we don’t have to check the characters in the strings or find subsequences explicitly. The reason behind this is the inherent property of strings and subsequences.
b are different, regardless of the characters they contain, it is guaranteed that at least one string cannot be a subsequence of the other. Hence, the longer string (or either if they have equal length) is an uncommon subsequence.
b are identical, they have the same set of characters, and any subsequence that can be formed by one can also be formed by the other. Thus, no uncommon subsequence exists.
In this detailed article, we delved into the Longest Uncommon Subsequence I problem on Leetcode. We uncovered the essential properties of strings and subsequences that lead to a simplified solution to this problem.