2981. Find Longest Special Substring That Occurs Thrice I
Description
You are given a string s
that consists of lowercase English letters.
A string is called special if it is made up of only a single character. For example, the string "abc"
is not special, whereas the strings "ddd"
, "zz"
, and "f"
are special.
Return the length of the longest special substring of s
which occurs at least thrice, or -1
if no special substring occurs at least thrice.
A substring is a contiguous non-empty sequence of characters within a string.
Example 1:
Input: s = "aaaa" Output: 2 Explanation: The longest special substring which occurs thrice is "aa": substrings "aaaa", "aaaa", and "aaaa". It can be shown that the maximum length achievable is 2.
Example 2:
Input: s = "abcdef" Output: -1 Explanation: There exists no special substring which occurs at least thrice. Hence return -1.
Example 3:
Input: s = "abcaba" Output: 1 Explanation: The longest special substring which occurs thrice is "a": substrings "abcaba", "abcaba", and "abcaba". It can be shown that the maximum length achievable is 1.
Constraints:
3 <= s.length <= 50
s
consists of only lowercase English letters.
Solutions
Solution 1: Binary Search + Sliding Window Counting
We notice that if there exists a special substring of length $x$ that appears at least three times, then a special substring of length $x-1$ must also exist. This exhibits a monotonicity, so we can use binary search to find the longest special substring.
We define the left boundary of the binary search as $l = 0$ and the right boundary as $r = n$, where $n$ is the length of the string. In each binary search, we take $mid = \lfloor \frac{l + r + 1}{2} \rfloor$. If a special substring of length $mid$ exists, we update the left boundary to $mid$. Otherwise, we update the right boundary to $mid - 1$. During the binary search, we use a sliding window to count the number of special substrings.
Specifically, we design a function $check(x)$ to indicate whether a special substring of length $x$ that appears at least three times exists.
In the function $check(x)$, we define a hash table or an array of length $26$ named $cnt$, where $cnt[i]$ represents the count of special substrings of length $x$ composed of the $i$-th lowercase letter. We traverse the string $s$. If the current character is $s[i]$, we move the pointer $j$ to the right until $s[j] \neq s[i]$. At this point, $s[i \cdots j-1]$ is a special substring of length $x$. We increase $cnt[s[i]]$ by $\max(0, j - i - x + 1)$, and then update the pointer $i$ to $j$.
After the traversal, we go through the array $cnt$. If there exists $cnt[i] \geq 3$, it means a special substring of length $x$ that appears at least three times exists, so we return $true$. Otherwise, we return $false$.
The time complexity is $O((n + |\Sigma|) \times \log n)$, and the space complexity is $O(|\Sigma|)$, where $n$ is the length of the string $s$, and $|\Sigma|$ represents the size of the character set. In this problem, the character set is lowercase English letters, so $|\Sigma| = 26$.
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