Find Longest Special Substring That Occurs Thrice II - Problem

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.

Input & Output

Example 1 — Basic Case

$ Input: s = "aaaa"

› Output: 2

💡 Note: Special substrings: "a" appears 4 times, "aa" appears 3 times, "aaa" appears 2 times, "aaaa" appears 1 time. The longest that occurs ≥3 times is "aa" with length 2.

Example 2 — Multiple Characters

$ Input: s = "abcdef"

› Output: -1

💡 Note: Each character appears only once, so no special substring can occur at least 3 times.

Example 3 — Mixed Pattern

$ Input: s = "abcaba"

› Output: 1

💡 Note: Only single characters are special here. "a" appears 3 times and "b" appears 2 times. The longest special substring that occurs ≥3 times is "a" with length 1.

Constraints

3 ≤ s.length ≤ 5 × 10⁴
s consists of only lowercase English letters.

Visualization

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Asked in

G Google 25 a Amazon 18 M Microsoft 12

The key insight is that for a consecutive block of identical characters of length n, we can mathematically calculate how many substrings of each length k exist (which is n-k+1). The optimal approach uses sliding window to find character blocks in O(n) time, then counts substring occurrences mathematically. Time: O(n), Space: O(26).

Common Approaches

✓ Binary Search

⏱️ Time: N/A Space: N/A

Two Pointers

⏱️ Time: N/A Space: N/A

Binary Search on Answer

⏱️ Time: O(n log n) Space: O(n)

Binary search on the possible answer (substring length from 1 to n). For each candidate length, check if any special substring of that length occurs at least 3 times using sliding window technique.

Brute Force

⏱️ Time: O(n³) Space: O(n²)

Generate all possible substrings, check if each is special (contains only one character), count occurrences of each special substring, and return the longest one that appears at least 3 times.

Sliding Window with Mathematical Counting

⏱️ Time: O(n) Space: O(26)

Use sliding window to identify all consecutive blocks of identical characters, then for each block of length n, mathematically calculate how many substrings of each length k can be formed (which is n-k+1).

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

✓ Linear Space

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Medium Frequency

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Smart Actions

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