longest-subsequence-repeated-k-times

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2014. Longest Subsequence Repeated k Times (Hard)

You are given a string s of length n, and an integer k. You are tasked to find the longest subsequence repeated k times in string s.

A subsequence is a string that can be derived from another string by deleting some or no characters without changing the order of the remaining characters.

A subsequence seq is repeated k times in the string s if seq * k is a subsequence of s, where seq * k represents a string constructed by concatenating seq k times.

• For example, "bba" is repeated 2 times in the string "bababcba", because the string "bbabba", constructed by concatenating "bba" 2 times, is a subsequence of the string "bababcba".

Return the longest subsequence repeated k times in string s. If multiple such subsequences are found, return the lexicographically largest one. If there is no such subsequence, return an empty string.

 

Example 1:

Input: s = "letsleetcode", k = 2
Output: "let"
Explanation: There are two longest subsequences repeated 2 times: "let" and "ete".
"let" is the lexicographically largest one.

Example 2:

Input: s = "bb", k = 2
Output: "b"
Explanation: The longest subsequence repeated 2 times is "b".

Example 3:

Input: s = "ab", k = 2
Output: ""
Explanation: There is no subsequence repeated 2 times. Empty string is returned.

 

Constraints:

• n == s.length
• 2 <= n, k <= 2000
• 2 <= n < k * 8
• s consists of lowercase English letters.

Related Topics

[Greedy] [String] [Backtracking] [Counting] [Enumeration]

Hints

Hint 1

The length of the longest subsequence does not exceed n/k. Do you know why?

Hint 2

Find the characters that could be included in the potential answer. A character occurring more than or equal to k times can be used in the answer up to (count of the character / k) times.

Hint 3

Try all possible candidates in reverse lexicographic order, and check the string for the subsequence condition.