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Select K Disjoint Special Substrings

Difficulty: Medium

Problem Description

Given a string s of length n and an integer k, determine whether it is possible to select k disjoint special substrings. A special substring is a substring where any character present inside the substring should not appear outside it in the string, and the substring is not the entire string s. All k substrings must be disjoint, meaning they cannot overlap. Return true if it is possible to select k such disjoint special substrings; otherwise, return false.

Key Insights

  • A special substring must consist of unique characters that do not appear elsewhere in the string.
  • The substring cannot be the entire string.
  • We need to find k such substrings that do not overlap.
  • The maximum number of potential disjoint special substrings is limited by the unique characters in the string.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem, we can use a greedy approach combined with a hash table (or a set) to track the characters in the string. The key steps are as follows:

  1. Character Frequency Count: Create a frequency map to count the occurrences of each character in the string.
  2. Identify Special Substrings: Iterate through the string to identify potential special substrings. A substring is special if all its characters have a frequency of 1 in the frequency map.
  3. Count Disjoint Special Substrings: For each identified special substring, ensure it does not overlap with previously found substrings and count how many such substrings can be formed.
  4. Check Against k: If the count of disjoint special substrings is greater than or equal to k, return true; otherwise, return false.

Code Solutions

def can_select_k_special_substrings(s, k):
    from collections import Counter

    # Count the frequency of each character
    freq = Counter(s)
    n = len(s)
    special_count = 0
    i = 0

    while i < n:
        # Start a potential special substring
        start = i
        while i < n and freq[s[i]] == 1:
            i += 1
        if start < i:  # Found a special substring
            special_count += 1
        i += 1  # Move to the next character after the current special substring

    return special_count >= k
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