#3137

Medium

LeetCode Problem Workspace

Minimum Number of Operations to Make Word K-Periodic

The problem requires calculating the minimum number of operations to make a string k-periodic using specific substring replacements.

hash table string counting

Problem Statement

You are given a string word of size n, and an integer k such that k divides n. In one operation, you can pick any two indices i and j, where both are divisible by k, and replace the substring starting at index i with the substring starting at index j. The task is to return the minimum number of such operations required to make the string k-periodic.

A string is k-periodic if it can be split into substrings of length k, and all substrings are identical. Your goal is to calculate how many operations are necessary to turn the given string into a k-periodic string using the fewest replacements. The indices i and j chosen for each operation must be divisible by k.

Examples

Example 1

Input: word = "leetcodeleet", k = 4

Output: 1

We can obtain a 4-periodic string by picking i = 4 and j = 0. After this operation, word becomes equal to "leetleetleet".

Example 2

Input: word = " leetcoleet ", k = 2

Output: 3

We can obtain a 2-periodic string by applying the operations in the table below.

Constraints

1 <= n == word.length <= 105
1 <= k <= word.length
k divides word.length.
word consists only of lowercase English letters.

Solution Approach

Frequency Calculation

The key to solving this problem lies in calculating the frequency of k-length substrings that start at indices divisible by k. Using a hash table, count how often each substring appears, and focus on the most frequent one, as fewer operations will be needed to replace the others with it.

Minimize Operations

Once the most frequent substring is identified, the number of operations needed is determined by how many other substrings need to be replaced to match this most frequent one. This minimizes the number of swaps required.

Efficient Calculation

To efficiently calculate the necessary transformations, use a counting mechanism to track the frequency of each substring of length k. With this information, you can easily determine how many substrings need to be modified.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity depends on the final approach, but it generally involves iterating through the string and processing substrings, which gives an overall complexity of O(n). The space complexity is also O(n) due to the storage required for substring frequencies.

What Interviewers Usually Probe

Look for a solution that makes use of hash tables for substring frequency calculation.
Focus on the understanding of substring counting and minimizing operations based on frequency analysis.
Evaluate how well the candidate can optimize the solution for large inputs by utilizing efficient data structures.

Common Pitfalls or Variants

Common pitfalls

Overcomplicating the problem by trying to manipulate the string directly instead of counting substring frequencies.
Failing to account for the fact that indices i and j must be divisible by k when performing operations.
Not considering edge cases, such as strings where no operations are needed or all characters are already the same.

Follow-up variants

What if k does not divide n? In this case, the problem is invalid, so ensure the constraint k divides n is met.
Consider the case where the string is already k-periodic, and no operations are needed.
Explore variations where the operations involve multiple substrings at once or restricted to certain positions.

FAQ

What is the minimum number of operations to make word k-periodic?

The minimum number of operations is determined by the number of substring replacements required to turn the string into a k-periodic form, with the fewest operations achieved by maximizing the frequency of one substring.

How do I calculate the frequency of substrings in this problem?

Use a hash table to store the frequencies of k-length substrings that start at indices divisible by k. This allows you to quickly identify the most frequent substring and minimize operations.

What if the string is already k-periodic?

If the string is already k-periodic, no operations are needed, and the answer would be 0 operations.

How does this problem connect to Hash Table and String topics?

The problem requires using hash tables to efficiently count substrings, which is a key technique for optimizing solutions involving string manipulation and transformations.

Can this approach be used for other periodic string problems?

Yes, the same pattern of counting substrings and minimizing operations can be applied to other periodic string problems, but each variant may have unique constraints or requirements.

terminal

Solution

Solution 1: Counting

We can divide the string `word` into substrings of length $k$, then count the occurrence of each substring, and finally return $n/k$ minus the count of the most frequently occurring substring.

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class Solution:
    def minimumOperationsToMakeKPeriodic(self, word: str, k: int) -> int:
        n = len(word)
        return n // k - max(Counter(word[i : i + k] for i in range(0, n, k)).values())

Continue Practicing

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