Minimum Number of Operations to Make Word K-Periodic

Minimum Number of Operations to Make Word K-Periodic

1. What is this problem about?

In the Minimum Number of Operations to Make Word K-Periodic coding problem, you are given a string of length n and an integer k (where n is divisible by k). A string is "k-periodic" if all its substrings of length k starting at indices 0, k, 2k, ... are identical. In one operation, you can replace any of these k-length blocks with any other string of length k. Your goal is the minimum operations to make the word k-periodic.

2. Why is this asked in interviews?

Companies like Google and Turing use this to test frequency analysis and the ability to work with "blocks" of data rather than individual characters. It's a variation of the "most frequent element" problem, but the "elements" here are substrings of length k.

3. Algorithmic pattern used

This utilizes the Hash Table, Counting, String interview pattern.

1. Break the string into n/k blocks, each of length k.
2. Use a Hash Table to count the frequency of each distinct block.
3. To minimize operations, we should keep the most frequent block and change all others.
4. Answer = (Total number of blocks) - (Frequency of the most common block).

4. Example explanation

String: "leetcodeleet", k=4 Blocks: "leet", "code", "leet"

1. Frequency: {"leet": 2, "code": 1}
2. Total blocks = 3.
3. Most frequent = "leet" (count 2).
4. Operations = 3 - 2 = 1. (We only need to change "code" to "leet").

5. Common mistakes candidates make

A common mistake is trying to change characters individually instead of entire blocks. The problem specifically asks for k-periodicity based on the provided k-length partitions. Another error is not correctly handling the string slicing or iterating with the wrong step size.

6. Interview preparation tip

When a problem involves periodicity or repeating patterns, identify the "base unit." Once you have the units (the substrings), the problem usually simplifies to finding the mode (most frequent element) and calculating how many items differ from that mode.