Hash Divided String

Problem Description

You are given a string s of length n and an integer k, where n is a multiple of k. Your task is to hash the string s into a new string called result, which has a length of n / k. First, divide s into n / k substrings, each with a length of k. Then, initialize result as an empty string. For each substring in order from the beginning, calculate the sum of the hash values of the characters in the substring, find the remainder of this sum when divided by 26, and identify the character in the English lowercase alphabet that corresponds to this remainder. Append that character to the end of result. Return result.

Key Insights

• Each character's hash value corresponds to its index in the English alphabet (e.g., 'a' = 0, 'b' = 1, ..., 'z' = 25).
• The string s is divided into substrings of length k and the number of such substrings is n / k.
• The final result string is constructed by appending characters derived from the modulo operation on the sum of hash values of each substring.

Space and Time Complexity

Time Complexity: O(n) - where n is the length of the string, as we process each character exactly once. Space Complexity: O(1) - only a constant amount of extra space is used for calculations, excluding the output string.

Solution

To solve this problem, we will:

1. Iterate through the input string s in steps of k to extract each substring.
2. For each substring, calculate the sum of the hash values of its characters.
3. Compute the remainder of this sum when divided by 26, which gives us the index of the character in the alphabet for the result string.
4. Append this character to the result string.
5. Finally, return the constructed result.

We will use a loop to traverse the string and a simple arithmetic operation to compute the hash values and their modulo.

Code Solutions