Longest Happy Prefix

We are asked to find the longest happy prefix of a given string s. A happy prefix is a non-empty prefix that is also a suffix (excluding itself).

Approach

We’ll use the Rolling Hash technique, which is often used to compare substrings in constant time. The idea is to maintain two hashes, one for the prefix and another for the suffix, and compare them at every step.

Initialize Prefix and Suffix Hashes: Start with hashes for both prefix and suffix as 0.
Iterate Through the String: Go through the string from left to right, simultaneously building the prefix and suffix.
Update Hashes: Calculate the hashes for the prefix and suffix. Use a fixed base and modulo to avoid integer overflow.
Check for Match: If the hashes match at any point, store the current prefix length.
Return Result: Return the substring corresponding to the longest matching prefix and suffix.

Implementation

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class Solution:
    def longestPrefix(self, s: str) -> str:
        n = len(s)
        prefix_hash = 0
        suffix_hash = 0
        base = 31
        modulo = 10 ** 9 + 7
        multiplier = 1
        longest_length = 0

        for i in range(n - 1):
            prefix_hash = (prefix_hash * base + ord(s[i]) - ord('a') + 1) % modulo
            suffix_hash = (suffix_hash + (ord(s[n - i - 1]) - ord('a') + 1) * multiplier) % modulo
            if prefix_hash == suffix_hash:
                longest_length = i + 1
            multiplier = (multiplier * base) % modulo

        return s[:longest_length]

Key Takeaways

Rolling Hash allows us to calculate and compare the hashes for the prefix and suffix simultaneously.
We use a fixed base and modulo to handle large numbers.
If the hashes match at any point, we update the length of the longest matching prefix and suffix.

Complexity Analysis

The time complexity is (O(n)), where (n) is the length of the given string s.
The space complexity is (O(1)), as we only use a constant amount of extra space.

Identifying Problem Isomorphism

“Longest Happy Prefix” can be approximately mapped to “Repeated Substring Pattern”.

In “Longest Happy Prefix”, the goal is to find the longest prefix which is also a suffix of the given non-empty string. In other words, you need to find a longest substring which starts at the beginning of the string and ends at the end of the string.

“Repeated Substring Pattern” is about determining whether a string can be made up entirely of a substring of itself, repeated one or more times. This is related to the “Longest Happy Prefix” problem in the sense that they both involve finding patterns within strings, and more specifically, repeated substrings.

The mapping is an approximate. While both problems involve finding a repeating substring, the exact requirements and outputs are different.

“Repeated Substring Pattern” is simpler as it only requires you to determine if the entire string can be made up of a repeating substring, while “Longest Happy Prefix” requires you to find the longest possible repeating substring from both start and end of the string.

10 Prerequisite LeetCode Problems

“1392. Longest Happy Prefix” involves working with strings and understanding string prefix and suffix properties. This can also be solved by using Rabin-Karp or KMP (Knuth–Morris–Pratt) algorithms. Here are 10 problems to prepare for it:

28. Implement strStr(): This problem asks you to implement a function that finds the first occurrence of a substring in a string.
14. Longest Common Prefix: This problem requires finding the longest common prefix string amongst an array of strings.
5. Longest Palindromic Substring: This problem is about finding substrings, but it requires a slightly more complex check because it’s about palindromes.
459. Repeated Substring Pattern: This problem can help you understand how repeated patterns in strings work, which is useful for understanding how string prefixes can be repeated.
214. Shortest Palindrome: This is another problem about palindromes. It can be solved using the KMP algorithm.
541. Reverse String II: This problem requires you to work with string manipulation and can be a good problem for understanding strings better.
387. First Unique Character in a String: This problem can help you understand how to work with character frequencies in strings.
686. Repeated String Match: This problem requires you to find the smallest number of times you can repeat a string to get another string as a substring.
76. Minimum Window Substring: This problem is about finding substrings, but with additional constraints that can challenge your understanding of strings.
3. Longest Substring Without Repeating Characters: This problem is about finding substrings without repeating characters, which is a useful skill for many string problems.

These problems should give you a thorough understanding of working with strings, substrings, prefixes, suffixes and the concepts used in algorithms like KMP or Rabin-Karp.

Problem Classification

Problem Statement:A string is called a happy prefix if is a non-empty prefix which is also a suffix (excluding itself).

Given a string s, return the longest happy prefix of s. Return an empty string "" if no such prefix exists.

Example 1:

Input: s = “level” Output: “l” Explanation: s contains 4 prefix excluding itself (“l”, “le”, “lev”, “leve”), and suffix (“l”, “el”, “vel”, “evel”). The largest prefix which is also suffix is given by “l”. Example 2:

Input: s = “ababab” Output: “abab” Explanation: “abab” is the largest prefix which is also suffix. They can overlap in the original string.

Constraints:

1 <= s.length <= 105 s contains only lowercase English letters.

Analyze the provided problem statement. Categorize it based on its domain, ignoring ‘How’ it might be solved. Identify and list out the ‘What’ components. Based on these, further classify the problem. Explain your categorizations.

Visual Model of the Problem

How to visualize the problem statement for this problem?

Problem Restatement

Could you start by paraphrasing the problem statement in your own words? Try to distill the problem into its essential elements and make sure to clarify the requirements and constraints. This exercise should aid in understanding the problem better and aligning our thought process before jumping into solving it.

Abstract Representation of the Problem

Could you help me formulate an abstract representation of this problem?

Given this problem, how can we describe it in an abstract way that emphasizes the structure and key elements, without the specific real-world details?

Terminology

Are there any specialized terms, jargon, or technical concepts that are crucial to understanding this problem or solution? Could you define them and explain their role within the context of this problem?

Problem Simplification and Explanation

Could you please break down this problem into simpler terms? What are the key concepts involved and how do they interact? Can you also provide a metaphor or analogy to help me understand the problem better?

Constraints

Given the problem statement and the constraints provided, identify specific characteristics or conditions that can be exploited to our advantage in finding an efficient solution. Look for patterns or specific numerical ranges that could be useful in manipulating or interpreting the data.

What are the key insights from analyzing the constraints?

Case Analysis

Could you please provide additional examples or test cases that cover a wider range of the input space, including edge and boundary conditions? In doing so, could you also analyze each example to highlight different aspects of the problem, key constraints and potential pitfalls, as well as the reasoning behind the expected output for each case? This should help in generating key insights about the problem and ensuring the solution is robust and handles all possible scenarios.

Identification of Applicable Theoretical Concepts

Can you identify any mathematical or algorithmic concepts or properties that can be applied to simplify the problem or make it more manageable? Think about the nature of the operations or manipulations required by the problem statement. Are there existing theories, metrics, or methodologies in mathematics, computer science, or related fields that can be applied to calculate, measure, or perform these operations more effectively or efficiently?

Problem Breakdown and Solution Methodology

Given the problem statement, can you explain in detail how you would approach solving it? Please break down the process into smaller steps, illustrating how each step contributes to the overall solution. If applicable, consider using metaphors, analogies, or visual representations to make your explanation more intuitive. After explaining the process, can you also discuss how specific operations or changes in the problem’s parameters would affect the solution? Lastly, demonstrate the workings of your approach using one or more example cases.

Inference of Problem-Solving Approach from the Problem Statement

How did you infer from the problem statement that this problem can be solved using ?

Could you please provide a stepwise refinement of our approach to solving this problem?
How can we take the high-level solution approach and distill it into more granular, actionable steps?
Could you identify any parts of the problem that can be solved independently?
Are there any repeatable patterns within our solution?

Solution Approach and Analysis

Thought Process

Explain the thought process by thinking step by step to solve this problem from the problem statement and code the final solution. Write code in Python3. What are the cues in the problem statement? What direction does it suggest in the approach to the problem? Generate insights about the problem statement.

From Brute Force to Optimal Solution

Could you please begin by illustrating a brute force solution for this problem? After detailing and discussing the inefficiencies of the brute force approach, could you then guide us through the process of optimizing this solution? Please explain each step towards optimization, discussing the reasoning behind each decision made, and how it improves upon the previous solution. Also, could you show how these optimizations impact the time and space complexity of our solution?

Coding Constructs

Consider the following piece of complex software code.

What are the high-level problem-solving strategies or techniques being used by this code?
If you had to explain the purpose of this code to a non-programmer, what would you say?
Can you identify the logical elements or constructs used in this code, independent of any programming language?
Could you describe the algorithmic approach used by this code in plain English?
What are the key steps or operations this code is performing on the input data, and why?
Can you identify the algorithmic patterns or strategies used by this code, irrespective of the specific programming language syntax?

Language Agnostic Coding Drills

Your mission is to deconstruct this code into the smallest possible learning units, each corresponding to a separate coding concept. Consider these concepts as unique coding drills that can be individually implemented and later assembled into the final solution.

Dissect the code and identify each distinct concept it contains. Remember, this process should be language-agnostic and generally applicable to most modern programming languages.
Once you’ve identified these coding concepts or drills, list them out in order of increasing difficulty. Provide a brief description of each concept and why it is classified at its particular difficulty level.
Next, describe the problem-solving approach that would lead from the problem statement to the final solution. Think about how each of these coding drills contributes to the overall solution. Elucidate the step-by-step process involved in using these drills to solve the problem. Please refrain from writing any actual code; we’re focusing on understanding the process and strategy.

Targeted Drills in Python

Now that you’ve identified and ordered the coding concepts from a complex software code in the previous exercise, let’s focus on creating Python-based coding drills for each of those concepts.

Begin by writing a separate piece of Python code that encapsulates each identified concept. These individual drills should illustrate how to implement each concept in Python. Please ensure that these are suitable even for those with a basic understanding of Python.
In addition to the general concepts, identify and write coding drills for any problem-specific concepts that might be needed to create a solution. Describe why these drills are essential for our problem.
Once all drills have been coded, describe how these pieces can be integrated together in the right order to solve the initial problem. Each drill should contribute to building up to the final solution.

Remember, the goal is to not only to write these drills but also to ensure that they can be cohesively assembled into one comprehensive solution.