Encode String with Shortest Length

We can use Dynamic Programming to encode the given string in the shortest possible way. Let’s create a 2D table dp where dp[i][j] will store the shortest encoded string for the substring s[i:j+1].

We can iterate through the given string and update the dp table using the following approach:

For every substring, we’ll look for patterns where the substring can be divided into repeated sections.
If we find such a pattern, we’ll encode it and compare the length with the original substring to find the shorter one.

Here’s the code for the given problem:

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class Solution:
    def encode(self, s: str) -> str:
        n = len(s)
        dp = [[""] * n for _ in range(n)]

        # Iterate through all possible substring lengths
        for length in range(1, n + 1):
            for i in range(n - length + 1):
                j = i + length - 1
                substring = s[i:j + 1]
                dp[i][j] = substring  # Initialize with the original substring

                # Check if the substring can be encoded in a shorter way
                for k in range(i, j):
                    if len(dp[i][k]) + len(dp[k + 1][j]) < len(dp[i][j]):
                        dp[i][j] = dp[i][k] + dp[k + 1][j]

                # Look for patterns in the substring
                pattern_pos = (substring + substring).find(substring, 1)
                if pattern_pos >= 0:
                    encoded_pattern = str(len(substring) // pattern_pos) + '[' + dp[i][i + pattern_pos - 1] + ']'
                    if len(encoded_pattern) < len(dp[i][j]):
                        dp[i][j] = encoded_pattern

        return dp[0][n - 1]

This code iterates through all possible substrings and looks for repeated patterns to encode them. The time complexity is (O(n^3)), and the space complexity is (O(n^2)).

Identifying Problem Isomorphism

“Encode String with Shortest Length” can be mapped to “Longest Duplicate Substring”.

These problems revolve around similar concepts, where string manipulation and searching for repetitive patterns play a central role. In “Encode String with Shortest Length”, the goal is to compress the string by identifying repeated substrings. In “Longest Duplicate Substring”, you’re tasked with finding the longest repetitive substring.

The common thread here is the necessity to identify repetitive patterns within a string. Moreover, you need to handle these patterns in an optimal way, considering both the length and frequency of repetition.

“Longest Duplicate Substring” is simpler as it only requires finding and returning the duplicate substring, while “Encode String with Shortest Length” involves an additional step of encoding the string in a particular format.

10 Prerequisite LeetCode Problems

“471. Encode String with Shortest Length” is about string manipulation and dynamic programming. Here are some simpler problems to prepare for this:

344. Reverse String: This is a basic problem to understand string manipulation.
3. Longest Substring Without Repeating Characters: This problem will teach you how to handle substrings and uniqueness in them.
14. Longest Common Prefix: This problem will help you get familiar with the concept of common prefixes in strings.
5. Longest Palindromic Substring: Here, you will get a deeper understanding of substrings and also palindromes.
647. Palindromic Substrings: This is another problem to enhance your understanding of palindromes.
72. Edit Distance: This problem will introduce you to dynamic programming with strings.
392. Is Subsequence: Here, you will learn how to identify if a string is a subsequence of another.
1143. Longest Common Subsequence: This problem uses dynamic programming to find common subsequences, a useful technique for string problems.
516. Longest Palindromic Subsequence: This problem is a combination of the concepts from problems 4 and 8.
139. Word Break: This problem deals with breaking a string into valid words, a necessary concept for the main problem.

“471. Encode String with Shortest Length” involves dynamic programming and string manipulation. Here are 4 more problems as preparation:

“300. Longest Increasing Subsequence”: This problem, while not specifically about strings, is a classic dynamic programming problem that will be useful practice.
“322. Coin Change”: This problem is a classic dynamic programming problem, the understanding of which can be transferred to solve other problems.
“53. Maximum Subarray”: This is a classic dynamic programming problem. It is not directly related to strings, but it is a good problem to understand the dynamic programming concept.
“152. Maximum Product Subarray”: Similar to the “Maximum Subarray” problem, this problem introduces a variation by asking for the maximum product instead.

These cover dynamic programming and string manipulation, you should be well-prepared to tackle the “471. Encode String with Shortest Length” problem.

Problem Classification

Problem Statement:Given a string s, encode the string such that its encoded length is the shortest.

The encoding rule is: k[encoded_string], where the encoded_string inside the square brackets is being repeated exactly k times. k should be a positive integer.

If an encoding process does not make the string shorter, then do not encode it. If there are several solutions, return any of them.

Example 1:

Input: s = “aaa” Output: “aaa” Explanation: There is no way to encode it such that it is shorter than the input string, so we do not encode it.

Example 2:

Input: s = “aaaaa” Output: “5[a]” Explanation: “5[a]” is shorter than “aaaaa” by 1 character.

Example 3:

Input: s = “aaaaaaaaaa” Output: “10[a]” Explanation: “a9[a]” or “9[a]a” are also valid solutions, both of them have the same length = 5, which is the same as “10[a]”.

Constraints:

1 <= s.length <= 150 s consists of 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.