Word Abbreviation

This problem requires us to find the minimal possible abbreviations for every word in the list. To do this, we’ll create a function to abbreviate words with a given prefix length, group words by their abbreviations, and then increase the prefix length for groups with collisions.

Python code:

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from collections import defaultdict

class Solution:
    def wordsAbbreviation(self, words: List[str]) -> List[str]:
        def abbreviate(word, prefix_len):
            if prefix_len + 2 >= len(word):
                return word
            return word[:prefix_len] + str(len(word) - prefix_len - 1) + word[-1]

        def unique_abbreviations(words, prefix_len):
            groups = defaultdict(list)
            for i, word in enumerate(words):
                abbr = abbreviate(word, prefix_len)
                groups[abbr].append(i)
            return groups

        result = ["" for _ in words]
        prefix_len = 1
        groups = unique_abbreviations(words, prefix_len)

        while groups:
            next_groups = defaultdict(list)
            for abbr, indices in groups.items():
                if len(indices) == 1:
                    result[indices[0]] = abbr
                else:
                    for i in indices:
                        next_abbr = abbreviate(words[i], prefix_len + 1)
                        next_groups[next_abbr].append(i)
            groups = next_groups
            prefix_len += 1

        return result

Explanation:

abbreviate function takes a word and a prefix length and returns the abbreviated form according to the problem’s rules.
unique_abbreviations function groups words by their abbreviations using the given prefix length.
The main part of the solution initializes the result list and iteratively resolves collisions by increasing the prefix length. If a group has only one word, we store the abbreviation in the result. If a group has more than one word, we continue to the next iteration with a longer prefix length.
The while loop continues until all collisions are resolved, and we return the final result.

This code ensures that the returned abbreviations are minimal and unique for each word in the given list.

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class Solution:
    def wordsAbbreviation(self, words: List[str]) -> List[str]:
        trie = {}
        for word in words:
            node = trie
            cands = [word[0] + word[-1]] + list(word[1:-1])
            for i, w in enumerate(cands):
                node = node.setdefault(w, {})
                rest = len(cands) - i - 1
                node[rest] = node.get(rest, 0) + 1

        ans = []
        for word in words:
            if len(word) <= 3: 
                ans.append(word)
                continue
            node = trie
            cands = [word[0] + word[-1]] + list(word[1:-1])
            for i, w in enumerate(cands):
                node = node[w]
                rest = len(cands) - i - 1
                if rest > 1 and node[rest] < 2:
                    ans.append(word[:i+1]+str(rest)+word[-1])
                    break
                elif rest <= 1:
                    ans.append(word)
                    break

        return ans

Identifying Problem Isomorphism

“Word Abbreviation” has an approximate isomorph: “Unique Word Abbreviation”

“Word Abbreviation” is about abbreviating a list of words, where the goal is to minimize the length of the abbreviation for each word, but still maintain the property that no two abbreviations are the same.

“Unique Word Abbreviation” is about managing a dictionary of words and determining whether a given word’s abbreviation is unique among all words in the dictionary. The abbreviation of a word is unique if either of the following conditions is satisfied: The word itself doesn’t exist in the dictionary or all words in the dictionary that have the same abbreviation are the same as the given word.

Both problems involve the concept of word abbreviations and explore the uniqueness of those abbreviations. They require strategic data organization and careful traversal of the given words or dictionary to yield the right outcomes.

“Word Abbreviation” is more complicated as it demands not only generating the abbreviations but also ensuring they are distinct for every word in the list. “Unique Word Abbreviation” just checks if a given word’s abbreviation is unique based on the existing dictionary.

10 Prerequisite LeetCode Problems

“527. Word Abbreviation” is a problem where you are given a list of n distinct words and need to find a unique abbreviation for each word such that:

It starts with the first letter of the word.
It ends with the last letter of the word.
Between the first and last letter, it contains the number of remaining characters.
The abbreviation must be as short as possible while keeping it unique among the abbreviations of all other words in the list.

Here are 10 problems to prepare for this one:

388. Longest Absolute File Path: In this problem, you need to understand and manipulate strings in a certain way to find the longest absolute file path.
293. Flip Game: This problem involves generating possible states of a string after certain operations, similar to generating abbreviations.
294. Flip Game II: It’s a more complicated version of the previous problem where you need to predict the outcome of a game involving flipping in strings.
459. Repeated Substring Pattern: In this problem, you check if a string can be constructed by taking a substring and repeating it. Understanding substrings is crucial for word abbreviation.
76. Minimum Window Substring: This problem helps with understanding and handling substrings, which could be helpful for creating abbreviations.
187. Repeated DNA Sequences: This problem involves finding all substrings of a specified length that occur more than once.
5. Longest Palindromic Substring: This problem will help you get more practice working with substrings.
10. Regular Expression Matching: This problem requires manipulation and matching of strings, which can be useful when determining if an abbreviation is unique.
49. Group Anagrams: This problem involves grouping words based on their characters. It could provide useful insight for the abbreviation problem where you might need to group words based on their abbreviations.
14. Longest Common Prefix: This problem requires you to find the longest common prefix among an array of strings. It could help you understand how to handle prefixes, which are part of creating abbreviations.

These cover string manipulation, substrings, and character counting which will be helpful for solving the “Word Abbreviation” problem.

Problem Classification

Problem Statement:Given an array of distinct strings words, return the minimal possible abbreviations for every word.

The following are the rules for a string abbreviation:

The initial abbreviation for each word is: the first character, then the number of characters in between, followed by the last character. If more than one word shares the same abbreviation, then perform the following operation: Increase the prefix (characters in the first part) of each of their abbreviations by 1. For example, say you start with the words [“abcdef”,“abndef”] both initially abbreviated as “a4f”. Then, a sequence of operations would be [“a4f”,“a4f”] -> [“ab3f”,“ab3f”] -> [“abc2f”,“abn2f”]. This operation is repeated until every abbreviation is unique. At the end, if an abbreviation did not make a word shorter, then keep it as the original word.

Example 1:

Input: words = [“like”,“god”,“internal”,“me”,“internet”,“interval”,“intension”,“face”,“intrusion”] Output: [“l2e”,“god”,“internal”,“me”,“i6t”,“interval”,“inte4n”,“f2e”,“intr4n”] Example 2:

Input: words = [“aa”,“aaa”] Output: [“aa”,“aaa”]

Constraints:

1 <= words.length <= 400 2 <= words[i].length <= 400 words[i] consists of lowercase English letters. All the strings of words are unique.

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.

Distilling the Problem to Its Core Elements

In order to have me distill a problem to its core, you could ask questions that prompt for a deeper analysis of the problem, understanding of the underlying concepts, and simplification of the problem’s essence. Here are some examples of such prompts:

Can you identify the fundamental concept or principle this problem is based upon? Please explain.
What is the simplest way you would describe this problem to someone unfamiliar with the subject?
What is the core problem we are trying to solve? Can we simplify the problem statement?
Can you break down the problem into its key components?
What is the minimal set of operations we need to perform to solve this problem?

These prompts guide the discussion towards simplifying the problem, stripping it down to its essential elements, and understanding the core problem to be solved.

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.

Provide names by categorizing these cases

What are the key insights from analyzing the different cases?

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?

Code Explanation and Design Decisions

Identify the initial parameters and explain their significance in the context of the problem statement or the solution domain.
Discuss the primary loop or iteration over the input data. What does each iteration represent in terms of the problem you’re trying to solve? How does the iteration advance or contribute to the solution?
If there are conditions or branches within the loop, what do these conditions signify? Explain the logical reasoning behind the branching in the context of the problem’s constraints or requirements.
If there are updates or modifications to parameters within the loop, clarify why these changes are necessary. How do these modifications reflect changes in the state of the solution or the constraints of the problem?
Describe any invariant that’s maintained throughout the code, and explain how it helps meet the problem’s constraints or objectives.
Discuss the significance of the final output in relation to the problem statement or solution domain. What does it represent and how does it satisfy the problem’s requirements?

Remember, the focus here is not to explain what the code does on a syntactic level, but to communicate the intent and rationale behind the code in the context of the problem being solved.

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.