Minimum Unique Word Abbreviation

This problem requires finding the shortest valid abbreviation for the given target string, ensuring that the abbreviation is not a valid abbreviation for any string in the dictionary.

To solve this problem, we can use a depth-first search to explore all possible abbreviations of the target string. By sorting the abbreviations based on their length, we can select the shortest one that is not a valid abbreviation for any string in the dictionary.

Here’s an implementation:

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from typing import List

class Solution:
    def minAbbreviation(self, target: str, dictionary: List[str]) -> str:
        # Function to generate all possible abbreviations for a given string
        def generateAbbreviations(word):
            result = []
            n = len(word)
            for i in range(1 << n):
                cur = ''
                count = 0
                for j in range(n):
                    if (i & (1 << j)) != 0:
                        if count > 0:
                            cur += str(count)
                            count = 0
                        cur += word[j]
                    else:
                        count += 1
                if count > 0:
                    cur += str(count)
                result.append(cur)
            return result

        # Function to check if an abbreviation is valid for a given word
        def isValidAbbreviation(word, abbr):
            i = j = 0
            while i < len(word) and j < len(abbr):
                if word[i] == abbr[j]:
                    i += 1
                    j += 1
                elif abbr[j].isdigit():
                    num = 0
                    while j < len(abbr) and abbr[j].isdigit():
                        num = num * 10 + int(abbr[j])
                        j += 1
                    i += num
                else:
                    return False
            return i == len(word) and j == len(abbr)

        # Generate abbreviations for the target string and sort by length
        abbreviations = generateAbbreviations(target)
        abbreviations.sort(key=len)

        # Check if an abbreviation is valid for any word in the dictionary
        for abbr in abbreviations:
            if all(not isValidAbbreviation(word, abbr) for word in dictionary):
                return abbr

        return target

This code first generates all possible abbreviations for the target string and sorts them by length. Then it checks if any abbreviation is valid for any word in the dictionary, returning the shortest one that is not. If there are multiple abbreviations with the same shortest length, it will return one of them.

10 Prerequisite LeetCode Problems

This requires string manipulation, bit manipulation, and backtracking skills. Here are 10 problems to build these skills:

“Reverse String” (LeetCode Problem #344): This problem introduces the basics of string manipulation.
“Valid Word Abbreviation” (LeetCode Problem #408): This problem provides practice for understanding the concept of word abbreviations.
“Generalized Abbreviation” (LeetCode Problem #320): This problem will help you generate all possible abbreviations of a word, which is essential for problem #411.
“Subsets” (LeetCode Problem #78): This problem introduces the concept of generating all possible combinations (in this case, subsets), which can be helpful for generating all possible abbreviations.
“Number of 1 Bits” (LeetCode Problem #191): This problem introduces the basics of bit manipulation.
“Reverse Bits” (LeetCode Problem #190): This problem is a step up in bit manipulation, requiring reversing the bits in a number.
“Add Binary” (LeetCode Problem #67): This problem further builds your bit manipulation skills.
“Letter Case Permutation” (LeetCode Problem #784): This problem involves generating all possible strings from a string with characters that can be either uppercase or lowercase, which can be helpful in problem #411 when generating all possible abbreviations.
“Palindrome Partitioning” (LeetCode Problem #131): This problem is helpful in understanding backtracking for generating possible partitions (or abbreviations in the case of problem #411) of a string.
“Permutations” (LeetCode Problem #46): This problem introduces recursion and backtracking, which can be helpful when generating all possible abbreviations and then backtracking to find the shortest unique one.

These cover string manipulation, bit manipulation, and backtracking, which are essential for tackling “Minimum Unique Word Abbreviation”.

Problem Classification

Problem Statement: A string can be abbreviated by replacing any number of non-adjacent substrings with their lengths. For example, a string such as “substitution” could be abbreviated as (but not limited to):

“s10n” (“s ubstitutio n”) “sub4u4” (“sub stit u tion”) “12” (“substitution”) “su3i1u2on” (“su bst i t u ti on”) “substitution” (no substrings replaced) Note that “s55n” (“s ubsti tutio n”) is not a valid abbreviation of “substitution” because the replaced substrings are adjacent.

The length of an abbreviation is the number of letters that were not replaced plus the number of substrings that were replaced. For example, the abbreviation “s10n” has a length of 3 (2 letters + 1 substring) and “su3i1u2on” has a length of 9 (6 letters + 3 substrings).

Given a target string target and an array of strings dictionary, return an abbreviation of target with the shortest possible length such that it is not an abbreviation of any string in dictionary. If there are multiple shortest abbreviations, return any of them.

Example 1:

Input: target = “apple”, dictionary = [“blade”] Output: “a4” Explanation: The shortest abbreviation of “apple” is “5”, but this is also an abbreviation of “blade”. The next shortest abbreviations are “a4” and “4e”. “4e” is an abbreviation of blade while “a4” is not. Hence, return “a4”. Example 2:

Input: target = “apple”, dictionary = [“blade”,“plain”,“amber”] Output: “1p3” Explanation: “5” is an abbreviation of both “apple” but also every word in the dictionary. “a4” is an abbreviation of “apple” but also “amber”. “4e” is an abbreviation of “apple” but also “blade”. “1p3”, “2p2”, and “3l1” are the next shortest abbreviations of “apple”. Since none of them are abbreviations of words in the dictionary, returning any of them is correct.

Constraints:

m == target.length n == dictionary.length 1 <= m <= 21 0 <= n <= 1000 1 <= dictionary[i].length <= 100 log2(n) + m <= 21 if n > 0 target and dictionary[i] consist of lowercase English letters. dictionary does not contain target.

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?

Alternatively, if you’re working on a specific problem, you might ask something like:

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.