Abbreviating the Product of a Range

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class Solution:
    def abbreviateProduct(self, left: int, right: int) -> str:
        suff = 1
        c = 0
        total = 0
        max_suff = 100000000000
        pref = 1.0

        for i in range(left, right + 1):
            pref *= i
            suff *= i
            while pref >= 100000:
                pref /= 10
                total = 6 if total == 0 else total + 1
            while suff % 10 == 0:
                suff //= 10
                c += 1
            suff %= max_suff

        s = str(suff)

        pref_str = str(int(pref))
        dots = "" if total - c <= 10 else "..."
        middle_part = "" if total - c < 5 else s[-min(5, total - c - 5):]
        exponential_part = "e" + str(c)

        result = pref_str + dots + middle_part + exponential_part

        return result

Too many down votes. Waste of time.

Identifying Problem Isomorphism

“Abbreviating the Product of a Range” (#2117) can be approximately mapped to “Factorial Trailing Zeroes”.

In “Abbreviating the Product of a Range”, you are given two integers left and right and the task is to find the product of all the integers from left to right (inclusive), then return it in the form of an abbreviation.

In “Factorial Trailing Zeroes”, you are given an integer n, and you have to return the number of trailing zeroes in n!. This involves finding the product of all integers from 1 to n (inclusive).

The reason for this mapping is that both problems involve finding the product of a sequence of numbers (whether it’s a range in an array or the numbers leading up to a factorial) and then performing a transformation on the result.

However, the transformation is different in each problem. In “Factorial Trailing Zeroes”, you’re counting the number of trailing zeroes, whereas in “Abbreviating the Product of a Range”, you’re abbreviating the product.

“Factorial Trailing Zeroes” is simpler because it only requires counting the number of trailing zeroes, which can be solved by counting the number of factors of 5 in the factorial. On the other hand, “Abbreviating the Product of a Range” requires calculating the product of a range of numbers and then abbreviating it, which is more complex.

10 Prerequisite LeetCode Problems

“2117. Abbreviating the Product of a Range” involves understanding of mathematical computations, strings and arrays. Here are 10 problems to prepare for it:

  1. Fibonacci Number: This problem introduces the basic usage of mathematical computations.

  2. Count Primes: This problem introduces more complicated mathematical computations.

  3. Power of Three: This problem gives you practice on problems related to numbers and math.

  4. Plus One: This problem involves manipulating arrays and basic arithmetic.

  5. Reverse Integer: This problem requires knowledge of integer operations.

  6. Add Binary: This problem involves addition of binary numbers represented as strings.

  7. Multiply Strings: This problem involves multiplication of numbers represented as strings.

  8. Factorial Trailing Zeroes: This problem introduces mathematical calculations involving factorials.

  9. Add Strings: This problem involves addition of numbers represented as strings.

  10. Single Number: This problem involves bitwise operations and will help with the understanding of bitwise operations in a mathematical context.

Solving these problems will help you get a better understanding of how to manipulate and perform mathematical operations on numbers and strings, which will be essential for solving “2117. Abbreviating the Product of a Range”.

Problem Classification

The problem falls under the Mathematics and String Manipulation domain. It involves mathematical computation of the product of a range of numbers and string manipulation to format the output.

What Components:

  1. Calculation of product of numbers in a given range.
  2. Counting trailing zeros in the product and removing them.
  3. Expressing the product in a particular format based on the number of digits in the product after removing trailing zeros.

This problem can be classified as a computation and formatting problem. The first part requires the computation of the product of numbers and the counting of trailing zeros. The second part requires the formatting of the computed product according to the problem’s rules.

The problem involves mathematical operations and string manipulation techniques. It requires understanding of factorials, trailing zeros in factorials, number of digits in a number, and string slicing.

Clarification Questions

What are the clarification questions we can ask about this problem?

Identifying Problem Isomorphism

Can you help me with finding the isomorphism for this problem?

Which problem does this problem map to the corresponding isomorphic problem on Leetcode ?

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 ?

Stepwise Refinement

  1. Could you please provide a stepwise refinement of our approach to solving this problem?

  2. How can we take the high-level solution approach and distill it into more granular, actionable steps?

  3. Could you identify any parts of the problem that can be solved independently?

  4. Are there any repeatable patterns within our solution?

Solution Approach and Analysis

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.

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.

  1. What are the high-level problem-solving strategies or techniques being used by this code?

  2. If you had to explain the purpose of this code to a non-programmer, what would you say?

  3. Can you identify the logical elements or constructs used in this code, independent of any programming language?

  4. Could you describe the algorithmic approach used by this code in plain English?

  5. What are the key steps or operations this code is performing on the input data, and why?

  6. 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.

  1. 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.

  2. 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.

  3. 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.

  1. 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.

  2. 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.

  3. 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.

Q&A

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