Integer to English Words
Refer LC editorial.


Identifying Problem Isomorphism
“Integer to English Words” is isomorphic to “Number to Words”. In both problems, the main task is to convert a numerical value into a specific string representation.
“Number to Words” involves converting a numerical input into words as per the phonetics and syntax of a specified language. The specifics of the implementation would depend on the language and its numerics, similar to how the solution to “Integer to English Words” depends on English number naming conventions.
Both problems require dividing the number into chunks (e.g., thousands, millions, billions) and then converting those chunks into words. Both also involve handling edge cases specific to the language’s number naming conventions.
In terms of complexity, both problems are somewhat comparable as the core logic is similar, though the specifics and edge cases can vary depending on the language’s number naming conventions.
10 Prerequisite LeetCode Problems
“Integer to English Words” requires an understanding of number manipulation, string manipulation, and mapping rules (like associating numbers to words). Here are 10 simpler problems to build the necessary skills:
“Reverse Integer” (LeetCode Problem #7): This problem introduces basic number manipulation techniques that are required to solve “Integer to English Words”.
“Palindrome Number” (LeetCode Problem #9): This problem further drills down on number manipulation.
“Count and Say” (LeetCode Problem #38): This problem provides an exercise in generating strings based on rules.
“Add Binary” (LeetCode Problem #67): This problem is a good practice for converting numbers into different forms.
“Number of 1 Bits” (LeetCode Problem #191): It gives you practice in converting integer values into another form and counting elements.
“Excel Sheet Column Number” (LeetCode Problem #171): This problem helps to understand the conversion from one representation to another, which is quite important in “Integer to English Words”.
“Reverse Words in a String III” (LeetCode Problem #557): This problem provides good practice for string manipulation, which is necessary in “Integer to English Words”.
“To Lower Case” (LeetCode Problem #709): This problem offers practice in changing the format of a string.
“Valid Number” (LeetCode Problem #65): This problem helps you better understand how to deal with string representations of numbers.
“Binary Gap” (LeetCode Problem #868): This problem provides practice in number manipulation and handling conditions based on those numbers.


Problem Classification
Conversion problem: The problem is about converting a nonnegative integer into its English word representation. This type of problem typically involves translating data from one form to another.
Number Theory problem: The problem requires understanding of positional notation in the decimal system, like units, tens, hundreds, thousands, etc. This falls into the domain of number theory.
Natural Language Processing problem: As the problem involves converting numerical data into natural language (English in this case), it touches upon aspects of natural language processing.
These classifications provide a highlevel understanding of the problem domain and the types of challenges that need to be addressed in the problem.
This problem asks to convert a number into its equivalent English words. This is a Number Translation Problem.
Language Agnostic Coding Drills
Basic Operations: Understand how to use basic operations like addition, subtraction, division, and multiplication. This will help in understanding the process of extracting individual digits from the number.
Working with Arrays: Understand how to create and use arrays. Arrays will be used to store different word mappings for digits, tens, teens, and suffixes.
Conditional Statements: Learn to use ifelse statements. They are used in this solution to handle different conditions and make decisions.
Loops: Understand how to use loops (while loops in this case). They are essential for handling operations that need to be repeated until a certain condition is met.
Array Indexing: Learn how to access elements in an array using their index. This is essential for mapping digits to their corresponding words.
Array Manipulation: Understand how to append and concatenate arrays. This is used in the solution to build the final array of words.
Strings Manipulation: Learn how to join elements of an array into a single string.
ProblemSolving Approach:
Start by defining arrays of words that correspond to individual digits, tens, teens, and suffixes like “Thousand”, “Million”, etc.
Initialize an empty array to store the words of the final result and a counter to keep track of the current position in the suffixes array.
Start a loop that continues as long as the number is greater than zero. In each iteration, the last three digits (a triplet) of the number are processed, and then these digits are removed from the number.
If the triplet is zero, just increase the counter and continue to the next iteration.
If the triplet is not zero, process the hundred’s, ten’s, and one’s place separately. For each place, find the corresponding word and append it to a temporary array. If the counter is greater than zero, also append the appropriate suffix to the temporary array.
After processing the triplet, concatenate the temporary array to the front of the final words array, and increase the counter.
After the loop ends, join all the words in the final array into a single string, with spaces between each word, and return this string as the result.
Targeted Drills in Python
 Basic Operations: Here’s an example of how to use basic arithmetic operations in Python.


 Working with Arrays: Here’s an example of creating and using an array in Python.


 Conditional Statements: Here’s an example of using ifelse statements in Python.


 Loops: Here’s an example of a while loop in Python.


 Array Indexing: Here’s an example of how to access elements in an array using their index in Python.


 Array Manipulation: Here’s an example of how to append elements to an array in Python.


 String Manipulation: Here’s an example of how to join elements of an array into a string in Python.


ProblemSpecific Drill:
For the number to words problem, you need to be able to extract the last three digits of a number (a triplet), and then remove these digits from the number. Here’s an example of how you can do this in Python.


Problem Classification
Problem Statement: Convert a nonnegative integer num to its English words representation.
Example 1:
Input: num = 123 Output: “One Hundred Twenty Three” Example 2:
Input: num = 12345 Output: “Twelve Thousand Three Hundred Forty Five” Example 3:
Input: num = 1234567 Output: “One Million Two Hundred Thirty Four Thousand Five Hundred Sixty Seven”
Constraints:
0 <= num <= 231  1
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 realworld 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 ProblemSolving Approach from the Problem Statement
How did you infer from the problem statement that this problem can be solved using ?
Stepwise Refinement
Could you please provide a stepwise refinement of our approach to solving this problem?
How can we take the highlevel 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
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.
What are the highlevel problemsolving strategies or techniques being used by this code?
If you had to explain the purpose of this code to a nonprogrammer, 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 languageagnostic 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 problemsolving 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 stepbystep 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 Pythonbased 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 problemspecific 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.
Q&A
Similar Problems
Given the problem [provide the problem], identify and list down 10 similar problems on LeetCode. These should cover similar concepts or require similar problemsolving approaches as the provided problem. Please also give a brief reason as to why you think each problem is similar to the given problem.