273. Integer to English Words - Detailed Explanation

Problem Statement

Description:
Given a non-negative integer, convert it to its English words representation.

Example 1:

• Input: 123
• Output: "One Hundred Twenty Three"
• Explanation:
  • The number 123 is broken down as:
    • Hundreds: One Hundred
    • Tens and Ones: Twenty Three

Example 2:

• Input: 12345
• Output: "Twelve Thousand Three Hundred Forty Five"
• Explanation:
  • The number 12345 is segmented into two parts:
    • Thousand part: Twelve Thousand (from 12)
    • Remaining part: Three Hundred Forty Five (from 345)

Example 3:

• Input: 1234567
• Output: "One Million Two Hundred Thirty Four Thousand Five Hundred Sixty Seven"
• Explanation:
  • The number 1234567 is segmented as:
    • Million part: One Million (from 1)
    • Thousand part: Two Hundred Thirty Four Thousand (from 234)
    • Remaining part: Five Hundred Sixty Seven (from 567)

Constraints:

• 0 <= num <= 2^31 - 1

2. Hints for the Solution

• Hint 1:
  Break the number into chunks of three digits. Each chunk represents units, thousands, millions, or billions. This segmentation helps in reusing a helper function to convert numbers less than 1000.

• Hint 2:
  Create helper mappings (arrays or dictionaries) for numbers less than 20, tens (20, 30, ... 90), and a mapping for the scales (Thousand, Million, Billion). Use these mappings to build the English representation for each three-digit segment.

Approaches to Solve the Problem

Approach 1: Naïve (Brute Force) Construction

Concept:

A brute force approach would try to process the number digit by digit (or group by group) by directly mapping each digit’s position to its English word. For instance, you could:

• Convert the integer to a string.
• Iterate through each character while keeping track of its positional value (ones, tens, hundreds, etc.).
• Use numerous conditional checks (especially for special cases like numbers below 20 or tens such as “Twenty”, “Thirty”, etc.).

Issues with the Brute Force Approach:

• Complexity in Handling Special Cases: Handling numbers from 10 to 19 (the “teens”) and numbers with zeros in between often leads to many if-else conditions.
• Repetitive Code: This method may lead to repetitive logic and can be hard to maintain or extend.
• Readability: The resulting code will be long and less intuitive, making it harder for others (or even yourself later) to understand.

Summary:

While the brute force approach is conceptually straightforward (mapping every digit with its place), it quickly becomes messy. This is why we recommend a more structured, divide-and-conquer approach.

Approach 2: Optimal Divide-and-Conquer (Recursive/Iterative Chunking)

Concept:

Break the integer into groups of three digits (since 1000 is the basic building block) and then convert each group using a helper function. After converting a group, append the corresponding scale (e.g., Thousand, Million, Billion).

Step-by-Step Walkthrough (Visual Example for 1,234,567):

1. Segmentation:

   • Segment 1 (Rightmost 3 digits): 567 → Converts to "Five Hundred Sixty Seven"
   • Segment 2 (Next 3 digits): 234 → Converts to "Two Hundred Thirty Four"
   • Segment 3 (Remaining digit): 1 → Converts to "One"

2. Scale Association:

   • For segment 1 (ones): no suffix
   • For segment 2: append "Thousand"
   • For segment 3: append "Million"

3. Combine Segments:

   • Final answer: "One Million Two Hundred Thirty Four Thousand Five Hundred Sixty Seven"

Why This Approach is Optimal:

• Reusability: The helper function for three-digit conversion is used repeatedly.
• Modularity: Separates the concerns (converting small numbers vs. appending scale words).
• Clarity: Each part of the number is handled in a consistent manner, leading to cleaner and more maintainable code.