Finding number plate based on registration number in JavaScript

The car registering system of a city assigns unique identifiers to customers and corresponding number plates to their vehicles. We need to create a JavaScript function that converts a customer ID into its corresponding number plate format.

Problem Statement

The car registration system assigns two types of identifiers:

• Customer ID ? A natural number between 0 and 17,558,423 (inclusive), assigned sequentially starting from 0

• Number Plate ? Contains a series of three Latin lowercase letters (a-z) followed by a three-digit serial number (000-999)

  Example: aaa001, aaa002, etc. Each number plate corresponds to a specific Customer ID in sequential order.

How the Mapping Works

The relationship between Customer ID and Number Plate follows this pattern:

• Customer ID 0 ? aaa001
• Customer ID 1 ? aaa002
• Customer ID 999 ? aab001
• Customer ID 1000 ? aab002

Solution

const findNumberPlate = (id = 0) => {
   const letters = 'abcdefghijklmnopqrstuvwxyz';
   
   // Calculate the numeric part (001-999, then reset)
   let num = String((id % 999) + 1);
   
   // Pad with leading zeros to make it 3 digits
   while(num.length !== 3) {
      num = '0' + num;
   }
   
   // Calculate letter combination based on groups of 999
   const letterIndex = Math.floor(id / 999);
   
   // Generate three letters using base-26 conversion
   const firstLetter = letters[letterIndex % 26];
   const secondLetter = letters[Math.floor(letterIndex / 26) % 26];
   const thirdLetter = letters[Math.floor(letterIndex / (26 * 26)) % 26];
   
   return firstLetter + secondLetter + thirdLetter + num;
};

// Test examples
console.log(findNumberPlate(0));      // First customer
console.log(findNumberPlate(1));      // Second customer  
console.log(findNumberPlate(999));    // 1000th customer
console.log(findNumberPlate(545664)); // Given example

aaa001
aaa002
aab001
ava665

Step-by-Step Breakdown

The algorithm works as follows:

1. Numeric Part: Calculate (id % 999) + 1 to get numbers 1-999, then pad with zeros
2. Letter Group: Use Math.floor(id / 999) to determine which letter combination group
3. Base-26 Conversion: Convert the group number to three letters using modulo operations

Key Points

• Each group of 999 customer IDs shares the same three letters
• The numeric part cycles from 001 to 999
• Letters follow alphabetical order: aaa, aab, aac, ..., aba, abb, etc.
• The function handles the full range of 17,558,423+ customer IDs

Conclusion

This solution efficiently converts customer IDs to number plates using modulo arithmetic and base-26 conversion. The algorithm ensures each customer gets a unique, sequential number plate in the required format.