Adding Extremely Large Numbers
Introduction
Hello and welcome! In this lesson we'll delve deep into a captivating problem involving large numbers — specifically, adding extraordinarily large numbers. As you may have noticed, traditional calculators and even some programming languages struggle when dealing with excessively large numbers. To handle such scenarios efficiently, we'll simulate this process manually using strings. By the end of this discussion, you'll be able to add together numbers that have thousands or even tens of thousands of digits. Intriguing, right? Let's get started!
Task Statement
In this task, we'll venture into the realm of large numbers, where we are given two exceedingly large positive integers. However, these aren't your average, everyday large numbers. They are so enormous they're represented as strings that can be up to 10,000 digits long!
Your mission, should you choose to accept it, is to write a TypeScript function that adds these two "string-numbers" together. The challenge is to perform the addition without converting these entire strings into integers.
In the end, your function should return the resulting sum, represented as a string. At first glance, this might seem daunting, but don't worry — we'll break it down step by step, emulating the way we manually add numbers.
Solution Building: Step 1
Before we dive into the code, let's first discuss the strategy we're going to follow. Remember that every digit in a number carries value, and the position of the digit determines its influence on the total value of the number. This system is known as place-value notation.
The first step involves initializing our variables. We'll use two numbers, i and j, to point to the current digit in num1 and num2, respectively. We'll also need a variable named carry to hold the carryovers from each addition operation. Lastly, we'll use an Array<string> named result to store our resultant number. During each iteration, we will append digits to the end of the array. At the end of the process, we'll reverse the array to ensure the digits are in the correct order for our final number.
We start iterating from the end (rightmost side) of each string because the rightmost digit is the least significant digit, and this is where we begin when performing manual addition. Processing the least significant digits first allows us to handle carryover operations easily and propagate any necessary changes to the more significant digits on the left.
