Adding Large Numbers Using Strings in Java
Introduction
Hello and welcome! Today, 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 today's task, we'll venture into the realm of large numbers, in which 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 Java method that adds these two "string-numbers" together. The challenge is to perform the addition without converting these entire strings into integers.
At the end, your method 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 integers, i and j, to point to the current digit in num1 and num2, respectively. We'll also need an int variable named carry to hold the carryovers from each addition operation. Lastly, we'll use an ArrayList<Character> named result to store our resultant number, where each digit from the addition is appended to the front.
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.
