Welcome to today's lesson! We will explore a fascinating problem involving large numbers by focusing on string manipulation in Scala. While Scala's BigInt can efficiently handle large numbers, our goal today is to delve into string manipulation techniques. By simulating the addition of large numbers with strings, you'll enhance your understanding of working with sequences of characters and gain insights into manual addition processes. By the end of this lesson, you'll be well-versed in adding numbers with thousands of digits represented as strings. Let's dive in!

In today's task, we are challenged to simulate the addition of extremely large positive integers represented as strings, each with a possible length of up to 10,000 digits. Although Scala's BigInt can handle such numbers seamlessly, we'll focus on string manipulation for educational purposes. Your mission is to implement a Scala function that adds these "string-numbers" without converting the entire strings into numerical forms directly. The result should also be represented as a string. While this may seem complex, we'll simplify it step-by-step.

Before coding, let's strategize. We'll use indices i and j to indicate the current digit of num1 and num2, respectively. A carry variable will manage carryovers from each addition. We'll utilize a ListBuffer to collect our result, where each digit from the addition will be added at the beginning.

Scala
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1import scala.collection.mutable.ListBuffer
2
3def solution(num1: String, num2: String): String = {
4  var i = num1.length - 1
5  var j = num2.length - 1
6  var carry = 0
7  val res = ListBuffer[Char]()
8}

Having initialized variables, we proceed by scanning through num1 and num2 from right to left, which means moving from the least significant digit to the most significant one. For each loop iteration, we extract digits n1 from num1 and n2 from num2. If i or j is less than 0, we've processed all the digits in one of the numbers; hence additional digits are considered as 0.

Scala
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1import scala.collection.mutable.ListBuffer
2
3def solution(num1: String, num2: String): String = {
4  var i = num1.length - 1
5  var j = num2.length - 1
6  var carry = 0
7  val res = ListBuffer[Char]()
8
9  while (i >= 0 || j >= 0 || carry > 0) {
10    val n1 = if (i >= 0) num1(i) - '0' else 0
11    val n2 = if (j >= 0) num2(j) - '0' else 0
12    // logic continuation in next step
13  }
14
15  ""
16}

After acquiring digits n1 and n2, we add them. The carry is included from previous column additions. The result can be a two-digit number; the tens place becomes the new carry, and the units place becomes the resultant digit curr. We prepend (add at the beginning) curr to res, decrement i and j, and continue. Lastly, we reverse res and convert the list to a string for our result.

Scala
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1import scala.collection.mutable.ListBuffer
2
3def solution(num1: String, num2: String): String = {
4  var i = num1.length - 1
5  var j = num2.length - 1
6  var carry = 0
7  val res = ListBuffer[Char]()
8
9  while (i >= 0 || j >= 0 || carry > 0) {
10    val n1 = if (i >= 0) num1(i) - '0' else 0
11    val n2 = if (j >= 0) num2(j) - '0' else 0
12    val total = n1 + n2 + carry
13    carry = if (total > 9) 1 else 0
14    val curr = (total % 10 + '0').toChar // convert back to character
15    res.prepend(curr)
16    i -= 1
17    j -= 1
18  }
19
20  res.mkString // convert ListBuffer to String
21}

Congratulations! You've successfully implemented a method for adding very large numbers using string manipulation in Scala. This exercise demonstrated the importance of mastering string and collection handling in Scala while reinforcing the fundamentals of the addition processes. Although Scala's BigInt readily manages such tasks, this challenge deepens your comprehension of character sequences. As your journey continues, utilize this approach to tackle further string manipulation problems. Embrace the learning journey, and happy coding!