Add to Array-Form of Integer

Problem Statement

The task at hand involves taking the digits of an integer represented as an array in left-to-right order, known as its array-form, and adding another integer k to it. The result of this addition must then be expressed in the same array-form. This problem challenges us to handle the operation directly on an array of digits, reflecting the same approach used in basic arithmetic.

Examples

Example 1

Input:

num = [1,2,0,0], k = 34

Output:

[1,2,3,4]

Explanation:

1200 + 34 = 1234

Example 2

Input:

num = [2,7,4], k = 181

Output:

[4,5,5]

Explanation:

274 + 181 = 455

Example 3

Input:

num = [2,1,5], k = 806

Output:

[1,0,2,1]

Explanation:

215 + 806 = 1021

Constraints

• 1 <= num.length <= 104
• 0 <= num[i] <= 9
• num does not contain any leading zeros except for the zero itself.
• 1 <= k <= 104

Approach and Intuition

The main trick in solving this problem is handling the carry in arithmetic correctly when adding the integer k to the number represented by array num. Here's how we can intuitively tackle this:

1. Convert the last k digits of the array to an integer and start the addition from there.
2. Use a loop that iterates from the least significant digit (end of the array) to the most significant (start of the array).
3. In every iteration, add k to the current digit.
4. If the sum of the current digit and k exceeds 9, handle the carry over.
5. Implement the carry operation by updating k with the carry value (sum divided by 10).
6. Append the result of sum % 10 to the resultant array to get the correct digit in place.
7. If after exhausting the array there's still some carry left (i.e., k is still greater than 0), continue resolving by adding digits to the result.

Given these steps, the process will simulate the traditional way we perform addition on paper, carrying over whenever a sum reaches two digits. Let's examine this method with the examples provided:

Explanation Through Examples

• Example 1:

  • Given num = [1,2,0,0] and k = 34.
  • Starting from the least significant digit, add k to each digit and resolve the carry.
  • The result is [1,2,3,4] which is indeed 1200 + 34 = 1234.

• Example 2:

  • For num = [2,7,4] and k = 181.
  • Perform the addition with carry operations; you get 274 + 181 = 455.
  • Resulting array-form fulfills the sum, [4,5,5].

• Example 3:

  • Given num = [2,1,5] and k = 806.
  • Following the described methodology, the resultant is 215 + 806 = 1021.
  • This converts perfectly into [1,0,2,1].

This approach leverages basic digit-by-digit addition and emphasizes understanding how carry figures in decimal addition. Thus, it aligns well with the constraints and ensures an accurate representation of sum in the array form.

Solutions

class Solution {
    public List<Integer> arrayFormSum(int[] numArray, int addNum) {
        int len = numArray.length;
        int carry = addNum;
        List<Integer> result = new ArrayList<>();

        int ix = len;
        while (--ix >= 0 || carry > 0) {
            if (ix >= 0)
                carry += numArray[ix];
            result.add(carry % 10);
            carry /= 10;
        }

        Collections.reverse(result);
        return result;
    }
}