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The problem is taken from LeetCode: “Add to Array-Form of Integer”.

Given an array num representing a non-negative integer num, and an integer k, return the array-form of the integer num + k. The array-form of an integer is an array representing its digits in left to right order.

Example 1:

• Input: num = [1,2,0,0], k = 34
• Output: [1,2,3,4]

Example 2:

• Input: num = [2,7,4], k = 181
• Output: [4,5,5]

Example 3:

• Input: num = [2,1,5], k = 806
• Output: [1,0,2,1]

Clarifying Questions

1. Can the array num be empty?
   • No, num will represent a non-negative integer, so it must contain at least one digit.
2. Can k be negative?
   • No, k is guaranteed to be a non-negative integer.

Strategy

1. Convert the array-form to an integer:
   • Traverse the array and recreate the integer it represents.
2. Add k to the integer value.
3. Convert the result back to an array-form:
   • Parse each digit of the resultant integer and store them in a list.

Code

def addToArrayForm(num, k):
    # Step 1: Convert array-form to an integer
    num_as_int = 0
    for digit in num:
        num_as_int = num_as_int * 10 + digit
    
    # Step 2: Add k to the integer value
    num_as_int += k
    
    # Step 3: Convert the result back to array-form
    result = [int(d) for d in str(num_as_int)]
    return result

Time Complexity

• Converting the array to an integer: O(n) where n is the length of the array.
• Adding k is a constant time operation: O(1).
• Converting the result back to an array: O(m) where m is the number of digits in the result (num_as_int + k).
• Thus, the overall time complexity is O(n + m).

In most cases, m (number of digits in the resultant sum) will be close to n, so the time complexity can be approximated to O(n).

Edge Cases

1. Single digit in num: Verify the function performs correctly when num has only one digit.
2. Carry over scenarios: Ensure proper handling of carries when adding k causes digits to reflect a carry over, e.g., num = [9, 9, 9] and k = 2.
3. Large values of k: Function must handle cases where k has more digits than num.

The above code provides a comprehensive solution to the problem by accurately converting the input format and performing the requested operation while considering time efficiency.

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