Programming platforms like Leetcode offer a plethora of challenges to help developers sharpen their problem-solving and coding skills. Among these challenges is the “Add to Array-Form of Integer” problem, which tests one’s understanding of array manipulation and basic arithmetic in programming. This article delves into the problem statement, breaks down potential solution strategies, and provides Python implementations.

### Table of Contents

- Problem Statement
- Initial Thought Process
- Iterative Solution
- Utilizing Python’s Strong Type Conversion
- Time and Space Complexity Analysis
- Conclusion

### 1. Problem Statement

For a non-negative integer `X`

, the array-form of `X`

is an array of its digits in left to right order. For example, if `X = 1231`

, then the array form is `[1,2,3,1]`

.

Given the array-form `A`

of a non-negative integer `X`

and an integer `K`

, return the array-form of the integer `X+K`

.

**Example:**

```
Input: A = [1,2,0,0], K = 34
Output: [1,2,3,4]
Explanation: 1200 + 34 = 1234
```

### 2. Initial Thought Process

The problem is essentially a variant of the elementary addition we learned in school. We have an integer in the form of an array and another integer, `K`

. Our task is to sum them up. A crucial thing to consider is the carry from each positional addition, which should be added to the next position.

### 3. Iterative Solution

We can iterate over the array-form of the number from the least significant digit (rightmost) while adding the value of `K`

position by position. We must also manage the carry as we progress.

**Python Implementation:**

```
def addToArrayForm(A, K):
carry = 0
result = []
# Convert K to a list of its digits
K = list(map(int, str(K)))
# While there are elements left in A or K or there's a carry left
while A or K or carry:
# Pop the last element from A or K (or use 0 if it's empty)
a = A.pop() if A else 0
k = K.pop() if K else 0
# Calculate the sum and the carry
temp_sum = a + k + carry
result.append(temp_sum % 10)
carry = temp_sum // 10
# Since we've built the result in reverse order, reverse it before returning
return result[::-1]
```

### 4. Utilizing Python’s Strong Type Conversion

Python’s flexibility with type conversions allows for a more concise solution. We can convert the array form to an integer, add `K`

, and then convert it back to the array form.

**Python Implementation:**

```
def addToArrayForm(A, K):
# Convert A to an integer, add K, and then convert the result to a list of digits
return [int(digit) for digit in str(int(''.join(map(str, A))) + K)]
```

### 5. Time and Space Complexity Analysis

**Iterative Solution:**- Time Complexity: O(max(n,m)), where n is the length of
`A`

and m is the number of digits in`K`

. - Space Complexity: O(max(n,m)) for the resultant array.

- Time Complexity: O(max(n,m)), where n is the length of
**Type Conversion Solution:**- Time Complexity: O(n+m) for the string conversion, addition, and then conversion back to an array.
- Space Complexity: O(n+m) for the resultant array and temporary strings.

The type conversion solution appears more concise, but the iterative approach provides a clearer understanding of the underlying arithmetic and can be more suitable for languages without Python’s type flexibility.

### 6. Conclusion

The “Add to Array-Form of Integer” problem on Leetcode provides an engaging way to brush up on array manipulation skills in Python. While the direct arithmetic approach might seem more involved, it mirrors the foundational concepts of addition we’re familiar with. On the other hand, Python’s dynamic typing offers an elegant way to solve this problem, showcasing the language’s power and flexibility.