The “Convert Integer to the Sum of Two No-Zero Integers” problem on Leetcode is an engaging problem that falls under the category of mathematical manipulation and basic programming. This article aims to offer an in-depth understanding of the problem, various ways to solve it, testing methodologies, and the complexities involved.

## Table of Contents

- Problem Description
- Initial Observations
- Brute-Force Approach
- Optimized Brute-Force Approach
- Using String Manipulation
- Testing Strategies
- Complexity Analysis
- Conclusion

## 1. Problem Description

The goal is to convert a given integer `n`

into the sum of two integers `a`

and `b`

such that neither of them contains the digit `0`

.

### Example

- Input:
`n = 11`

- Output:
`[2,9]`

### Constraints

`2 <= n <= 10^4`

## 2. Initial Observations

- Both numbers
`a`

and`b`

should not have the digit`0`

. - We can iterate through the numbers lesser than
`n`

to find the pair`(a, b)`

such that`a + b = n`

.

## 3. Brute-Force Approach

A straightforward way to solve this problem is to iterate through all the numbers lesser than `n`

and check for the pair `(a, b)`

that satisfies the conditions.

### Algorithm

- Loop from
`1`

to`n - 1`

. - For each iteration, calculate
`b = n - a`

. - Check if either
`a`

or`b`

contains the digit`0`

. - If not, return
`[a, b]`

.

### Python Code

```
def getNoZeroIntegers(n):
for a in range(1, n):
b = n - a
if '0' not in str(a) and '0' not in str(b):
return [a, b]
```

## 4. Optimized Brute-Force Approach

Though the brute-force approach works well, we can optimize it a bit. We only need to iterate up to `n // 2`

because `a`

and `b`

will mirror around this point.

### Algorithm

- Loop from
`1`

to`n // 2`

. - Calculate
`b = n - a`

. - Check for zero digits in
`a`

and`b`

. - If not found, return
`[a, b]`

.

### Python Code

```
def getNoZeroIntegers(n):
for a in range(1, n // 2 + 1):
b = n - a
if '0' not in str(a) and '0' not in str(b):
return [a, b]
```

## 5. Using String Manipulation

We can utilize Python’s powerful string manipulation to quickly check for zeros in `a`

and `b`

.

### Algorithm

- Convert the numbers to string and use the
`in`

operator to check for the character ‘0’.

### Python Code

```
def getNoZeroIntegers(n):
for a in range(1, n // 2 + 1):
b = n - a
if all('0' not in str(x) for x in [a, b]):
return [a, b]
```

## 6. Testing Strategies

- Test with the minimum allowed value of
`n`

. - Test with even and odd values of
`n`

. - Test with a value of
`n`

that is a power of 10. - Test with the maximum allowed value of
`n`

.

## 7. Complexity Analysis

**Brute-Force Approach**- Time Complexity: O(n)
- Space Complexity: O(1)

**Optimized Brute-Force Approach**- Time Complexity: O(n/2)=O(n)
- Space Complexity: O(1)

**Using String Manipulation**- Time Complexity: O(n) (we must consider the time taken to convert integers to strings)
- Space Complexity: O(1)

## 8. Conclusion

The “Convert Integer to the Sum of Two No-Zero Integers” problem on LeetCode is an excellent opportunity to exercise basic programming and mathematical reasoning. Although the problem seems straightforward, the various approaches to solving it and their associated trade-offs make it an interesting study. This problem is particularly useful for beginners and for those looking to brush up on their Python skills.