algoadvance

Given an integer n, return a list of two integers [A, B] where:

  1. A and B are both positive integers.
  2. A + B = n
  3. Neither A nor B contains any zero digit.

If there are multiple answers, you can return any of them.

Clarifying Questions

  1. Range of n: What is the range of input integer n? (Usually, for LeetCode problems, this would be specified, but for the sake of this problem, you can assume that n is a positive integer greater than 1).
  2. Output: Is any valid pair acceptable, or do we need to find all pairs? (The problem states that any valid pair can be returned).

These questions help understand the constraints and requirements more clearly.

Since this is a problem requiring to avoid any digits being zero, let’s move on to the coding solution.

Strategy

  1. Split Search: Start with A from 1 to n-1. If A contains no zero digits then check if B = n - A contains no zero digits as well.
  2. Check Function: Implement a helper function to check if a number contains zero.
  3. Return Result: Once a valid pair is found, return it.

Code

Here’s the implementation of the above strategy:

def has_no_zero(n: int) -> bool:
    """Helper function to check if a number has any zero digits."""
    return '0' not in str(n)

def getNoZeroIntegers(n: int) -> [int, int]:
    for A in range(1, n):
        B = n - A
        if has_no_zero(A) and has_no_zero(B):
            return [A, B]

# Example Usage
n = 101
print(getNoZeroIntegers(n))  # Example output: [2, 99] or any other valid pair

Time Complexity

Overall, the time complexity is O(n * log(n)), which is efficient given the typical constraints for an integer value.

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