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Convert Integer to the Sum of Two No-Zero Integers

Easy

Hudson River Trading

1 view

Topics:

ArraysGreedy Algorithms

No-Zero integer is a positive integer that does not contain any 0 in its decimal representation.

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

a and b are No-Zero integers.
a + b = n

The test cases are generated so that there is at least one valid solution. If there are many valid solutions, you can return any of them.

Example 1:

Input: n = 2
Output: [1,1]
Explanation: Let a = 1 and b = 1.
Both a and b are no-zero integers, and a + b = 2 = n.

Example 2:

Input: n = 11
Output: [2,9]
Explanation: Let a = 2 and b = 9.
Both a and b are no-zero integers, and a + b = 11 = n.
Note that there are other valid answers as [8, 3] that can be accepted.

Constraints:

2 <= n <= 10⁴

Convert Integer to the Sum of Two No-Zero Integers

Easy

Hudson River Trading

1 view

Topics:

ArraysGreedy Algorithms

No-Zero integer is a positive integer that does not contain any 0 in its decimal representation.

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

a and b are No-Zero integers.
a + b = n

The test cases are generated so that there is at least one valid solution. If there are many valid solutions, you can return any of them.

Example 1:

Input: n = 2
Output: [1,1]
Explanation: Let a = 1 and b = 1.
Both a and b are no-zero integers, and a + b = 2 = n.

Example 2:

Input: n = 11
Output: [2,9]
Explanation: Let a = 2 and b = 9.
Both a and b are no-zero integers, and a + b = 11 = n.
Note that there are other valid answers as [8, 3] that can be accepted.

Constraints:

2 <= n <= 10⁴

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What is the range of possible values for the input integer n?
If multiple pairs of A and B satisfy the conditions, is there a preference for which pair I should return (e.g., minimize A, minimize B, or any valid pair is acceptable)?
Is '0' considered a No-Zero integer, or is the constraint specifically about the digits present in the number?
Is the input 'n' guaranteed to be greater than zero?
Can you provide a few example inputs and expected outputs to ensure my understanding of the problem is correct?

Brute Force Solution

Approach

The goal is to find two numbers that add up to a given number, but neither of these numbers can contain the digit zero. The brute force way to do this is to simply try every possible pair of numbers.

Here's how the algorithm would work step-by-step:

Start with the number one and check if the original number minus one contains a zero.
If neither one nor the result of the subtraction contains a zero, then you have found the answer.
If either number contains a zero, move on to the next number, two.
Check if the original number minus two contains a zero.
Keep doing this, trying every number from one up to one less than the original number.
For each number you try, make sure that neither it nor the result of subtracting it from the original number contains a zero.
The first time you find a pair where neither number contains a zero, you have found a valid solution, so you can stop.

Code Implementation

def convert_integer_to_sum_of_two_no_zero_integers(number_to_convert):
    first_number = 1

    while first_number < number_to_convert:
        second_number = number_to_convert - first_number

        # Checking if the current numbers contain zero
        if '0' not in str(first_number) and '0' not in str(second_number):

            return [first_number, second_number]

        first_number += 1

    return []

Try it yourself on LeetCode

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates from 1 up to n-1 (where n is the input integer). For each number in this range, it checks if the number and its complement (n minus the number) contain a zero. The 'contains zero' check iterates through the digits of a number. Since the maximum number of digits in n is log(n), the 'contains zero' check takes O(log n) time. The outer loop iterates n times. But since the problem states to return as soon as a solution is found, it will stop as soon as it has found a valid solution, therefore the while loop will run a maximum of n times. So, the time complexity is O(n * log n) for checking 'contains zero' but because the prompt has implied to just consider the outer loop we approximate to just O(n).

Space Complexity

O(1) – The provided solution iterates through numbers from 1 to n-1, checking each pair. It doesn't explicitly use any auxiliary data structures like arrays, lists, or hash maps to store intermediate results. The only variables used are for the current number being tested and potentially the result of subtraction, both of which consume constant space regardless of the input integer 'n'. Therefore, the space complexity is O(1).

Optimal Solution

Approach

The goal is to split a number into two parts, ensuring neither part contains the digit zero. The best way is to start with one part as 1 and increment it, checking if both parts satisfy the 'no-zero' condition.

Here's how the algorithm would work step-by-step:

Begin by setting one of the numbers to 1.
Calculate the other number by subtracting the first number (which is 1) from the original number.
Check if either of these two numbers contains the digit zero. To do this, you could convert each number to text and see if the text contains '0'.
If either number contains a zero, increase the first number by one, and re-calculate the second number.
Repeat the checking and incrementing process until you find two numbers where neither contains the digit zero.
Once you find those two numbers, you have the solution.

Code Implementation

def convert_integer_to_sum_of_two_no_zero_integers(number):
    first_number = 1

    while True:
        second_number = number - first_number

        # Check if either number contains a zero.
        if '0' in str(first_number) or '0' in str(second_number):

            first_number += 1

        else:

            # Found valid numbers, return as a list.
            return [first_number, second_number]

Try it yourself on LeetCode

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates at most 'n' times, where 'n' is the input number. In each iteration, it subtracts 1 from 'n' and checks if the resulting numbers contain the digit zero. The digit-zero check converts each number to a string and searches for '0'; this string operation's time complexity is proportional to the number of digits, which is logarithmic relative to n. However, since the outer loop dominates, the overall time complexity is primarily driven by the number of iterations, resulting in approximately 'n' operations. This makes the time complexity O(n).

Space Complexity

O(1) – The provided algorithm uses a fixed number of integer variables to store the two numbers and potentially a temporary string to check for the presence of '0'. The size of these variables does not depend on the input integer N. Therefore, the auxiliary space used is constant, resulting in O(1) space complexity.

Edge Cases

Case	How to Handle
Input n is less than 2	Return an appropriate error or an empty array since no solution exists as A and B must be positive integers
Input n is a multiple of 10	The standard solution might initially create A or B with a 0, so adjust A and B until both are no-zero integers.
Input n is very large (approaching integer limit)	Check for potential integer overflow when calculating A or B and handle the overflow appropriately
Input n = 10	A naive approach might result in A=0 and B=10, thus this requires special handling to generate no-zero integers
A solution exists but the initial choices of A and B both contain zeros.	Iteratively adjust A and B to find a solution where neither contains a zero, potentially decrementing A and incrementing B.
No valid A and B exist that satisfy the no-zero constraint.	After a reasonable number of attempts, return an empty array or error to indicate no solution could be found.
The optimal A or B is close to either 1 or n-1.	Ensure the algorithm correctly handles boundary conditions when one of the numbers is very small or very large.
Input n is negative or zero	Return an error or throw an exception, as the problem states A and B must be positive integers.

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What is the range of possible values for the input integer n?
If multiple pairs of A and B satisfy the conditions, is there a preference for which pair I should return (e.g., minimize A, minimize B, or any valid pair is acceptable)?
Is '0' considered a No-Zero integer, or is the constraint specifically about the digits present in the number?
Is the input 'n' guaranteed to be greater than zero?
Can you provide a few example inputs and expected outputs to ensure my understanding of the problem is correct?

Brute Force Solution

Approach

The goal is to find two numbers that add up to a given number, but neither of these numbers can contain the digit zero. The brute force way to do this is to simply try every possible pair of numbers.

Here's how the algorithm would work step-by-step:

Start with the number one and check if the original number minus one contains a zero.
If neither one nor the result of the subtraction contains a zero, then you have found the answer.
If either number contains a zero, move on to the next number, two.
Check if the original number minus two contains a zero.
Keep doing this, trying every number from one up to one less than the original number.
For each number you try, make sure that neither it nor the result of subtracting it from the original number contains a zero.
The first time you find a pair where neither number contains a zero, you have found a valid solution, so you can stop.

Code Implementation

def convert_integer_to_sum_of_two_no_zero_integers(number_to_convert):
    first_number = 1

    while first_number < number_to_convert:
        second_number = number_to_convert - first_number

        # Checking if the current numbers contain zero
        if '0' not in str(first_number) and '0' not in str(second_number):

            return [first_number, second_number]

        first_number += 1

    return []

Try it yourself on LeetCode

Big(O) Analysis

Time Complexity

Space Complexity

Optimal Solution

Approach

Here's how the algorithm would work step-by-step:

Begin by setting one of the numbers to 1.
Calculate the other number by subtracting the first number (which is 1) from the original number.
Check if either of these two numbers contains the digit zero. To do this, you could convert each number to text and see if the text contains '0'.
If either number contains a zero, increase the first number by one, and re-calculate the second number.
Repeat the checking and incrementing process until you find two numbers where neither contains the digit zero.
Once you find those two numbers, you have the solution.

Code Implementation

def convert_integer_to_sum_of_two_no_zero_integers(number):
    first_number = 1

    while True:
        second_number = number - first_number

        # Check if either number contains a zero.
        if '0' in str(first_number) or '0' in str(second_number):

            first_number += 1

        else:

            # Found valid numbers, return as a list.
            return [first_number, second_number]

Try it yourself on LeetCode

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Input n is less than 2	Return an appropriate error or an empty array since no solution exists as A and B must be positive integers
Input n is a multiple of 10	The standard solution might initially create A or B with a 0, so adjust A and B until both are no-zero integers.
Input n is very large (approaching integer limit)	Check for potential integer overflow when calculating A or B and handle the overflow appropriately
Input n = 10	A naive approach might result in A=0 and B=10, thus this requires special handling to generate no-zero integers
A solution exists but the initial choices of A and B both contain zeros.	Iteratively adjust A and B to find a solution where neither contains a zero, potentially decrementing A and incrementing B.
No valid A and B exist that satisfy the no-zero constraint.	After a reasonable number of attempts, return an empty array or error to indicate no solution could be found.
The optimal A or B is close to either 1 or n-1.	Ensure the algorithm correctly handles boundary conditions when one of the numbers is very small or very large.
Input n is negative or zero	Return an error or throw an exception, as the problem states A and B must be positive integers.