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Separate the Digits in an Array

Easy

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Arrays

Given an array of positive integers nums, return an array answer that consists of the digits of each integer in nums after separating them in the same order they appear in nums.

To separate the digits of an integer is to get all the digits it has in the same order.

For example, for the integer 10921, the separation of its digits is [1,0,9,2,1].

Example 1:

Input: nums = [13,25,83,77]
Output: [1,3,2,5,8,3,7,7]
Explanation: 
- The separation of 13 is [1,3].
- The separation of 25 is [2,5].
- The separation of 83 is [8,3].
- The separation of 77 is [7,7].
answer = [1,3,2,5,8,3,7,7]. Note that answer contains the separations in the same order.

Example 2:

Input: nums = [7,1,3,9]
Output: [7,1,3,9]
Explanation: The separation of each integer in nums is itself.
answer = [7,1,3,9].

Constraints:

1 <= nums.length <= 1000
1 <= nums[i] <= 10⁵

Separate the Digits in an Array

Easy

Asked by:

2 views

Topics:

Arrays

Given an array of positive integers nums, return an array answer that consists of the digits of each integer in nums after separating them in the same order they appear in nums.

To separate the digits of an integer is to get all the digits it has in the same order.

For example, for the integer 10921, the separation of its digits is [1,0,9,2,1].

Example 1:

Input: nums = [13,25,83,77]
Output: [1,3,2,5,8,3,7,7]
Explanation: 
- The separation of 13 is [1,3].
- The separation of 25 is [2,5].
- The separation of 83 is [8,3].
- The separation of 77 is [7,7].
answer = [1,3,2,5,8,3,7,7]. Note that answer contains the separations in the same order.

Example 2:

Input: nums = [7,1,3,9]
Output: [7,1,3,9]
Explanation: The separation of each integer in nums is itself.
answer = [7,1,3,9].

Constraints:

1 <= nums.length <= 1000
1 <= nums[i] <= 10⁵

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 values for the integers within the input array? Can they be negative?
Can the input array be empty or null?
Should the order of digits within the final output array be preserved relative to their original number? (e.g., digits of the first number appear before digits of the second).
Should the final output array contain only unique digits, or are duplicates from the same or different numbers allowed?
What data type should the separated digits be returned in? Should it be an array of integers, or strings, or something else?

Brute Force Solution

Approach

The brute force approach to separating digits involves examining each number in the input and extracting its digits one by one. We repeat this process for every number in the original collection, gathering all digits into a new combined collection. This effectively flattens the digits from the original structure.

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

Take the first number from the list.
Break down that number into its individual digits.
Add those digits to a new, separate list.
Repeat this process of taking a number, breaking it down, and adding its digits for every number in the original list.
After you have processed all the numbers, you will have a single list containing all the individual digits from all the original numbers.

Code Implementation

def separate_digits_brute_force(numbers):
    separated_digits = []

    # Iterate through each number in the input list
    for number in numbers:

        # Convert the number to a string to extract digits
        number_string = str(number)

        # Extract each digit from the string
        for digit_char in number_string:

            # Convert digit character back to integer
            digit = int(digit_char)

            # Add the digit to the result list
            separated_digits.append(digit)

    return separated_digits

Try it yourself on LeetCode

Big(O) Analysis

Time Complexity

O(N * M) – Let N be the number of integers in the input array nums, and let M be the maximum number of digits in any integer within nums. For each of the N integers, we extract its digits. In the worst case, extracting digits takes time proportional to the number of digits M in that integer. Therefore, the overall time complexity is O(N * M), representing that for each number, we do at most M operations.

Space Complexity

O(N) – The provided solution describes creating a new list to hold all the individual digits extracted from the input array. In the worst-case scenario, if all numbers in the input array are single-digit numbers, the new list will contain N elements, where N is the number of elements in the original input array. Therefore, the auxiliary space required is proportional to the input size N. This results in a space complexity of O(N).

Optimal Solution

Approach

The goal is to take a list of numbers and create a new list where each digit from every number is separated out. We want to do this in a simple and efficient way. The strategy is to go through each number, pull out its digits one by one, and add them to the new list.

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

Start with an empty new list to hold all the separated digits.
Look at the first number in the original list.
Break the number down into its individual digits. For example, if the number is 123, you would separate it into 1, 2, and 3.
Add each of those separated digits to the end of the new list.
Move on to the next number in the original list and repeat the separation process.
Keep doing this until you have gone through all of the numbers in the original list.
The new list now contains all of the separated digits from the original numbers.

Code Implementation

def separate_digits_in_array(numbers):
    separated_digits_list = []

    for number in numbers:
        # Convert the number to a string to iterate through its digits.
        number_string = str(number)

        for digit_char in number_string:
            # Convert the digit character back to an integer.
            digit = int(digit_char)

            # Append each digit to the new list.
            separated_digits_list.append(digit)

    return separated_digits_list

def separate_digits_in_array_alt(numbers):
    separated_digits_list = []

    for number in numbers:
        # Ensure the number is positive for the algorithm.
        number = abs(number)
        digits = []

        # Extract digits in reverse order.
        while number > 0:
            digit = number % 10
            digits.append(digit)
            number //= 10

        # Append digits in correct order.
        digits.reverse()

        # Add digits to final list. 
        separated_digits_list.extend(digits)

    return separated_digits_list

def separate_digits_in_array_optimal(numbers):
    separated_digits_list = []

    for number in numbers:
        number_string = str(number)

        # Direct conversion avoids extra variable.
        for digit_char in number_string:
            separated_digits_list.append(int(digit_char))

    return separated_digits_list

def separate_digits_in_array_functional(numbers):
    #Use list comprehension for a concise solution.
    return [int(digit) for number in numbers for digit in str(number)]

def separate_digits_in_array_complex(numbers):
    separated_digits_list = []
    for number in numbers:
        if number == 0:
            separated_digits_list.append(0)
            continue

        digits = []
        is_negative = number < 0
        number = abs(number)

        while number > 0:
            digit = number % 10
            digits.append(digit)
            number //= 10

        digits.reverse()

        # Correctly handle negative numbers.
        if is_negative and digits:
            separated_digits_list.append(-digits[0])
            separated_digits_list.extend(digits[1:])
        else:
            separated_digits_list.extend(digits)

    return separated_digits_list

Try it yourself on LeetCode

Big(O) Analysis

Time Complexity

O(N) – Let n be the total number of digits across all numbers in the input array. The algorithm iterates through the input array of numbers. For each number, it extracts the digits. The number of digits extracted across all numbers is represented by 'n'. Appending each extracted digit to the result list takes constant time. Therefore, the time complexity is directly proportional to the total number of digits, resulting in O(N) time complexity, where N is the total number of digits.

Space Complexity

O(D) – The algorithm creates a new list to store the separated digits. In the worst-case scenario, where all input numbers consist of many digits, the number of digits in the new list is proportional to the total number of digits across all input numbers. Let D be the total number of digits in all input numbers. Then the space complexity is O(D), as the new list would grow linearly with the total number of digits.

Edge Cases

Case	How to Handle
Null or undefined input array	Return an empty list or throw an IllegalArgumentException to handle invalid input.
Empty input array	Return an empty list as there are no digits to separate.
Array containing only a single number (e.g., [123])	Separate the digits of that single number and return the resulting list.
Array contains numbers with leading zeros (e.g., [012, 34])	Treat the leading zeros as part of the number when separating the digits.
Array contains negative numbers (e.g., [-12, 3])	Handle the negative sign appropriately, either by including it with the first digit or treating the input as absolute values.
Array contains large numbers that might cause integer overflow when processing	Use a data type that can accommodate larger numbers, such as long or BigInteger, or handle the overflow case explicitly.
Array with very large numbers (many digits), performance considerations	Avoid string conversions within inner loops to minimize runtime overhead.
Array containing zero or all elements are zero	The algorithm should correctly handle the digit separation for numbers containing zero.

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 values for the integers within the input array? Can they be negative?
Can the input array be empty or null?
Should the order of digits within the final output array be preserved relative to their original number? (e.g., digits of the first number appear before digits of the second).
Should the final output array contain only unique digits, or are duplicates from the same or different numbers allowed?
What data type should the separated digits be returned in? Should it be an array of integers, or strings, or something else?

Brute Force Solution

Approach

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

Take the first number from the list.
Break down that number into its individual digits.
Add those digits to a new, separate list.
Repeat this process of taking a number, breaking it down, and adding its digits for every number in the original list.
After you have processed all the numbers, you will have a single list containing all the individual digits from all the original numbers.

Code Implementation

def separate_digits_brute_force(numbers):
    separated_digits = []

    # Iterate through each number in the input list
    for number in numbers:

        # Convert the number to a string to extract digits
        number_string = str(number)

        # Extract each digit from the string
        for digit_char in number_string:

            # Convert digit character back to integer
            digit = int(digit_char)

            # Add the digit to the result list
            separated_digits.append(digit)

    return separated_digits

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:

Start with an empty new list to hold all the separated digits.
Look at the first number in the original list.
Break the number down into its individual digits. For example, if the number is 123, you would separate it into 1, 2, and 3.
Add each of those separated digits to the end of the new list.
Move on to the next number in the original list and repeat the separation process.
Keep doing this until you have gone through all of the numbers in the original list.
The new list now contains all of the separated digits from the original numbers.

Code Implementation

def separate_digits_in_array(numbers):
    separated_digits_list = []

    for number in numbers:
        # Convert the number to a string to iterate through its digits.
        number_string = str(number)

        for digit_char in number_string:
            # Convert the digit character back to an integer.
            digit = int(digit_char)

            # Append each digit to the new list.
            separated_digits_list.append(digit)

    return separated_digits_list

def separate_digits_in_array_alt(numbers):
    separated_digits_list = []

    for number in numbers:
        # Ensure the number is positive for the algorithm.
        number = abs(number)
        digits = []

        # Extract digits in reverse order.
        while number > 0:
            digit = number % 10
            digits.append(digit)
            number //= 10

        # Append digits in correct order.
        digits.reverse()

        # Add digits to final list. 
        separated_digits_list.extend(digits)

    return separated_digits_list

def separate_digits_in_array_optimal(numbers):
    separated_digits_list = []

    for number in numbers:
        number_string = str(number)

        # Direct conversion avoids extra variable.
        for digit_char in number_string:
            separated_digits_list.append(int(digit_char))

    return separated_digits_list

def separate_digits_in_array_functional(numbers):
    #Use list comprehension for a concise solution.
    return [int(digit) for number in numbers for digit in str(number)]

def separate_digits_in_array_complex(numbers):
    separated_digits_list = []
    for number in numbers:
        if number == 0:
            separated_digits_list.append(0)
            continue

        digits = []
        is_negative = number < 0
        number = abs(number)

        while number > 0:
            digit = number % 10
            digits.append(digit)
            number //= 10

        digits.reverse()

        # Correctly handle negative numbers.
        if is_negative and digits:
            separated_digits_list.append(-digits[0])
            separated_digits_list.extend(digits[1:])
        else:
            separated_digits_list.extend(digits)

    return separated_digits_list

Try it yourself on LeetCode

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Null or undefined input array	Return an empty list or throw an IllegalArgumentException to handle invalid input.
Empty input array	Return an empty list as there are no digits to separate.
Array containing only a single number (e.g., [123])	Separate the digits of that single number and return the resulting list.
Array contains numbers with leading zeros (e.g., [012, 34])	Treat the leading zeros as part of the number when separating the digits.
Array contains negative numbers (e.g., [-12, 3])	Handle the negative sign appropriately, either by including it with the first digit or treating the input as absolute values.
Array contains large numbers that might cause integer overflow when processing	Use a data type that can accommodate larger numbers, such as long or BigInteger, or handle the overflow case explicitly.
Array with very large numbers (many digits), performance considerations	Avoid string conversions within inner loops to minimize runtime overhead.
Array containing zero or all elements are zero	The algorithm should correctly handle the digit separation for numbers containing zero.