algoadvance

You are given a list of positive integers nums. You need to return a list containing the digits of each number separated into individual elements in the same order they appear in the original list.

For example, if the input list is [123, 45, 7], the output should be [1, 2, 3, 4, 5, 7].

Clarifying Questions

1. Input Range: Are there any constraints on the size of the numbers in the array or the array itself?
   • Assume the numbers are within the typical range for integers handled in Python.
2. Negative Numbers: Are the numbers always positive as stated?
   • Yes, the problem specifies they are positive integers.
3. Order: Should the digits be returned in the exact order they appear in the input list?
   • Yes, the digits must preserve the order from the input list.

Strategy

1. Iterate through the List: Loop through each number in the input list nums.
2. Extract Digits: Convert each number to a string to easily iterate over each digit.
3. Append Digits: Convert each digit back to an integer and append it to the result list.
4. Return the Result: After processing all numbers, return the resulting list of digits.

We maintain the order of digits by sequentially processing numbers and their digits.

Time Complexity

• Time Complexity: O(n * k), where n is the number of integers in the list and k is the average number of digits per integer. This complexity arises because we need to process each digit of each number.
• Space Complexity: O(n * k), as we need additional space to store all digits separately.

Code

Here is the implementation of the strategy discussed above:

def separate_digits(nums):
    result = []
    for num in nums:
        result.extend([int(digit) for digit in str(num)])
    return result

# Test the function with an example case
print(separate_digits([123, 45, 7]))  # Expected output: [1, 2, 3, 4, 5, 7]

This function will iterate over each number in the provided list nums, convert each number to a string to extract individual digits, then convert those digits back to integers, and add them to the result list. Finally, it returns the consolidated list of separated digits.

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