Python Coding Test Course, Sorting Digits in Descending Order

1. Problem Definition

The goal of this problem is to sort the given digits in descending order to form the largest possible number. The input number is an integer, and our task is to return the largest number possible using the digits of this number.

Example Input/Output

  • Input: 2183
  • Output: 8321

2. Approach to the Problem

This problem involves extracting the individual digits of the number and then sorting them in descending order. In Python, we can easily perform such sorting operations using the sort() method of a list. The specific steps are as follows:

  1. Convert the integer to a string.
  2. Split the string into individual digits (characters) to create a list.
  3. Sort the list in descending order.
  4. Merge the sorted list back into a string, convert it to an integer, and return it.

3. Algorithm Implementation

Now, let’s solve the problem using Python code based on the above approach.

def sort_digits_descending(n):
    # Step 1: Convert integer to string
    str_n = str(n)
    
    # Step 2: Convert string to list
    digits = list(str_n)
    
    # Step 3: Sort the list in descending order
    digits.sort(reverse=True)
    
    # Step 4: Merge the sorted list back into a string and convert to integer
    sorted_n = int(''.join(digits))
    
    return sorted_n

4. Code Explanation

The function sort_digits_descending takes the parameter n and performs the entire process. Each step works as follows:

  • String Conversion: Converts the integer to a string using str(n).
  • List Conversion: Converts each character (digit) of the string into a list using list(str_n).
  • Sorting: Sorts the list in descending order using sort(reverse=True).
  • Merging: Merges the list back into a string using "".join(digits), and converts it to an integer using int() before returning it.

5. Test Cases

Let’s use several test cases to verify that our function works correctly.

print(sort_digits_descending(2183)) # 8321
print(sort_digits_descending(1450)) # 5410
print(sort_digits_descending(9876543210)) # 9876543210
print(sort_digits_descending(0)) # 0
print(sort_digits_descending(1001)) # 1100

6. Result Analysis

After checking the results of each test case, we found that the expected output was returned in all cases. The function was implemented very simply and efficiently using Python’s built-in features.

7. Optimization and Considerations

The code written above has a time complexity of O(m log m) for sorting the digits, where m is the number of digits in the input integer. Since the maximum number of digits for integers is limited to 10, there are no performance issues, but it may be necessary to consider making it valid for larger numbers or reducing complexity for efficiency.

8. Conclusion

We have implemented an algorithm to sort the given integer in descending order to create the largest possible value. In this process, we were able to solve the problem simply with the use of Python’s list methods and string manipulation features. Future considerations for additional optimization and alternative approaches are encouraged. This will help improve problem-solving skills in coding tests.