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You are given an integer num. The num is represented in the form of a string. Your task is to find the maximum possible difference you can get by changing one single digit of num to any other digit (0-9). You must ensure the number remains valid after the change (i.e., it must not have any leading zeros unless the number itself is zero).

Clarifying Questions

  1. Should the result be always a positive difference?
    • Yes, you’re aiming to maximize the absolute difference between the original and the modified number.
  2. Is num guaranteed to not have leading zeros (except for when num itself is zero)?
    • Yes, except for the case where num itself is zero.
  3. What should be returned if num itself is zero?
    • If num is zero, then any remapping would lead to the same result as no other number is smaller than zero but zero itself; hence the maximum difference will be zero.
  4. Can the number be negative?
    • No, the problem constraints indicate that num is always a positive integer.

Strategy

  1. Identify the Maximum and Minimum Possible Numbers:
    • To maximize the difference, we should look at changing the digits in two ways:
      1. Change any digit to 9.
      2. Change any digit to 0 or 1 (depending on its position).
  2. Generate Potential Numbers:
    • For the highest possible value:
      • Find the first non-9 digit and change all identical digits to 9.
    • For the lowest possible value:
      • If the first digit is not already 1, change the first digit to 1.
      • Otherwise, find the first non-0, non-1 digit and change all identical digits to 0.
  3. Compute the Difference:
    • Compute the difference between the modified values and return the maximum difference.

Code

def maxDifferenceByRemappingDigit(num: str) -> int:
    # Calculate highest possible number by changing some digit to 9
    highest_num = list(num)
    for i in range(len(num)):
        if num[i] != '9':
            high_digit = num[i]
            break
    highest_num = "".join(['9' if x == high_digit else x for x in num])
    
    # Calculate lowest possible number by changing some digit to 0 or 1
    lowest_num = list(num)
    if num[0] != '1':
        for i in range(len(num)):
            if num[i] != '1':
                low_digit = num[i]
                break
        lowest_num = num[0] + "".join(['0' if x == low_digit else x for x in num[1:]])
    else:
        for i in range(1, len(num)):
            if num[i] != '0' and num[i] != '1':
                low_digit = num[i]
                break
        lowest_num = "".join(['0' if x == low_digit else x for x in num])
        
    # Convert strings back to integers
    highest_num = int(highest_num)
    lowest_num = int(lowest_num)

    # Return the maximum difference
    return highest_num - lowest_num

# Example usage:
num = "123456"
print(maxDifferenceByRemappingDigit(num))  # Output will be the maximum difference

Time Complexity

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