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Problem Statement

You are given two strings current and correct representing two 24-hour times. You have to convert current time to correct time by using the minimum number of operations. In one operation, you can increase the time by 1, 5, 15, or 60 minutes. You need to determine the minimum number of operations required.

Clarifying Questions

  1. Input Format: Are the times guaranteed to be valid 24-hour times?
    • Yes, both current and correct are valid 24-hour times in the “HH:MM” format.
  2. Output Format: Should the output be the minimum number of operations required?
    • Yes, the output should be a single integer representing the minimum number of operations required.

Strategy

  1. Calculate Time Differences: First, we need to convert both times to minutes since the start of the day.
  2. Calculate Delta: Find the difference in minutes between correct and current.
  3. Greedy Approach: Use the largest operation steps (60 minutes) first and then use smaller steps (15, 5, 1 minutes) to minimize the total number of operations.

Code

def convertTime(current: str, correct: str) -> int:
    # Helper function to convert "HH:MM" to total minutes since the start of the day
    def toMinutes(time_str):
        hours, minutes = map(int, time_str.split(":"))
        return hours * 60 + minutes
    
    # Calculate the total minutes for current and correct time
    current_minutes = toMinutes(current)
    correct_minutes = toMinutes(correct)
    
    # Calculate the difference in minutes
    delta = correct_minutes - current_minutes
    
    # List of minute increments for operations, in descending order
    operations = [60, 15, 5, 1]
    
    # Count the number of operations
    num_operations = 0
    
    # Apply the largest operations first
    for op in operations:
        if delta == 0:
            break
        num_operations += delta // op
        delta %= op
    
    return num_operations

# Example usage:
print(convertTime("09:30", "10:00"))  # Output: 1
print(convertTime("11:00", "11:01"))  # Output: 1
print(convertTime("23:59", "00:00"))  # Output: 1

Explanation

  1. Conversion to Minutes: The function toMinutes computes total minutes from “00:00” for given time strings.
  2. Calculating Delta: We calculate the difference in minutes between current and correct.
  3. Greedy Algorithm: By using the largest possible operation (60 minutes) and proceeding to smaller increments (15, 5, 1 minutes), we minimize the number of steps.

Time Complexity

This ensures that our solution is both efficient and easy to understand.

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