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Minimum Cost to Set Cooking Time

Difficulty: Medium

Problem Description

You are given integers startAt, moveCost, pushCost, and targetSeconds. Initially, your finger is on the digit startAt. Moving your finger above any specific digit costs moveCost units of fatigue, and pushing the digit below the finger costs pushCost units of fatigue. You need to determine the minimum cost to set the microwave to cook for targetSeconds seconds.

Key Insights

  • The cooking time can be represented in the format of MMSS (minutes and seconds).
  • The total seconds must be converted to a valid MMSS format, considering the constraints.
  • The finger can move between digits, and both moving and pushing have associated costs.
  • You need to consider every valid combination of digits that can form the desired time.

Space and Time Complexity

Time Complexity: O(1) - The number of valid cooking times is fixed, so the time taken does not grow with input size. Space Complexity: O(1) - Only a fixed amount of space is used for calculations, regardless of the input size.

Solution

To solve this problem, we can enumerate all possible valid combinations of digits that represent the cooking time. For each combination, we calculate the total cost, considering both the movement and the pressing of the digits. By keeping track of the minimum cost across all valid combinations, we can return the desired result.

  1. Convert the target seconds into minutes and seconds.
  2. Generate all valid combinations of 4 digits that represent the cooking time.
  3. For each combination:
    • Calculate the movement cost from the current position to the next digit.
    • Calculate the push cost for each digit.
    • Sum these costs to get the total cost for that combination.
  4. Track the minimum cost encountered.

Code Solutions

def minCost(startAt, moveCost, pushCost, targetSeconds):
    total_cost = float('inf')
    target_minutes = targetSeconds // 60
    target_seconds = targetSeconds % 60

    # Valid cooking times range from 0001 to 9999
    for minutes in range(100):
        for seconds in range(60):
            if minutes * 60 + seconds == targetSeconds:
                # Format minutes and seconds to 4 digits
                cooking_time = f"{minutes:02}{seconds:02}"
                cost = 0
                current_pos = startAt

                # Calculate cost for this cooking time
                for digit in cooking_time:
                    digit = int(digit)
                    if current_pos != digit:
                        cost += moveCost  # Move to the digit
                    cost += pushCost  # Push the digit
                    current_pos = digit

                total_cost = min(total_cost, cost)

    return total_cost
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