Minimum Cost to Set Cooking Time

Minimum Cost to Set Cooking Time

1. What is this problem about?

Minimum Cost to Set Cooking Time is a creative math and enumeration problem. You are given a microwave where you can enter a time using up to 4 digits (MM:SS). However, the microwave is flexible: "90 seconds" can be entered as 90 or as 01:30 (which is 130 on the keypad). Each button press has a pushCost, and moving your finger from one button to another has a moveCost. Given a targetSeconds and a startAt finger position, you need to find the minimum cost to enter a valid time that equals the target.

2. Why is this asked in interviews?

This question, asked by companies like Google, tests a candidate's ability to think outside the box and handle multiple representations of the same value. The Minimum Cost to Set Cooking Time interview question requires careful case analysis and enumeration of all valid ways to represent time on a microwave keypad. It evaluates attention to detail, especially regarding the 99-second limit for the "seconds" part in some configurations versus the "minutes" part.

3. Algorithmic pattern used

The algorithmic pattern used is Enumeration and Math. There are generally only two ways to represent a given number of seconds on a microwave:

1. minutes = totalSeconds / 60, seconds = totalSeconds % 60.
2. minutes = (totalSeconds / 60) - 1, seconds = (totalSeconds % 60) + 60. (Note: You must ensure minutes $\leq 99$ and seconds $\leq 99$). For each valid representation, you calculate the cost of pressing the digits sequentially, adding moveCost whenever the next digit is different from the current finger position. This "Math, Enumeration interview pattern" is about exploring a small set of possibilities thoroughly.

4. Example explanation

Target: 76 seconds. startAt: 1. moveCost: 10. pushCost: 1.

• Representation 1: 01:16 (Enter 116)
  • Start at 1. Push 1 (1). Move to 1 (0). Push 1 (1). Move to 6 (10). Push 6 (1). Total = 13.
• Representation 2: 76 seconds (Enter 76)
  • Start at 1. Move to 7 (10). Push 7 (1). Move to 6 (10). Push 6 (1). Total = 22. The minimum cost is 13.

5. Common mistakes candidates make

In the Minimum Cost to Set Cooking Time coding problem, many candidates forget to handle leading zeros correctly. On a microwave, you don't need to press 0 for 01:30; you can just press 130. Another mistake is failing to check if the minutes value exceeds 99 or if the seconds value exceeds 99 when using the "minus one minute" representation. Some also forget that moving the finger only incurs a cost if the target digit is different from the previous digit, not the starting position for every single press.

6. Interview preparation tip

When faced with a problem that has multiple valid inputs for the same output, try to enumerate all possible inputs. If the number of inputs is small, simple calculation for each is much faster than a complex search algorithm. This "Enumeration interview pattern" is common in problems involving keypads, dates, or time formats.