#2162

Medium

LeetCode Problem Workspace

Minimum Cost to Set Cooking Time

Calculate the minimum fatigue to set a microwave cooking time using digit moves and pushes efficiently.

Problem Statement

You have a microwave that accepts cooking times using four digits representing minutes and seconds. The first two digits are minutes, the last two are seconds. The microwave normalizes inputs shorter than four digits by prepending zeroes. For example, pushing 960 is treated as 0960, representing 9 minutes and 60 seconds.

You are given integers startAt, moveCost, pushCost, and targetSeconds. Initially, your finger is on digit startAt. Moving the finger to a different digit costs moveCost units, and pressing a digit costs pushCost units. Determine the minimum total cost to set the microwave to exactly targetSeconds, considering all possible digit sequences that normalize correctly.

Examples

Example 1

Input: startAt = 1, moveCost = 2, pushCost = 1, targetSeconds = 600

Output: 6

The following are the possible ways to set the cooking time.

1 0 0 0, interpreted as 10 minutes and 0 seconds. The finger is already on digit 1, pushes 1 (with cost 1), moves to 0 (with cost 2), pushes 0 (with cost 1), pushes 0 (with cost 1), and pushes 0 (with cost 1). The cost is: 1 + 2 + 1 + 1 + 1 = 6. This is the minimum cost.
0 9 6 0, interpreted as 9 minutes and 60 seconds. That is also 600 seconds. The finger moves to 0 (with cost 2), pushes 0 (with cost 1), moves to 9 (with cost 2), pushes 9 (with cost 1), moves to 6 (with cost 2), pushes 6 (with cost 1), moves to 0 (with cost 2), and pushes 0 (with cost 1). The cost is: 2 + 1 + 2 + 1 + 2 + 1 + 2 + 1 = 12.
9 6 0, normalized as 0960 and interpreted as 9 minutes and 60 seconds. The finger moves to 9 (with cost 2), pushes 9 (with cost 1), moves to 6 (with cost 2), pushes 6 (with cost 1), moves to 0 (with cost 2), and pushes 0 (with cost 1). The cost is: 2 + 1 + 2 + 1 + 2 + 1 = 9.

Example 2

Input: startAt = 0, moveCost = 1, pushCost = 2, targetSeconds = 76

Output: 6

The optimal way is to push two digits: 7 6, interpreted as 76 seconds. The finger moves to 7 (with cost 1), pushes 7 (with cost 2), moves to 6 (with cost 1), and pushes 6 (with cost 2). The total cost is: 1 + 2 + 1 + 2 = 6 Note other possible ways are 0076, 076, 0116, and 116, but none of them produces the minimum cost.

Constraints

0 <= startAt <= 9
1 <= moveCost, pushCost <= 105
1 <= targetSeconds <= 6039

Solution Approach

Enumerate all valid time splits

Generate all combinations of minutes and seconds where 0 <= minutes <= 99 and 0 <= seconds <= 99, ensuring minutes * 60 + seconds equals targetSeconds. Discard invalid combinations exceeding 99 seconds.

Compute cost per sequence

For each valid minute-second pair, construct the corresponding digit sequence normalized to four digits. Start from startAt and accumulate moveCost when moving to a different digit and pushCost when pressing digits. Keep track of the minimum total cost.

Select minimum fatigue

After evaluating all sequences, select the one with the lowest total cost. Return this value as the minimum fatigue required to set the microwave correctly.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity depends on the number of valid minute-second pairs (up to 100*100) and digit sequence evaluations. Space complexity depends on storing sequences and intermediate costs, generally O(1) extra memory beyond input.

What Interviewers Usually Probe

Are you accounting for the normalization of input digits to four-digit sequences?
Can you calculate the cost efficiently without generating unnecessary digit sequences?
How do you ensure the minimum total fatigue among all possible combinations?

Common Pitfalls or Variants

Common pitfalls

Ignoring normalization and counting sequences shorter than four digits incorrectly.
Not handling finger movement costs when consecutive digits are the same.
Assuming seconds can exceed 59 without normalization, producing invalid sequences.

Follow-up variants

Calculate minimum cost if the microwave accepts three-digit sequences only.
Determine the cost when some digits are locked and cannot be moved to.
Optimize for a target time range instead of a single targetSeconds.

FAQ

What is the best approach to solve Minimum Cost to Set Cooking Time?

Enumerate all minute-second splits matching targetSeconds, compute total cost for each sequence, and pick the minimum.

How do I handle input normalization for fewer than four digits?

Prepend zeroes to make the sequence four digits and then interpret the first two as minutes and last two as seconds.

Do I need to consider consecutive identical digits differently?

Yes, moving the finger to the same digit has zero move cost, only pushCost applies.

Is it necessary to check all combinations of minutes and seconds?

Only combinations where minutes*60 + seconds equals targetSeconds are valid; others can be skipped.

Which pattern does this problem mainly test?

This problem is a Math plus Enumeration pattern, requiring systematic exploration of valid minute-second sequences.

terminal

Solution

Solution 1

#### Python3

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class Solution:
    def minCostSetTime(
        self, startAt: int, moveCost: int, pushCost: int, targetSeconds: int
    ) -> int:
        def f(m, s):
            if not 0 <= m < 100 or not 0 <= s < 100:
                return inf
            arr = [m // 10, m % 10, s // 10, s % 10]
            i = 0
            while i < 4 and arr[i] == 0:
                i += 1
            t = 0
            prev = startAt
            for v in arr[i:]:
                if v != prev:
                    t += moveCost
                t += pushCost
                prev = v
            return t

        m, s = divmod(targetSeconds, 60)
        ans = min(f(m, s), f(m - 1, s + 60))
        return ans

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