Practice/Google/Leetcode 2162. Minimum Cost to Set Cooking Time

Leetcode 2162. Minimum Cost to Set Cooking Time

CodingMust

Problem

You're programming a microwave with a numeric keypad (digits 0-9). Your finger starts at a given digit startAt. To set the cooking time, you need to input a time in MM:SS format (minutes and seconds), but you don't actually press a colon - you just enter up to 4 digits that represent MMSS.

Each action has an associated fatigue cost:

• Pressing a digit costs pushCost units of fatigue
• Moving your finger from one digit to a different digit costs moveCost units of fatigue (staying on the same digit between presses costs 0)

Given a target cooking duration in seconds (targetSeconds), determine the minimum total fatigue cost needed to input a valid time representation.

Valid time constraints:

• Minutes must be between 0 and 99 (inclusive)
• Seconds must be between 0 and 99 (inclusive)
• The total time (minutes × 60 + seconds) must equal targetSeconds
• You can omit leading zeros (e.g., for 3:05 you can enter "305" instead of "0305")

Requirements

1. Find all valid ways to represent targetSeconds as MM:SS format
2. For each valid representation, calculate the total fatigue cost
3. Return the minimum cost among all valid representations
4. Handle cases where multiple time representations are possible

Constraints

• 0 ≤ startAt ≤ 9
• 1 ≤ moveCost, pushCost ≤ 10⁵
• 0 ≤ targetSeconds ≤ 5999 (maximum is 99:59)
• Time complexity should be O(1) since we have at most 100 possible minute/second splits to check

Examples

Example 1:

` Input: startAt = 1, moveCost = 2, pushCost = 1, targetSeconds = 600 Output: 6 Explanation:

• 600 seconds = 10 minutes and 0 seconds
• We can enter "1000" (10:00)
• Starting at 1: press 1 (cost=1), move to 0 (cost=2), press 0 (cost=1), stay at 0 (cost=0), press 0 (cost=1), stay at 0 (cost=0), press 0 (cost=1)
• Total: 1 + 2 + 1 + 1 + 1 = 6 `

Example 2:

` Input: startAt = 0, moveCost = 1, pushCost = 2, targetSeconds = 76 Output: 6 Explanation:

• 76 seconds can be represented as:
  • "116" (1:16): move 0→1 (cost=1) + push 1 (cost=2) + stay (cost=0) + push 1 (cost=2) + move 1→6 (cost=1) + push 6 (cost=2) = 8
  • "0076" (0:76): push 0 (cost=2) + stay (cost=0) + push 0 (cost=2) + move 0→7 (cost=1) + push 7 (cost=2) + move 7→6 (cost=1) + push 6 (cost=2) = 10
• Wait, let me recalculate "116": We start at 0, move to 1 (1), push 1 (2), stay at 1 (0), push 1 (2), move to 6 (1), push 6 (2) = 8
• The minimum is actually from carefully checking both options `

Example 3:

` Input: startAt = 5, moveCost = 3, pushCost = 4, targetSeconds = 0 Output: 7 Explanation:

• 0 seconds can only be entered as "0" (single digit representing 0:00)
• Move from 5 to 0 (cost=3) + push 0 (cost=4) = 7 `