LeetCode #2162 — MEDIUM

Minimum Cost to Set Cooking Time

Move from brute-force thinking to an efficient approach using math strategy.

Solve on LeetCode
The Problem

Problem Statement

A generic microwave supports cooking times for:

  • at least 1 second.
  • at most 99 minutes and 99 seconds.

To set the cooking time, you push at most four digits. The microwave normalizes what you push as four digits by prepending zeroes. It interprets the first two digits as the minutes and the last two digits as the seconds. It then adds them up as the cooking time. For example,

  • You push 9 5 4 (three digits). It is normalized as 0954 and interpreted as 9 minutes and 54 seconds.
  • You push 0 0 0 8 (four digits). It is interpreted as 0 minutes and 8 seconds.
  • You push 8 0 9 0. It is interpreted as 80 minutes and 90 seconds.
  • You push 8 1 3 0. It is interpreted as 81 minutes and 30 seconds.

You are given integers startAt, moveCost, pushCost, and targetSeconds. Initially, your finger is on the digit startAt. Moving the finger above any specific digit costs moveCost units of fatigue. Pushing the digit below the finger once costs pushCost units of fatigue.

There can be multiple ways to set the microwave to cook for targetSeconds seconds but you are interested in the way with the minimum cost.

Return the minimum cost to set targetSeconds seconds of cooking time.

Remember that one minute consists of 60 seconds.

Example 1:

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

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: A generic microwave supports cooking times for: at least 1 second. at most 99 minutes and 99 seconds. To set the cooking time, you push at most four digits. The microwave normalizes what you push as four digits by prepending zeroes. It interprets the first two digits as the minutes and the last two digits as the seconds. It then adds them up as the cooking time. For example, You push 9 5 4 (three digits). It is normalized as 0954 and interpreted as 9 minutes and 54 seconds. You push 0 0 0 8 (four digits). It is interpreted as 0 minutes and 8 seconds. You push 8 0 9 0. It is interpreted as 80 minutes and 90 seconds. You push 8 1 3 0. It is interpreted as 81 minutes and 30 seconds. You are given integers startAt, moveCost, pushCost, and targetSeconds. Initially, your finger is on the digit startAt. Moving the finger above any specific digit costs moveCost units of fatigue. Pushing the

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Math

Example 1

1
2
1
600

Example 2

0
1
2
76

Related Problems

  • Minimum Time Difference (minimum-time-difference)
Step 02

Core Insight

What unlocks the optimal approach

  • Define a separate function Cost(mm, ss) where 0 <= mm <= 99 and 0 <= ss <= 99. This function should calculate the cost of setting the cooking time to mm minutes and ss seconds
  • The range of the minutes is small (i.e., [0, 99]), how can you use that?
  • For every mm in [0, 99], calculate the needed ss to make mm:ss equal to targetSeconds and minimize the cost of setting the cooking time to mm:ss
  • Be careful in some cases when ss is not in the valid range [0, 99].
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2162: Minimum Cost to Set Cooking Time
class Solution {
    public int minCostSetTime(int startAt, int moveCost, int pushCost, int targetSeconds) {
        int m = targetSeconds / 60;
        int s = targetSeconds % 60;
        return Math.min(
            f(m, s, startAt, moveCost, pushCost), f(m - 1, s + 60, startAt, moveCost, pushCost));
    }

    private int f(int m, int s, int prev, int moveCost, int pushCost) {
        if (m < 0 || m > 99 || s < 0 || s > 99) {
            return Integer.MAX_VALUE;
        }
        int[] arr = new int[] {m / 10, m % 10, s / 10, s % 10};
        int i = 0;
        for (; i < 4 && arr[i] == 0; ++i)
            ;
        int t = 0;
        for (; i < 4; ++i) {
            if (arr[i] != prev) {
                t += moveCost;
            }
            t += pushCost;
            prev = arr[i];
        }
        return t;
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(log n)
Space
O(1)

Approach Breakdown

ITERATIVE
O(n) time
O(1) space

Simulate the process step by step — multiply n times, check each number up to n, or iterate through all possibilities. Each step is O(1), but doing it n times gives O(n). No extra space needed since we just track running state.

MATH INSIGHT
O(log n) time
O(1) space

Math problems often have a closed-form or O(log n) solution hidden behind an O(n) simulation. Modular arithmetic, fast exponentiation (repeated squaring), GCD (Euclidean algorithm), and number theory properties can dramatically reduce complexity.

Shortcut: Look for mathematical properties that eliminate iteration. Repeated squaring → O(log n). Modular arithmetic avoids overflow.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Overflow in intermediate arithmetic

Wrong move: Temporary multiplications exceed integer bounds.

Usually fails on: Large inputs wrap around unexpectedly.

Fix: Use wider types, modular arithmetic, or rearranged operations.