What is the time complexity of Minimum Cost to Set Cooking Time?

The optimal solution has a time complexity of O(1).

What data structures are used to solve Minimum Cost to Set Cooking Time?

This problem uses Math, Enumeration. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Minimum Cost to Set Cooking Time?

Insight 1: The core idea is to recognize that there are only a few valid ways to represent the target time as a sequence of digits on the microwave, given the maximum 4-digit constraint. Insight 2: We need to explore at least two representations: one where we directly represent the minutes and seconds, and another where we 'borrow' a minute and add it to the seconds, if applicable.

Which companies ask LeetCode 2162. Minimum Cost to Set Cooking Time in interviews?

This problem is frequently asked at GE Digital.

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Minimum Cost to Set Cooking Time - LeetCode 2162 Solution

Minimum Cost to Set Cooking Time - Complete Solution Guide

Minimum Cost to Set Cooking Time is LeetCode problem 2162, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

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 (f

Detailed Explanation

The problem asks to find the minimum cost to set a cooking time on a microwave. The microwave accepts a sequence of at most four digits, which are interpreted as minutes and seconds (first two digits are minutes, last two are seconds). The cost is determined by `moveCost` (moving the finger between digits) and `pushCost` (pressing a digit). We are given a `startAt` digit (the initial position of the finger), `moveCost`, `pushCost`, and `targetSeconds`. The goal is to explore different valid digit sequences that sum up to `targetSeconds` and find the sequence with the minimum total cost.

Solution Approach

The provided solution calculates the minimum cost by considering two possible time representations: (1) the standard representation of `minutes` and `seconds` derived directly from `targetSeconds`, and (2) a representation where one minute is 'borrowed' from the minutes and added to the seconds. The solution then calculates the cost for each representation using the `calculate_cost` function, which iterates through the digits of the representation, calculates the move cost if the current digit differs from the previous one, and adds the push cost for each digit. The minimum of these costs is then returned.

Step-by-Step Algorithm

Step 1: Calculate `minutes` and `seconds` from `targetSeconds` by dividing by 60 and taking the remainder, respectively.
Step 2: Define a helper function `calculate_cost` which takes a sequence of digits as a string and the starting digit position. It calculates the cost of pushing the digits of the sequence starting at the provided digit. The cost calculation factors in moveCost and pushCost.
Step 3: Calculate the cost for the standard representation of the time (minutes * 100 + seconds). Only perform this if `minutes` is less than 100, to ensure validity of the minute component.
Step 4: Calculate the cost for the alternative representation where one minute is borrowed. This is only valid if `minutes` is greater than 0 and if `seconds` is less than or equal to 39. Check for these conditions.
Step 5: Return the minimum of the costs calculated in steps 3 and 4.

Key Insights

Insight 1: The core idea is to recognize that there are only a few valid ways to represent the target time as a sequence of digits on the microwave, given the maximum 4-digit constraint.
Insight 2: We need to explore at least two representations: one where we directly represent the minutes and seconds, and another where we 'borrow' a minute and add it to the seconds, if applicable.
Insight 3: Leading zeros can significantly affect the cost, so we need to consider cases with fewer than 4 digits (e.g., directly inputting the seconds). The normalization of inputting less than 4 digits automatically prepends the needed 0s.
Insight 4: A careful analysis of the constraints shows that the value of minutes can be at most 100, because the maximum possible value of targetSeconds is 6039, and 6039 / 60 is approximately 100. Therefore the maximum value minutes * 100 + seconds can take is 99 * 100 + 99 = 9999 so only 4 digits are relevant

Complexity Analysis

Time Complexity: O(1)

Space Complexity: O(1)

Topics

This problem involves: Math, Enumeration.

Companies

Asked at: GE Digital.

Minimum Cost to Set Cooking Time | LeetCode 2162

Medium

Math Enumeration

Time: O(1)Space: O(1)

Solution Code

Available in:

class Solution {
    public int minCostSetTime(int startAt, int moveCost, int pushCost, int targetSeconds) {
        
        // Helper function to calculate the cost of a given sequence
        class Helper {
            public int calculate_cost(String sequence, int start) {
                int current_pos = start;
                int total_cost = 0;
                for (char digit_char : sequence.toCharArray()) {
                    int digit = Character.getNumericValue(digit_char);
                    if (digit != current_pos) {
                        total_cost += moveCost;
                    }
                    total_cost += pushCost;
                    current_pos = digit;
                }
                return total_cost;
            }
        }
        
        Helper helper = new Helper();

        int min_total_cost = Integer.MAX_VALUE;

        int minutes = targetSeconds / 60;
        int seconds = targetSeconds % 60;
        
        // Option 1: Standard representation (e.g., 76 seconds -> 1 min 16 sec)
        if (minutes < 100) {
            String time_str = String.valueOf(minutes * 100 + seconds);
            min_total_cost = Math.min(min_total_cost, helper.calculate_cost(time_str, startAt));
        }

        // Option 2: Borrow a minute (e.g., 76 seconds -> 0 min 76 sec)
        // This is valid if minutes > 0 and the resulting seconds are <= 99.
        if (minutes > 0 && seconds <= 39) {
            int m2 = minutes - 1;
            int s2 = seconds + 60;
            // Given targetSeconds <= 6039, minutes <= 100, so m2 <= 99.
            // This ensures m2 is a valid minute value.
            String time_str = String.valueOf(m2 * 100 + s2);
            min_total_cost = Math.min(min_total_cost, helper.calculate_cost(time_str, startAt));
        }
            
        return min_total_cost;
    }
}

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Problem Info

Description

Problem 2162: Minimum Cost to Set Cooking Time - Detailed explanation and solution approaches.

Topics

Math Enumeration

Companies

GE Digital

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:2162

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

5 steps

1
Step 1: Calculate `minutes` and `seconds` from `targetSeconds` by dividing by 60 and taking the remainder, respectively.
2
Step 2: Define a helper function `calculate_cost` which takes a sequence of digits as a string and the starting digit position. It calculates the cost of pushing the digits of the sequence starting at the provided digit. The cost calculation factors in moveCost and pushCost.
3
Step 3: Calculate the cost for the standard representation of the time (minutes * 100 + seconds). Only perform this if `minutes` is less than 100, to ensure validity of the minute component.
4
Step 4: Calculate the cost for the alternative representation where one minute is borrowed. This is only valid if `minutes` is greater than 0 and if `seconds` is less than or equal to 39. Check for these conditions.
5
Step 5: Return the minimum of the costs calculated in steps 3 and 4.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(1)

⚡ Constant time - Super fast! Same speed regardless of input size.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The code performs a fixed number of calculations and string operations. The number of iterations in calculate_cost is at most 4 (the maximum number of digits), which is a constant. The space used is constant as we only store a few integer variables.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Brute Force with all possible 4 digit numbers

Iterate through all possible 4-digit numbers (0000 to 9999), convert to total seconds, and compute the cost if it matches targetSeconds. This approach is less efficient.

Time: O(10000)Space: O(1)

Trade-offs: This approach is much less efficient than the solution. It would be appropriate if the constraints on `targetSeconds` were much larger or the conversion rules were more complex. This approach isn't very good given the constraints are small.

✨

Key Insights

1Insight 1: The core idea is to recognize that there are only a few valid ways to represent the target time as a sequence of digits on the microwave, given the maximum 4-digit constraint.
2Insight 2: We need to explore at least two representations: one where we directly represent the minutes and seconds, and another where we 'borrow' a minute and add it to the seconds, if applicable.
3Insight 3: Leading zeros can significantly affect the cost, so we need to consider cases with fewer than 4 digits (e.g., directly inputting the seconds). The normalization of inputting less than 4 digits automatically prepends the needed 0s.
4Insight 4: A careful analysis of the constraints shows that the value of minutes can be at most 100, because the maximum possible value of targetSeconds is 6039, and 6039 / 60 is approximately 100. Therefore the maximum value minutes * 100 + seconds can take is 99 * 100 + 99 = 9999 so only 4 digits are relevant

📚

Key Terms Explained

For Students

Edge Cases

Edge case 1: `targetSeconds` is a small number (e.g., 10). The solution correctly calculates the cost for '0010' or '10', handling cases with leading zeros.
Edge case 2: `minutes` is 0. In this case, only one representation is considered (0 minutes, seconds), so the alternative representation is skipped.
Edge case 3: `minutes` is greater than 0 but `seconds` > 39 after borrowing a minute. In this case, the second representation will not be tested.
Edge case 4: When `targetSeconds` results to minutes >= 100. The main implementation ensures the first approach will not take values above 99 for the `minutes` therefore the cost calculation will always lead to a valid result.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not considering the 'borrow a minute' alternative representation.

✗Common mistake 2: Incorrectly calculating the cost due to not accounting for the initial finger position or the cost of moving between digits.

✗Common mistake 3: Not handling leading zeros properly and failing to prepend them when creating time strings.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Optimizing user interaction cost in embedded systems with limited input methods (e.g., setting timers on appliances).

🏦Real-world scenario 2: Minimizing the energy consumption of a device that uses physical buttons or a keypad for input, where each button press and movement consumes energy.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Consider multiple approaches before coding. Mentioning alternatives shows breadth of knowledge.

⚠️ Watch Out

Always test your solution with edge cases: empty input, single element, and boundary values.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: June 3, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 14

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 7

❓

Frequently Asked Questions

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Minimum Cost to Set Cooking Time"?

For this medium-level Math problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether enumeration techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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