What is the time complexity of Minimum Initial Energy to Finish Tasks?

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

What data structures are used to solve Minimum Initial Energy to Finish Tasks?

This problem uses Array, Greedy, Sorting. Understanding these concepts is essential for solving this Hard problem efficiently.

What are the key insights for solving Minimum Initial Energy to Finish Tasks?

Insight 1: The key insight is realizing that the order in which we perform the tasks significantly affects the initial energy needed. A naive approach might not yield the optimal result. Insight 2: Sorting the tasks based on the difference between the minimum energy required and the actual energy consumed (minimum - actual) is crucial. Tasks with a larger difference should be done earlier. This is because doing tasks with higher (minimum - actual) gives you more leeway on your starting energy to finish more tasks.

Which companies ask LeetCode 1665. Minimum Initial Energy to Finish Tasks in interviews?

This problem is frequently asked at Akuna Capital.

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Minimum Initial Energy to Finish Tasks - LeetCode 1665 Solution

Minimum Initial Energy to Finish Tasks - Complete Solution Guide

Minimum Initial Energy to Finish Tasks is LeetCode problem 1665, a Hard level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given an array tasks where tasks[i] = [actual i , minimum i ] : actual i is the actual amount of energy you spend to finish the i th task. minimum i is the minimum amount of energy you require to begin the i th task. For example, if the task is [10, 12] and your current energy is 11 , you cannot start this task. However, if your current energy is 13 , you can complete this task, and your energy will be 3 after finishing it. You can finish the tasks in any order you like. Return the minim

Detailed Explanation

The problem asks us to find the minimum initial energy needed to complete a set of tasks. Each task has an `actual` energy cost to perform and a `minimum` energy requirement to even start the task. We can perform the tasks in any order, and our goal is to find the smallest amount of initial energy that allows us to complete *all* tasks. The input is an array of tasks, where each task is a pair of integers [actual_energy, minimum_energy].

Solution Approach

The solution utilizes a greedy approach. It sorts the tasks based on the difference between the minimum required energy and the actual energy spent. The tasks are then iterated through in sorted order. The minimum initial energy is determined by keeping track of the current energy and updating it as we complete each task. For each task, we check if the current energy is sufficient to start the task. If it is, we subtract the actual energy spent. Otherwise, we increase the initial energy needed to the minimum required for the task and then subtract the actual energy.

Step-by-Step Algorithm

Step 1: Sort the tasks array. The sorting criteria is based on `minimum - actual` energy. Specifically, tasks with larger `minimum - actual` values should come first.
Step 2: Initialize `energy_needed` to 0. This variable will store the minimum initial energy required.
Step 3: Iterate through the sorted `tasks` array.
Step 4: For each `task` (consisting of `actual` and `minimum` energy):
Step 5: Determine if the current `energy_needed` is enough to start the task. This is done by comparing `energy_needed` with `minimum`.
Step 6: If `energy_needed` is less than `minimum`, update `energy_needed` to `minimum`. This ensures you have enough energy to begin the task.
Step 7: Add the `actual` energy spent to the `energy_needed`. This effectively accounts for the energy required to start and complete the task.
Step 8: After processing all tasks, return `energy_needed`. This is the minimum initial energy needed to complete all the tasks.

Key Insights

Insight 1: The key insight is realizing that the order in which we perform the tasks significantly affects the initial energy needed. A naive approach might not yield the optimal result.
Insight 2: Sorting the tasks based on the difference between the minimum energy required and the actual energy consumed (minimum - actual) is crucial. Tasks with a larger difference should be done earlier. This is because doing tasks with higher (minimum - actual) gives you more leeway on your starting energy to finish more tasks.
Insight 3: While processing the tasks, keep track of the energy needed. If the current energy is not enough to start a task, increase the initial energy needed to the minimum energy required for that task.

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(1)

Topics

This problem involves: Array, Greedy, Sorting.

Companies

Asked at: Akuna Capital.

Minimum Initial Energy to Finish Tasks | LeetCode 1665

Hard

Array Greedy Sorting

Time: O(n log n)Space: O(1)

Solution Code

Available in:

import java.util.Arrays;

class Solution {
    public int minimumEffort(int[][] tasks) {
        Arrays.sort(tasks, (a, b) -> (a[1] - a[0]) - (b[1] - b[0]));
        
        int energy_needed = 0;
        for (int[] task : tasks) {
            int actual = task[0];
            int minimum = task[1];
            energy_needed = Math.max(energy_needed + actual, minimum);
        }
        
        return energy_needed;
    }
}

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Problem Info

Description

Problem 1665: Minimum Initial Energy to Finish Tasks - Detailed explanation and solution approaches.

Topics

Array Greedy Sorting

Companies

Akuna Capital

Stats

Difficulty:Hard

Languages:4

Companies:1

Problem #:1665

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

8 steps

1
Step 1: Sort the tasks array. The sorting criteria is based on `minimum - actual` energy. Specifically, tasks with larger `minimum - actual` values should come first.
2
Step 2: Initialize `energy_needed` to 0. This variable will store the minimum initial energy required.
3
Step 3: Iterate through the sorted `tasks` array.
4
Step 4: For each `task` (consisting of `actual` and `minimum` energy):
5
Step 5: Determine if the current `energy_needed` is enough to start the task. This is done by comparing `energy_needed` with `minimum`.
6
Step 6: If `energy_needed` is less than `minimum`, update `energy_needed` to `minimum`. This ensures you have enough energy to begin the task.
7
Step 7: Add the `actual` energy spent to the `energy_needed`. This effectively accounts for the energy required to start and complete the task.
8
Step 8: After processing all tasks, return `energy_needed`. This is the minimum initial energy needed to complete all the tasks.

💡

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(n log n)

✨ Log-linear - Great for sorting algorithms!

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is determined by the sorting algorithm used. The `sort` function in Python, Java, and C++ typically use O(n log n) sorting algorithms. The space complexity is O(1) because the algorithm only uses a few extra variables, regardless of the input size. However, in C, an additional O(n) space is used because of malloc and free for the `Task` array.

📖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

Dynamic Programming

It may be possible to use dynamic programming by exploring different task orderings, but this will be less efficient and not feasible for the given constraints. DP would require trying all possible permutations which is O(n!).

Time: O(n!)Space: O(n)

Trade-offs: DP is far less efficient and will not work within the time limits.

✨

Key Insights

1Insight 1: The key insight is realizing that the order in which we perform the tasks significantly affects the initial energy needed. A naive approach might not yield the optimal result.
2Insight 2: Sorting the tasks based on the difference between the minimum energy required and the actual energy consumed (minimum - actual) is crucial. Tasks with a larger difference should be done earlier. This is because doing tasks with higher (minimum - actual) gives you more leeway on your starting energy to finish more tasks.
3Insight 3: While processing the tasks, keep track of the energy needed. If the current energy is not enough to start a task, increase the initial energy needed to the minimum energy required for that task.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Greedy Algorithm

Making the best choice at each step without looking ahead.

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: When all tasks have `actual` equal to `minimum`. In this case, the sorting will not change the order of tasks, and the algorithm will correctly calculate the sum of all `actual` values as the minimum energy needed.
Edge case 2: When all tasks have very large `minimum` values. The algorithm correctly handles this by ensuring that the initial energy needed is at least as large as the largest `minimum` value.
Edge case 3: When all tasks have `actual` equal to 1 and `minimum` equal to 10000. The sorting algorithm will correctly prioritize these tasks, because it has to begin with high energy.
Edge case 4: Empty input array. While the problem statement says `1 <= tasks.length`, it's good practice to consider an empty input `tasks = []`. In this case, the solution would return 0 which is correct.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not sorting the tasks based on the (minimum - actual) difference. A common mistake is to sort the tasks based on either the `actual` or the `minimum` value alone, which does not guarantee the optimal solution.

✗Common mistake 2: Incorrectly calculating the energy needed. A mistake is not updating the `energy_needed` when it's less than the `minimum` required for a task, leading to insufficient energy to complete the tasks.

✗Common mistake 3: Integer Overflow. When dealing with large number of tasks, and large actual and minimum energy needed, we have to be mindful of possible integer overflow issue.

✅

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: Task scheduling with resource constraints. For example, imagine scheduling jobs on a machine that needs a certain setup energy, and consumes a certain amount of energy. Jobs with a high 'setup' to 'usage' ratio should be prioritised.

🏦Real-world scenario 2: Resource allocation in project management. When allocating resources for different tasks in a project, prioritizing tasks with a higher 'entry barrier' (minimum requirement) compared to their actual resource consumption can minimize the initial resource requirement.

💡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

Hard problems often combine multiple techniques. Break the problem into sub-problems.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

👨‍💻 From Experience

I encountered a variation of this problem in a system design interview. The key was recognizing the underlying pattern.

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: July 16, 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

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 13

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 6

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

@InterviewProJun 29

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

What are common greedy problem patterns?

Activity selection (sort by end time), interval scheduling (sort by start/end), Huffman coding (always combine smallest), fractional knapsack (sort by value/weight ratio), and minimum spanning tree. Look for problems where local decisions don't affect future options.

Is it okay to not fully solve hard problems in interviews?

Yes! Interviewers care more about your problem-solving process than the final answer. Demonstrate: clear communication, systematic approach, ability to recognize when to pivot strategies, and graceful handling of hints. Partial progress with good reasoning is valued.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Minimum Initial Energy to Finish Tasks"?

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

🤖 Need help with this problem?