What is the time complexity of Button with Longest Push Time?

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

What data structures are used to solve Button with Longest Push Time?

This problem uses Array. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Button with Longest Push Time?

The problem requires iterating through the sorted `events` array and calculating the time difference between consecutive events to find the duration of each button press. Keeping track of the maximum time and the corresponding button index is crucial. We need to handle cases where multiple buttons have the same maximum time.

Which companies ask LeetCode 3386. Button with Longest Push Time in interviews?

This problem is frequently asked at J.P. Morgan.

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Button with Longest Push Time - LeetCode 3386 Solution

Button with Longest Push Time - Complete Solution Guide

Button with Longest Push Time is LeetCode problem 3386, a Easy 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 a 2D array events which represents a sequence of events where a child pushes a series of buttons on a keyboard. Each events[i] = [index i , time i ] indicates that the button at index index i was pressed at time time i . The array is sorted in increasing order of time . The time taken to press a button is the difference in time between consecutive button presses. The time for the first button is simply the time at which it was pressed. Return the index of the button that took the l

Detailed Explanation

The problem asks you to find the index of the button that was held down for the longest time. The input is a 2D array `events` where each inner array `[index_i, time_i]` represents a button press. `index_i` is the button's index, and `time_i` is the time it was pressed. The `events` array is sorted by `time_i`. The time a button is held is the difference between the current press time and the previous press time (or just the press time for the first press of a button). If multiple buttons have the same longest hold time, return the button with the smallest index.

Solution Approach

The solution uses a single pass through the `events` array. It initializes `max_time` and `max_index` with the time and index of the first event. Then, it iterates through the remaining events, calculating the time difference between consecutive events. If the time difference is greater than `max_time`, it updates `max_time` and `max_index`. If the time difference is equal to `max_time`, it updates `max_index` to the smaller of the current `max_index` and the current event's index. Finally, it returns `max_index`.

Step-by-Step Algorithm

Initialize `max_time` and `max_index` with the first event's time and index.
Iterate through the `events` array starting from the second event.
Calculate the time difference between the current event and the previous event.
If the time difference is greater than `max_time`, update `max_time` and `max_index` with the current event's time and index.
If the time difference is equal to `max_time`, update `max_index` to the minimum of `max_index` and the current event's index.
After iterating through all events, return `max_index`.

Key Insights

The problem requires iterating through the sorted `events` array and calculating the time difference between consecutive events to find the duration of each button press.
Keeping track of the maximum time and the corresponding button index is crucial. We need to handle cases where multiple buttons have the same maximum time.
The sorted nature of the input simplifies the calculation of time differences; we only need to consider adjacent events.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array.

Companies

Asked at: J.P. Morgan.

Button with Longest Push Time | LeetCode 3386

Easy

Array

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

Solution Code

Available in:

class Solution {
    public int buttonWithLongestTime(int[][] events) {
        int longestTime = events[0][1];
        int longestButton = events[0][0];
        for (int i = 1; i < events.length; i++) {
            int time = events[i][1] - events[i - 1][1];
            if (time > longestTime) {
                longestTime = time;
                longestButton = events[i][0];
            } else if (time == longestTime && events[i][0] < longestButton) {
                longestButton = events[i][0];
            }
        }
        return longestButton;
    }
}

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Problem Info

Description

Problem 3386: Button with Longest Push Time - Detailed explanation and solution approaches.

Topics

Array

Companies

J.P. Morgan

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:3386

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

6 steps

1
Initialize `max_time` and `max_index` with the first event's time and index.
2
Iterate through the `events` array starting from the second event.
3
Calculate the time difference between the current event and the previous event.
4
If the time difference is greater than `max_time`, update `max_time` and `max_index` with the current event's time and index.
5
If the time difference is equal to `max_time`, update `max_index` to the minimum of `max_index` and the current event's index.
6
After iterating through all events, return `max_index`.

💡

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)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The solution iterates through the `events` array once, performing constant-time operations in each iteration. No additional data structures proportional to the input size are used, hence the constant space complexity.

📖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

Using a HashMap

Store the button press times in a HashMap, where the key is the button index, and the value is a list of press times. Then, calculate the time differences for each button and find the maximum.

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

Trade-offs: This approach uses more space but offers no significant time complexity advantage. The provided solution is more efficient in terms of space.

✨

Key Insights

1The problem requires iterating through the sorted `events` array and calculating the time difference between consecutive events to find the duration of each button press.
2Keeping track of the maximum time and the corresponding button index is crucial. We need to handle cases where multiple buttons have the same maximum time.
3The sorted nature of the input simplifies the calculation of time differences; we only need to consider adjacent events.

📚

Key Terms Explained

For Students

Array

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

Edge Cases

Empty `events` array: The provided solutions handle this implicitly because they start with the first element; it's safe to assume there will always be at least one element.
All buttons having the same press time: The solution correctly handles this by prioritizing the button with the smallest index.

⚠️

Common Mistakes to Avoid

✗Forgetting to handle the case where multiple buttons have the same longest press time: Simply updating `max_index` without considering the minimum index would lead to incorrect results.

✗Incorrectly calculating the time difference: Failing to subtract the previous event's time from the current event's time will produce wrong results.

✅

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?

💼Analyzing user interaction data: Determining which buttons or features of a system are used most frequently or for the longest duration.

🏦Network traffic analysis: Identifying network connections or data transfers with the longest durations.

💡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

Don't rush. Explain your thought process clearly. Easy problems are often about communication.

⚠️ Watch Out

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

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: October 25, 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

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

@AlgoMasterJul 13

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

@InterviewProJul 6

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

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 "Button with Longest Push Time"?

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

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