What is the time complexity of Widest Vertical Area Between Two Points Containing No Points?

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

What data structures are used to solve Widest Vertical Area Between Two Points Containing No Points?

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

What are the key insights for solving Widest Vertical Area Between Two Points Containing No Points?

Insight 1: We only need to consider the x-coordinates of the points. The y-coordinates are irrelevant for determining the widest vertical area. Insight 2: Sorting the x-coordinates allows for efficient calculation of the maximum width between adjacent points. After sorting, the widest gap will represent the widest vertical area.

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Widest Vertical Area Between Two Points Containing No Points - LeetCode 1637 Solution

Q: Which companies ask LeetCode 1637. Widest Vertical Area Between Two Points Containing No Points in interviews?

This problem is frequently asked at General Motors.

Widest Vertical Area Between Two Points Containing No Points - Complete Solution Guide

Widest Vertical Area Between Two Points Containing No Points is LeetCode problem 1637, 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

Given n points on a 2D plane where points[i] = [x i , y i ] , Return the widest vertical area between two points such that no points are inside the area. A vertical area is an area of fixed-width extending infinitely along the y-axis (i.e., infinite height). The widest vertical area is the one with the maximum width. Note that points on the edge of a vertical area are not considered included in the area. Example 1: Input: points = [[8,7],[9,9],[7,4],[9,7]] Output: 1 Explanation: Both the red a

Detailed Explanation

The problem asks to find the widest vertical area between two points in a given set of points on a 2D plane, such that no other points are within this vertical area. A vertical area is defined as an area with a fixed width extending infinitely along the y-axis. Points exactly on the edges of the area are not considered to be inside the area. The input is a list of points, where each point is represented as a list/array of two integers [x, y]. The output is the maximum width of such a vertical area.

Solution Approach

The solution efficiently finds the widest vertical area by first extracting and sorting the x-coordinates of all points. Then, it iterates through the sorted x-coordinates, calculating the difference between consecutive coordinates and updating the maximum width found so far. This approach leverages sorting to significantly reduce the computational complexity.

Step-by-Step Algorithm

Step 1: Extract the x-coordinates from the input `points` array.
Step 2: Sort the extracted x-coordinates in ascending order.
Step 3: Initialize `maxWidth` to 0.
Step 4: Iterate through the sorted x-coordinates, calculating the difference between consecutive coordinates.
Step 5: Update `maxWidth` if the current difference is greater than the current `maxWidth`.
Step 6: Return the final `maxWidth`.

Key Insights

Insight 1: We only need to consider the x-coordinates of the points. The y-coordinates are irrelevant for determining the widest vertical area.
Insight 2: Sorting the x-coordinates allows for efficient calculation of the maximum width between adjacent points. After sorting, the widest gap will represent the widest vertical area.
Insight 3: The maximum width is determined by the largest difference between consecutive x-coordinates after sorting. This avoids nested loops and results in a more efficient solution.

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(n)

Topics

This problem involves: Array, Sorting.

Companies

Asked at: General Motors.

Widest Vertical Area Between Two Points Containing No Points | LeetCode 1637

Easy

Array Sorting

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

Solution Code

Available in:

import java.util.Arrays;

class Solution {
    public int maxWidthOfVerticalArea(int[][] points) {
        int n = points.length;
        int[] xCoordinates = new int[n];
        for (int i = 0; i < n; i++) {
            xCoordinates[i] = points[i][0];
        }
        Arrays.sort(xCoordinates);
        int maxWidth = 0;
        for (int i = 1; i < n; i++) {
            maxWidth = Math.max(maxWidth, xCoordinates[i] - xCoordinates[i - 1]);
        }
        return maxWidth;
    }
}

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Problem Info

Description

Problem 1637: Widest Vertical Area Between Two Points Containing No Points - Detailed explanation and solution approaches.

Topics

Array Sorting

Companies

General Motors

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:1637

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
Step 1: Extract the x-coordinates from the input `points` array.
2
Step 2: Sort the extracted x-coordinates in ascending order.
3
Step 3: Initialize `maxWidth` to 0.
4
Step 4: Iterate through the sorted x-coordinates, calculating the difference between consecutive coordinates.
5
Step 5: Update `maxWidth` if the current difference is greater than the current `maxWidth`.
6
Step 6: Return the final `maxWidth`.

💡

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(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The dominant operation is sorting the x-coordinates, which takes O(n log n) time in the average and worst cases using efficient sorting algorithms like merge sort or quicksort. Extracting the x-coordinates and iterating through them takes O(n) time. The space complexity is O(n) due to the creation of a new array to store the x-coordinates.

📖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

Compare every pair of points, calculate the width, and keep track of the maximum width. This involves nested loops.

Time: O(n^2)Space: O(1)

Trade-offs: This approach is significantly less efficient than the sorting-based solution, especially for larger input sizes. It's only practical for very small datasets.

✨

Key Insights

1Insight 1: We only need to consider the x-coordinates of the points. The y-coordinates are irrelevant for determining the widest vertical area.
2Insight 2: Sorting the x-coordinates allows for efficient calculation of the maximum width between adjacent points. After sorting, the widest gap will represent the widest vertical area.
3Insight 3: The maximum width is determined by the largest difference between consecutive x-coordinates after sorting. This avoids nested loops and results in a more efficient solution.

📚

Key Terms Explained

For Students

Array

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

Sorting

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

Edge Cases

Edge case 1: If there are only two points, the width is simply the absolute difference of their x-coordinates. The algorithm handles this correctly.
Edge case 2: If all points have the same x-coordinate, the widest vertical area is 0. The algorithm handles this gracefully because the difference between consecutive identical x-coordinates will be 0.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to sort the x-coordinates before calculating the differences. This will lead to an incorrect result.

✗Common mistake 2: Incorrectly handling the edge case where all points have the same x-coordinate. The result should be 0 in this case.

✅

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: Finding the maximum gap in a sequence of events, such as the largest time interval between consecutive customer arrivals at a store.

🏦Real-world scenario 2: Identifying the widest safe passage between obstacles in a 2D environment (like a robot navigating a warehouse).

💡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: June 18, 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 13

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

@CodeNinjaJul 6

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJun 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 should I learn from easy problems?

Easy problems introduce core patterns that appear in harder problems. Master basic operations (iteration, conditionals, simple data structures), recognize common patterns (counting, searching, basic transformations), and practice explaining your thought process clearly.

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 "Widest Vertical Area Between Two Points Containing No Points"?

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 sorting techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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