What is the time complexity of Coordinate With Maximum Network Quality?

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

What data structures are used to solve Coordinate With Maximum Network Quality?

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

What are the key insights for solving Coordinate With Maximum Network Quality?

Insight 1: The problem is essentially a brute-force search within a limited coordinate space (0 to 50 for both x and y). Since the constraints are small (maximum coordinate value is 50), iterating through all possible coordinates is feasible. Insight 2: We need to efficiently calculate the Euclidean distance between a candidate coordinate and each tower, and determine if the tower is within the given radius.

Which companies ask LeetCode 1620. Coordinate With Maximum Network Quality in interviews?

This problem is frequently asked at Lyft, peak6.

JavaScript is required for the full interactive experience. However, all content is accessible without JavaScript.

Coordinate With Maximum Network Quality - LeetCode 1620 Solution

Coordinate With Maximum Network Quality - Complete Solution Guide

Coordinate With Maximum Network Quality is LeetCode problem 1620, 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

You are given an array of network towers towers , where towers[i] = [x i , y i , q i ] denotes the i th network tower with location (x i , y i ) and quality factor q i . All the coordinates are integral coordinates on the X-Y plane, and the distance between the two coordinates is the Euclidean distance . You are also given an integer radius where a tower is reachable if the distance is less than or equal to radius . Outside that distance, the signal becomes garbled, and the tower is not reachabl

Detailed Explanation

The problem asks us to find the coordinate (cx, cy) on the X-Y plane that maximizes the network quality, given a list of network towers with their locations (xi, yi) and quality factors qi, and a radius. The network quality at a coordinate (x, y) is the sum of the signal qualities from all reachable towers. A tower is reachable if its distance to the coordinate is less than or equal to the given radius. The signal quality of a tower at a coordinate is calculated as floor(qi / (1 + d)), where d is the Euclidean distance between the tower and the coordinate. If multiple coordinates have the same maximum network quality, we must return the lexicographically smallest non-negative coordinate. The constraints specify the ranges for the tower counts, coordinates, quality factors, and the radius.

Solution Approach

The solution iterates through all possible integral coordinates (cx, cy) from (0, 0) to (50, 50). For each coordinate, it calculates the network quality by iterating through all the towers. For each tower, it calculates the squared distance to the current coordinate. If the squared distance is within the squared radius, the signal quality is calculated and added to the total network quality for that coordinate. After calculating the network quality for each coordinate, the solution compares it to the current maximum quality and updates the best coordinate if the current quality is higher or if it's the same but lexicographically smaller.

Step-by-Step Algorithm

Step 1: Initialize `max_quality` to -1 and `best_coord` to [0, 0].
Step 2: Iterate through all possible coordinates (cx, cy) where cx ranges from 0 to 50 and cy ranges from 0 to 50.
Step 3: For each coordinate (cx, cy), initialize `current_quality` to 0.
Step 4: Iterate through all towers.
Step 5: For each tower (tx, ty, q), calculate the squared Euclidean distance d_sq between (cx, cy) and (tx, ty).
Step 6: If d_sq is less than or equal to the squared radius, calculate the signal quality signal = floor(q / (1 + sqrt(d_sq))).
Step 7: Add signal to `current_quality`.
Step 8: After iterating through all towers, compare `current_quality` with `max_quality`.
Step 9: If `current_quality` is greater than `max_quality`, update `max_quality` to `current_quality` and `best_coord` to [cx, cy].
Step 10: After iterating through all possible coordinates, return `best_coord`.

Key Insights

Insight 1: The problem is essentially a brute-force search within a limited coordinate space (0 to 50 for both x and y). Since the constraints are small (maximum coordinate value is 50), iterating through all possible coordinates is feasible.
Insight 2: We need to efficiently calculate the Euclidean distance between a candidate coordinate and each tower, and determine if the tower is within the given radius.
Insight 3: Remember to use the floor function when calculating the signal quality. Handle lexicographical ordering correctly when updating the best coordinate.

Complexity Analysis

Time Complexity: O(N)

Space Complexity: O(1)

Topics

This problem involves: Array, Enumeration.

Companies

Asked at: Lyft, peak6.

Coordinate With Maximum Network Quality | LeetCode 1620

Medium

Array Enumeration

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

Solution Code

Available in:

class Solution {
    public int[] bestCoordinate(int[][] towers, int radius) {
        int max_quality = -1;
        int[] best_coord = {0, 0};
        
        int radius_sq = radius * radius;

        for (int cx = 0; cx <= 50; cx++) {
            for (int cy = 0; cy <= 50; cy++) {
                int current_quality = 0;
                for (int[] tower : towers) {
                    int tx = tower[0];
                    int ty = tower[1];
                    int q = tower[2];
                    int d_sq = (cx - tx) * (cx - tx) + (cy - ty) * (cy - ty);
                    if (d_sq <= radius_sq) {
                        double d = Math.sqrt(d_sq);
                        int signal = (int) Math.floor(q / (1 + d));
                        current_quality += signal;
                    }
                }
                
                if (current_quality > max_quality) {
                    max_quality = current_quality;
                    best_coord[0] = cx;
                    best_coord[1] = cy;
                }
            }
        }
        
        return best_coord;
    }
}

View Full Solution on GitHubGitHub Solution View on LeetCodeLeetCode

Problem Info

Description

Problem 1620: Coordinate With Maximum Network Quality - Detailed explanation and solution approaches.

Topics

Array Enumeration

Companies

Lyftpeak6

Stats

Difficulty:Medium

Languages:4

Companies:2

Problem #:1620

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

10 steps

1
Step 1: Initialize `max_quality` to -1 and `best_coord` to [0, 0].
2
Step 2: Iterate through all possible coordinates (cx, cy) where cx ranges from 0 to 50 and cy ranges from 0 to 50.
3
Step 3: For each coordinate (cx, cy), initialize `current_quality` to 0.
4
Step 4: Iterate through all towers.
5
Step 5: For each tower (tx, ty, q), calculate the squared Euclidean distance d_sq between (cx, cy) and (tx, ty).
6
Step 6: If d_sq is less than or equal to the squared radius, calculate the signal quality signal = floor(q / (1 + sqrt(d_sq))).
7
Step 7: Add signal to `current_quality`.
8
Step 8: After iterating through all towers, compare `current_quality` with `max_quality`.
9
Step 9: If `current_quality` is greater than `max_quality`, update `max_quality` to `current_quality` and `best_coord` to [cx, cy].
10
Step 10: After iterating through all possible coordinates, return `best_coord`.

💡

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)

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The outer loops iterate through a fixed range of 0 to 50 for both x and y coordinates. This gives a fixed number of iterations. The inner loop iterates through the towers array. Therefore, the dominant factor is the number of towers. Since the problem states towers.length <= 50, this is essentially a constant. Consequently, Time complexity O(N), Space Complexity O(1)

📖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

Optimization with Bounding Box

Instead of iterating through all coordinates from 0 to 50, determine the bounding box encompassing all towers (min/max x and y). Then, expand this bounding box by the radius and iterate only within this smaller region. This could be more efficient if the towers are clustered in a smaller area than the entire 0-50 range.

Time: O(M*N), where M is the area of the bounding box expanded by the radius and N is the number of towers.Space: O(1)

Trade-offs: This approach can be faster if the towers are localized. However, it adds overhead to calculate the bounding box. In the worst case (towers spread across the entire grid), it becomes similar to the original approach. It can be beneficial when the coordinates of the towers are not distributed evenly across the space from 0-50.

✨

Key Insights

1Insight 1: The problem is essentially a brute-force search within a limited coordinate space (0 to 50 for both x and y). Since the constraints are small (maximum coordinate value is 50), iterating through all possible coordinates is feasible.
2Insight 2: We need to efficiently calculate the Euclidean distance between a candidate coordinate and each tower, and determine if the tower is within the given radius.
3Insight 3: Remember to use the floor function when calculating the signal quality. Handle lexicographical ordering correctly when updating the best coordinate.

📚

Key Terms Explained

For Students

Array

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

Edge Cases

Edge case 1: Empty towers array. The code handles this gracefully because the inner loop won't execute, and the initial best_coord [0, 0] will be returned.
Edge case 2: Single tower. The code correctly calculates the quality based on that single tower and updates the best_coord.
Edge case 3: Multiple coordinates having same maximum quality. The code inherently handles this using the `>` comparison. Because the outer loop is nested from left to right, if there are multiple valid coordinates with the same quality, the first smallest coordinate will be automatically selected.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not squaring the radius and distance. You can optimize the code by comparing the squared distance with the squared radius. Avoid using the square root unless necessary as it is computationally expensive.

✗Common mistake 2: Not using the floor function. The problem explicitly states to use the floor function for signal quality. Forgetting this will lead to incorrect results.

✗Common mistake 3: Not considering lexicographical order. If multiple coordinates result in the same maximum quality, the lexicographically smallest one must be returned. The problem provides details on what lexicographically smaller means, so this is important to remember.

✅

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: Cell Tower Placement: This problem models a simplified version of cell tower placement. Optimizing network quality by strategically placing cell towers to maximize signal strength for users is a key application.

🏦Real-world scenario 2: Wi-Fi Hotspot Optimization: Finding the best location for a Wi-Fi router in a building to maximize signal coverage and quality for users in different rooms.

💡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

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ Watch Out

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

👨‍💻 From Experience

This problem pattern appears frequently in real codebases. I've used similar logic when building production systems.

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 1, 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

❓

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.

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 "Coordinate With Maximum Network Quality"?

For this medium-level Array 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.

🤖 Need help with this problem?