How do you solve Coordinate With Maximum Network Quality on LeetCode?

Coordinate With Maximum Network Quality (LeetCode #1620) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * r²) time complexity and O(n) space complexity. Key insight: Focus on the relevant area around the towers instead of all coordinates.

What is the brute force solution for Coordinate With Maximum Network Quality?

The brute force approach for Coordinate With Maximum Network Quality is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves checking every possible coordinate within the bounds defined by the towers and calculating the network quality for each. This method is straightforward but inefficient for larger inputs. The optimal Optimal Solution approach improves this to O(n * r²).

What algorithm or data structure is used to solve Coordinate With Maximum Network Quality?

Coordinate With Maximum Network Quality uses the following concepts: Array, Enumeration. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Coordinate With Maximum Network Quality?

Clarify the constraints and edge cases before diving into coding. Think aloud to show your thought process and reasoning. Test your solution with multiple examples to ensure correctness.

What are common mistakes when solving Coordinate With Maximum Network Quality?

Not considering the lexicographical order when updating best coordinates. Failing to check all reachable coordinates based on the radius.

#1620

Coordinate With Maximum Network Quality

Medium

ArrayEnumerationHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n * r²)
Space	O(1)	O(n)

💡

Intuition

Time O(n * r²)Space O(n)

The optimal solution leverages the fact that we only need to consider coordinates that are directly influenced by the towers. Instead of checking every coordinate, we can focus on the tower locations and their immediate surroundings, significantly reducing the number of calculations.

⚙️

Algorithm

4 steps

1Step 1: Initialize a map to store the quality at each coordinate that we will calculate.
2Step 2: For each tower, calculate its influence on its surrounding coordinates within the radius.
3Step 3: For each coordinate influenced by a tower, update the quality based on the tower's quality and distance.
4Step 4: After processing all towers, find the coordinate with the maximum quality, ensuring to return the lexicographically smallest one in case of ties.

solution.py16 lines

1def maxNetworkQuality(towers, radius):
2    from collections import defaultdict
3    quality_map = defaultdict(int)
4    for tx, ty, tq in towers:
5        for x in range(tx - radius, tx + radius + 1):
6            for y in range(ty - radius, ty + radius + 1):
7                d = ((tx - x) ** 2 + (ty - y) ** 2) ** 0.5
8                if d <= radius:
9                    quality_map[(x, y)] += tq // (1 + d)
10    max_quality = -1
11    best_coordinate = None
12    for (x, y), quality in quality_map.items():
13        if quality > max_quality or (quality == max_quality and (best_coordinate is None or (x, y) < best_coordinate)):
14            max_quality = quality
15            best_coordinate = (x, y)
16    return list(best_coordinate)

ℹ

Complexity note: The time complexity is O(n * r²) because for each tower, we check all coordinates within a square of side length 2 * radius. The space complexity is O(n) due to the storage of quality values in a map.

1Focus on the relevant area around the towers instead of all coordinates.
2Use a map to efficiently accumulate quality scores.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.