Is Maximum Number of Darts Inside of a Circular Dartboard easy or hard?

The problem is classified as Hard on LeetCode because it requires geometric reasoning rather than common algorithm templates. Candidates must derive circle centers from pairs of points and carefully handle precision when checking distances within radius r.

Maximum Number of Darts Inside of a Circular Dartboard Python/Java solution

Python and Java implementations usually iterate through every pair of points, compute the two possible circle centers with radius r, and count how many points lie inside each circle. Distance checks use the Euclidean formula with floating-point comparisons. The overall complexity is O(n^3) with constant extra space.

What is the best approach for Maximum Number of Darts Inside of a Circular Dartboard?

The most reliable approach computes circle centers defined by every pair of darts whose distance is at most 2r. Each pair produces up to two valid centers of a circle with radius r. Counting how many darts fall inside each candidate circle gives the maximum. This deterministic geometric approach runs in O(n^3) time and is widely accepted in interviews.

Is Maximum Number of Darts Inside of a Circular Dartboard asked at Google/Amazon/Meta?

Geometry-heavy problems like this appear in interviews at companies such as Google and Meta, especially for roles that emphasize algorithmic problem solving. It tests understanding of coordinate geometry, distance calculations, and careful floating-point handling rather than standard data structures alone.

What data structure is used in Maximum Number of Darts Inside of a Circular Dartboard?

The input is typically stored as an array of coordinate pairs. The main logic relies on geometric calculations such as Euclidean distance, midpoints, and perpendicular offsets. No complex data structures are required beyond iterating through the array and tracking counts.

What is the time complexity of Maximum Number of Darts Inside of a Circular Dartboard?

The standard geometric solution runs in O(n^3) time. You examine O(n^2) pairs of darts, compute up to two candidate circle centers, and count points inside the circle in O(n). Space complexity remains O(1) because only a few variables are used for distance and center calculations.

1453. Maximum Number of Darts Inside of a Circular Dartboard - Practice Online

Q: How to solve Maximum Number of Darts Inside of a Circular Dartboard in O(n)?

An exact deterministic O(n) algorithm is not known for the general case. However, randomized methods can approximate the optimal center by sampling candidate circle centers and counting points inside. Each iteration runs in O(n), and with enough samples the expected runtime becomes O(k·n) while producing near-optimal results.

Alice is throwing n darts on a very large wall. You are given an array darts where darts[i] = [x_i, y_i] is the position of the i^th dart that Alice threw on the wall.

Bob knows the positions of the n darts on the wall. He wants to place a dartboard of radius r on the wall so that the maximum number of darts that Alice throws lie on the dartboard.

Given the integer r, return the maximum number of darts that can lie on the dartboard.

Example 1:

Input: darts = [[-2,0],[2,0],[0,2],[0,-2]], r = 2
Output: 4
Explanation: Circle dartboard with center in (0,0) and radius = 2 contain all points.

Example 2:

Input: darts = [[-3,0],[3,0],[2,6],[5,4],[0,9],[7,8]], r = 5
Output: 5
Explanation: Circle dartboard with center in (0,4) and radius = 5 contain all points except the point (7,8).

Constraints:

1 <= darts.length <= 100
darts[i].length == 2
-10⁴ <= x_i, y_i <= 10⁴
All the darts are unique
1 <= r <= 5000