How do you solve Count Lattice Points Inside a Circle on LeetCode?

Count Lattice Points Inside a Circle (LeetCode #2249) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * r) time complexity and O(n * r) space complexity. Key insight: Understanding the geometry of circles helps in reducing unnecessary checks.

What is the brute force solution for Count Lattice Points Inside a Circle?

The brute force approach for Count Lattice Points Inside a Circle is Brute Force, with O(n * r²) time complexity and O(n * r²) space complexity. We can check each lattice point within the bounding box of each circle to see if it lies inside any circle. This approach is straightforward but inefficient as it checks many unnecessary points. The optimal Optimal Solution approach improves this to O(n * r).

What algorithm or data structure is used to solve Count Lattice Points Inside a Circle?

Count Lattice Points Inside a Circle uses the following concepts: Array, Hash Table, Math, Geometry, Enumeration. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Count Lattice Points Inside a Circle?

Always clarify the definition of lattice points with the interviewer. Discuss the bounding box approach to show your understanding of geometry. Mention edge cases like overlapping circles and how they affect counting.

What are common mistakes when solving Count Lattice Points Inside a Circle?

Not considering points on the circumference. Overlooking the need to check only within the bounding box.

#2249

Count Lattice Points Inside a Circle

Medium

ArrayHash TableMathGeometryEnumerationHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n * r)Space O(n * r)

Instead of checking every point in the bounding box, we can directly calculate the number of lattice points that lie within the circle using geometry. This reduces unnecessary checks and improves efficiency.

⚙️

Algorithm

5 steps

1Step 1: For each circle, calculate the bounding box as before.
2Step 2: For each integer x-coordinate in the bounding box, calculate the maximum y-coordinate that lies within the circle using the circle equation.
3Step 3: Count the integer y-coordinates from the minimum to the maximum for each valid x-coordinate.
4Step 4: Use a set to store unique lattice points to ensure no duplicates.
5Step 5: Return the size of the set as the result.

solution.py9 lines

1def countLatticePoints(circles):
2    points = set()
3    for x, y, r in circles:
4        for i in range(x - r, x + r + 1):
5            max_y = y + int((r ** 2 - (i - x) ** 2) ** 0.5)
6            min_y = y - int((r ** 2 - (i - x) ** 2) ** 0.5)
7            for j in range(min_y, max_y + 1):
8                points.add((i, j))
9    return len(points)

ℹ

Complexity note: This approach is more efficient because we only calculate the valid y-coordinates for each x-coordinate, reducing the number of checks significantly compared to the brute-force method.

1Understanding the geometry of circles helps in reducing unnecessary checks.
2Using sets ensures unique counting of lattice points.

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