How do you solve Maximize the Distance Between Points on a Square on LeetCode?

Maximize the Distance Between Points on a Square (LeetCode #3464) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: Manhattan distance is additive and can be optimized using sorting.

What is the time complexity of Maximize the Distance Between Points on a Square?

The optimal solution for Maximize the Distance Between Points on a Square runs in O(n log n) time and uses O(1) space. Sorting the points takes O(n log n), and the binary search with checks takes O(n), leading to an overall efficient solution.

What is the brute force solution for Maximize the Distance Between Points on a Square?

The brute force approach for Maximize the Distance Between Points on a Square is Brute Force, with O(n²) time complexity and O(1) space complexity. Select all combinations of k points and calculate the minimum Manhattan distance for each combination. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximize the Distance Between Points on a Square?

Maximize the Distance Between Points on a Square uses the following concepts: Array, Math, Binary Search, Geometry, Sorting. The recommended patterns to study are: Binary Search, Greedy.

What are the interview tips for Maximize the Distance Between Points on a Square?

Explain your thought process clearly. Discuss edge cases and constraints. Practice similar problems to build intuition.

What are common mistakes when solving Maximize the Distance Between Points on a Square?

Not considering all points on the boundary. Failing to check distance properly during selection.

#3464

Maximize the Distance Between Points on a Square

Hard

ArrayMathBinary SearchGeometrySortingBinary SearchGreedy

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n log n)Space O(1)

Use binary search to find the maximum possible minimum Manhattan distance. This reduces the number of combinations we need to check.

⚙️

Algorithm

3 steps

1Step 1: Sort points based on their coordinates in a clockwise manner around the square.
2Step 2: Use binary search to determine the maximum minimum distance, checking if it's possible to select k points with at least that distance apart.
3Step 3: For each distance in the binary search, use a greedy approach to select points that satisfy the distance condition.

solution.py15 lines

1def max_min_distance_optimal(side, points, k):
2    points.sort(key=lambda p: (p[0], p[1]))
3    def can_place(distance):
4        count, last = 1, points[0]
5        for i in range(1, len(points)):
6            if abs(points[i][0] - last[0]) + abs(points[i][1] - last[1]) >= distance:
7                count += 1
8                last = points[i]
9        return count >= k
10    low, high = 0, 2 * side
11    while low < high:
12        mid = (low + high + 1) // 2
13        if can_place(mid): low = mid
14        else: high = mid - 1
15    return low

ℹ

Complexity note: Sorting the points takes O(n log n), and the binary search with checks takes O(n), leading to an overall efficient solution.

1Manhattan distance is additive and can be optimized using sorting.
2Binary search helps efficiently narrow down the maximum minimum distance.

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