Maximum Area Rectangle With Point Constraints I

Maximum Area Rectangle With Point Constraints I - Problem

Array Math Binary Indexed Tree Segment Tree Geometry Sorting Enumeration Medium

You are given an array points where points[i] = [xi, yi] represents the coordinates of a point on an infinite plane.

Your task is to find the maximum area of a rectangle that:

Can be formed using four of these points as its corners
Does not contain any other point inside or on its border
Has its edges parallel to the axes

Return the maximum area that you can obtain or -1 if no such rectangle is possible.

Input & Output

Example 1 — Valid Rectangle Found

$ Input: points = [[1,1],[1,3],[3,1],[3,3],[2,2]]

› Output: -1

💡 Note: Points [1,1], [1,3], [3,1], [3,3] could form a 2×2 rectangle with area 4, but point [2,2] is inside this rectangle, making it invalid. No other valid rectangles can be formed.

Example 2 — No Valid Rectangle

$ Input: points = [[1,1],[1,3],[3,1],[3,3],[2,2]]

› Output: -1

💡 Note: The only potential rectangle has point [2,2] inside it, making it invalid. No other combination of 4 points can form a valid rectangle.

Example 3 — Multiple Valid Rectangles

$ Input: points = [[1,1],[1,3],[3,1],[3,3],[4,4],[4,6],[6,4],[6,6]]

› Output: 4

💡 Note: Two valid rectangles: [1,1],[1,3],[3,1],[3,3] with area 4, and [4,4],[4,6],[6,4],[6,6] with area 4. Maximum area is 4.

Constraints

4 ≤ points.length ≤ 3000
-10⁵ ≤ xi, yi ≤ 10⁵
All points are distinct

Visualization

Tap to expand

Asked in

G Google 25 M Microsoft 18 a Amazon 15 f Meta 12

The key insight is to recognize that a valid rectangle needs exactly 4 corner points with no other points inside or on the border. The optimal approach uses diagonal pairs to reduce from O(n⁴) brute force to O(n³) by checking only O(n²) potential diagonal combinations. Time: O(n³), Space: O(n)

Common Approaches

✓ Backtracking

⏱️ Time: N/A Space: N/A

Brute Force - Check All Combinations

⏱️ Time: O(n⁴) Space: O(1)

For each combination of 4 points, check if they form a valid axis-aligned rectangle and verify no other points lie inside or on the border. Keep track of the maximum area found.

Sort and Sweep Optimization

⏱️ Time: O(n³) Space: O(n)

Sort points by coordinates and use sweep line technique to efficiently find potential rectangle pairs. For each pair of points that could form a diagonal, check if the other two corners exist and verify no points are inside.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

✓ Linear Space

8.4K Views

Medium Frequency

~35 min Avg. Time

245 Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen