How do you solve Find Maximum Area of a Triangle on LeetCode?

Find Maximum Area of a Triangle (LeetCode #3588) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Triangles with sides parallel to axes can be formed by grouping points.

What is the time complexity of Find Maximum Area of a Triangle?

The optimal solution for Find Maximum Area of a Triangle runs in O(n log n) time and uses O(n) space. We group points in O(n) and sort them, leading to O(n log n) complexity.

What is the brute force solution for Find Maximum Area of a Triangle?

The brute force approach for Find Maximum Area of a Triangle is Brute Force, with O(n²) time complexity and O(1) space complexity. We can check every combination of three points to see if they form a triangle with at least one side parallel to the axes. This method guarantees that we consider all possibilities. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Find Maximum Area of a Triangle?

Find Maximum Area of a Triangle uses the following concepts: Array, Hash Table, Math, Greedy, Geometry, Enumeration. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Find Maximum Area of a Triangle?

Explain your thought process clearly. Discuss edge cases, like when fewer than three points are provided. Practice coding similar geometric problems.

What are common mistakes when solving Find Maximum Area of a Triangle?

Forgetting to check if there are at least two points for base or height. Not considering all combinations when using brute force.

#3588

Find Maximum Area of a Triangle

Medium

ArrayHash TableMathGreedyGeometryEnumerationHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

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

We can optimize by grouping points based on their x and y coordinates. This allows us to quickly find potential triangles without checking every combination.

⚙️

Algorithm

3 steps

1Step 1: Group points by their x-coordinates and y-coordinates.
2Step 2: For each unique x and y, find the maximum and minimum y values to form potential triangles.
3Step 3: Calculate the area using the base and height derived from these points.

solution.py19 lines

1from collections import defaultdict
2
3def maxArea(coords):
4    x_map = defaultdict(list)
5    y_map = defaultdict(list)
6    for x, y in coords:
7        x_map[x].append(y)
8        y_map[y].append(x)
9    max_area = -1
10    for x in x_map:
11        if len(x_map[x]) >= 2:
12            y_values = sorted(x_map[x])
13            base = y_values[-1] - y_values[0]
14            for y in y_map:
15                if len(y_map[y]) >= 2:
16                    x_values = sorted(y_map[y])
17                    height = x_values[-1] - x_values[0]
18                    max_area = max(max_area, base * height)
19    return max_area if max_area != -1 else -1

ℹ

Complexity note: We group points in O(n) and sort them, leading to O(n log n) complexity.

1Triangles with sides parallel to axes can be formed by grouping points.
2Sorting y-values and x-values helps in quickly calculating base and height.

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