Leetcode #812: Largest Triangle Area
In this guide, we solve Leetcode #812 Largest Triangle Area in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given an array of points on the X-Y plane points where points[i] = [xi, yi], return the area of the largest triangle that can be formed by any three different points. Answers within 10-5 of the actual answer will be accepted.
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Geometry, Array, Math
Intuition
There is a mathematical invariant or formula that directly leads to the result.
Using math avoids unnecessary loops and reduces complexity.
Approach
Derive the formula or update rule, then compute the answer directly.
Handle edge cases like overflow or zero carefully.
Steps:
- Identify the math relationship.
- Compute the result with a loop or formula.
- Handle edge cases.
Example
Input: points = [[0,0],[0,1],[1,0],[0,2],[2,0]]
Output: 2.00000
Explanation: The five points are shown in the above figure. The red triangle is the largest.
Python Solution
class Solution:
def largestTriangleArea(self, points: List[List[int]]) -> float:
ans = 0
for x1, y1 in points:
for x2, y2 in points:
for x3, y3 in points:
u1, v1 = x2 - x1, y2 - y1
u2, v2 = x3 - x1, y3 - y1
t = abs(u1 * v2 - u2 * v1) / 2
ans = max(ans, t)
return ans
Complexity
The time complexity is , where is the number of points. The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.