Largest Triangle Area - Leetcode Solution

The problem statement can be found on LeetCode

Problem Statement

Given an array of points in a 2D plane, find the maximum area of a triangle formed by any three of the points.

Solution

The problem at hand can be solved using the Shoelace formula. Given three points in the 2D plane denoted by (x1, y1), (x2, y2), and (x3, y3), the area of the triangle formed by these three points can be calculated using the Shoelace formula as:

area = 0.5 * | x1 * y2 + x2 * y3 + x3 * y1 - y1 * x2 - y2 * x3 - y3 * x1 |

The Shoelace formula calculates the area of the triangle formed by three points in the 2D plane using the determinant of a 3x3 matrix. The absolute value of the determinant is half the area of the triangle.

Using this formula, we can iterate through all possible combinations of three points from the array of points and find the maximum area.

Algorithm:

1. Initialize maxArea to 0.
2. Iterate through all possible combinations of three points from the array of points.
3. Calculate the area of the triangle formed by the three points using the Shoelace formula.
4. If this area is greater than maxArea, update maxArea with the new area.
5. Return maxArea.

Pseudo Code:

function largestTriangleArea(points): maxArea = 0 for i from 0 to n-3: for j from i+1 to n-2: for k from j+1 to n-1: x1, y1 = points[i] x2, y2 = points[j] x3, y3 = points[k] area = 0.5 * abs(x1 * y2 + x2 * y3 + x3 * y1 - y1 * x2 - y2 * x3 - y3 * x1) maxArea = max(maxArea, area) return maxArea

Time Complexity: O(n^3) Space Complexity: O(1)

As the time complexity of this algorithm is O(n^3), it may not be very efficient for a large number of points. However, for small inputs, this algorithm should work fine.

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