Largest triangle area

Array Math Geometry

71.5% acceptance

Feb 22, 2026

844

1739

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.

Solution

Rust

Time O(n³)

Space O(1)

LeetCode

solution.rs

/*
 * 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.
 * Example 1:
 * 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.
 * Example 2:
 * Input: points = [[1,0],[0,0],[0,1]]
 * Output: 0.50000
 * Constraints:
 * 3 <= points.length <= 50
 * -50 <= xi, yi <= 50
 * All the given points are unique.
 */
impl Solution {
  pub fn largest_triangle_area(points: Vec<Vec<i32>>) -> f64 {
    let n = points.len();
    let mut ans = 0f64;
    for i in 0..n {
      for j in i+1..n {
        for k in j+1..n {
          let (ax,ay) = (points[i][0] as f64, points[i][1] as f64);
          let (bx,by) = (points[j][0] as f64, points[j][1] as f64);
          let (cx,cy) = (points[k][0] as f64, points[k][1] as f64);
          let area = ((ax*(by-cy) + bx*(cy-ay) + cx*(ay-by))/2.0).abs();
          ans = ans.max(area);
        }
      }
    }
    ans
  }
}