Question

812. Largest Triangle Area

中文文档

Description

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.

Solutions

Solution 1

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

class Solution {
  public double largestTriangleArea(int[][] points) {
    double ans = 0;
    for (int[] p1 : points) {
      int x1 = p1[0], y1 = p1[1];
      for (int[] p2 : points) {
        int x2 = p2[0], y2 = p2[1];
        for (int[] p3 : points) {
          int x3 = p3[0], y3 = p3[1];
          int u1 = x2 - x1, v1 = y2 - y1;
          int u2 = x3 - x1, v2 = y3 - y1;
          double t = Math.abs(u1 * v2 - u2 * v1) / 2.0;
          ans = Math.max(ans, t);
        }
      }
    }
    return ans;
  }
}

class Solution {
public:
  double largestTriangleArea(vector<vector<int>>& points) {
    double ans = 0;
    for (auto& p1 : points) {
      int x1 = p1[0], y1 = p1[1];
      for (auto& p2 : points) {
        int x2 = p2[0], y2 = p2[1];
        for (auto& p3 : points) {
          int x3 = p3[0], y3 = p3[1];
          int u1 = x2 - x1, v1 = y2 - y1;
          int u2 = x3 - x1, v2 = y3 - y1;
          double t = abs(u1 * v2 - u2 * v1) / 2.0;
          ans = max(ans, t);
        }
      }
    }
    return ans;
  }
};

func largestTriangleArea(points [][]int) float64 {
  ans := 0.0
  for _, p1 := range points {
    x1, y1 := p1[0], p1[1]
    for _, p2 := range points {
      x2, y2 := p2[0], p2[1]
      for _, p3 := range points {
        x3, y3 := p3[0], p3[1]
        u1, v1 := x2-x1, y2-y1
        u2, v2 := x3-x1, y3-y1
        t := float64(abs(u1*v2-u2*v1)) / 2.0
        ans = math.Max(ans, t)
      }
    }
  }
  return ans
}

func abs(x int) int {
  if x < 0 {
    return -x
  }
  return x
}