[Swift]LeetCode812. 最大三角形面积 | Largest Triangle Area

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You have a list of points in the plane. Return the area of the largest triangle that can be formed by any 3 of the points.

Example:
Input: points = [[0,0],[0,1],[1,0],[0,2],[2,0]]
Output: 2
Explanation: 
The five points are show in the figure below. The red triangle is the largest.

Notes:

• 3 <= points.length <= 50.
• No points will be duplicated.
•  -50 <= points[i][j] <= 50.
• Answers within 10^-6 of the true value will be accepted as correct.

---

给定包含多个点的集合，从其中取三个点组成三角形，返回能组成的最大三角形的面积。

示例:
输入: points = [[0,0],[0,1],[1,0],[0,2],[2,0]]
输出: 2
解释: 
这五个点如下图所示。组成的橙色三角形是最大的，面积为2。

注意:

• 3 <= points.length <= 50.
• 不存在重复的点。
•  -50 <= points[i][j] <= 50.
• 结果误差值在 10^-6 以内都认为是正确答案。

---

24ms

class Solution {
    func largestTriangleArea(_ points: [[Int]]) -> Double {
        var res:Double = 0
        for i in points
        {
            for j in points
            {
                for k in points
                {
                    res = max(res, 0.5 * fabs(Double(i[0] * j[1] + j[0] * k[1] + k[0] * i[1] - j[0] * i[1] - k[0] * j[1] - i[0] * k[1])))
                }
            }
        }
        return res
    }
}

---

24ms

class Solution {
    func largestTriangleArea(_ points: [[Int]]) -> Double {
        
        var result = 0.0
        for i in 0..<points.count {
            for j in i+1..<points.count {
                for k in j+1..<points.count {
                    result = max(result, area(points[i], points[j], points[k]))
                }
            }
        }
        return result
    }
    
    fileprivate func area(_ a:[Int], _ b: [Int], _ c:[Int]) -> Double {
                
        
            return 0.5 * abs(Double(a[0] * b[1] + b[0] * c[1] + c[0] * a[1]) -
                             Double(a[1] * b[0] + b[1] * c[0] + c[1] * a[0]) )
    }
}

---

36ms

class Solution {
    func largestTriangleArea(_ points: [[Int]]) -> Double {
        var maxA = 0.0
        for i in 0..<points.count - 2 {
            for j in (i + 1)..<points.count - 1 {
                for k in (j + 1)..<points.count {
                    maxA = max(maxA, area(points[i], points[j], points[k]))
                }
            }
        }
        return maxA
    }
    
    func area(_ point1: [Int], _ point2: [Int], _ point3: [Int]) -> Double {
        let x1 = point1[0]
        let y1 = point1[1]
        let x2 = point2[0]
        let y2 = point2[1]
        let x3 = point3[0]
        let y3 = point3[1]
        return abs(0.5*Double(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2)))
    }
}

---

40ms

class Solution {
    func largestTriangleArea(_ points: [[Int]]) -> Double {
        var maxArea = 0.0
        
        let cnt = points.count
        if cnt < 3 {
            return 0
        }

        for i in 0..<cnt-2 {
            for j in i+1..<cnt-1 {
                for k in j+1..<cnt {
                    let x1 = points[i][0]
                    let y1 = points[i][1]
                    
                    let x2 = points[j][0]
                    let y2 = points[j][1]
                    
                    let x3 = points[k][0]
                    let y3 = points[k][1]
                    
                    let temp = (x2-x1)*(y3-y1)-(x3-x1)*(y2-y1)
                    let area = abs(0.5*Double(temp))

                    maxArea = max(maxArea, area)
                }
            }
        }

        return maxArea
    }
}

---

88ms

class Solution {

    let x = 0
    let y = 1

    func largestTriangleArea(_ points: [[Int]]) -> Double {
        var ans = 0.0
        for x in stride(from: 0, through: points.count - 3, by: 1) {
            for y in stride(from: x + 1, through: points.count - 2, by: 1) {
                for z in stride(from: y + 1, through: points.count - 1, by: 1) {
                    let array = [points[x], points[y], points[z]]
                    ans = max(ans, area(array))
                }
            }
        }
        return ans
    }

    private func area(_ points: [[Int]]) -> Double {
        var ans = points[0][x] * points[1][y]
        ans += points[1][x] * points[2][y]
        ans += points[2][x] * points[0][y]

        ans -= points[0][y] * points[1][x]
        ans -= points[1][y] * points[2][x]
        ans -= points[2][y] * points[0][x]

        return abs(0.5 * Double(ans))
    }
}

---

100ms

class Solution {
    func area(_ x:[Int], _ y:[Int], _ z:[Int] ) -> Double{
        let a = Double(x[0]*y[1])
        let b = Double(y[0]*z[1])
        let c = Double(z[0]*x[1])
        let d = Double(x[0]*z[1])
        let e = Double(y[0]*x[1])
        let f = Double(z[0]*y[1])
        let g = a + b + c - d - e - f
        return 0.5 * g
    }
    func largestTriangleArea(_ points: [[Int]]) -> Double {
        var res:Double = 0
        for i in 0..<points.count {
            for j in 0..<points.count{
                if i == j {
                    continue
                }
                for k in (j+1)..<points.count{
                    if (k == i || k == j){
                        continue
                    }
                    let temp:Double = area(points[i], points[j], points[k])
                    if res < temp {
                        res = temp
                    }                    
                }
            }
        }
        
        return res
    }
}