[Swift]LeetCode441. 排列硬币 | Arranging Coins

★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★
➤微信公众号：山青咏芝（shanqingyongzhi）
➤博客园地址：山青咏芝（https://www.cnblogs.com/strengthen/）
➤GitHub地址：https://github.com/strengthen/LeetCode
➤原文地址：https://www.cnblogs.com/strengthen/p/10339427.html 
➤如果链接不是山青咏芝的博客园地址，则可能是爬取作者的文章。
➤原文已修改更新！强烈建议点击原文地址阅读！支持作者！支持原创！
★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★

热烈欢迎，请直接点击！！！

进入博主App Store主页，下载使用各个作品！！！

注：博主将坚持每月上线一个新app！！！

You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins.

Given n, find the total number of fullstaircase rows that can be formed.

n is a non-negative integer and fits within the range of a 32-bit signed integer.

Example 1:

n = 5

The coins can form the following rows:
¤
¤ ¤
¤ ¤

Because the 3rd row is incomplete, we return 2. 

Example 2:

n = 8

The coins can form the following rows:
¤
¤ ¤
¤ ¤ ¤
¤ ¤

Because the 4th row is incomplete, we return 3.

---

你总共有 n 枚硬币，你需要将它们摆成一个阶梯形状，第 k 行就必须正好有 k 枚硬币。

给定一个数字 n，找出可形成完整阶梯行的总行数。

n 是一个非负整数，并且在32位有符号整型的范围内。

示例 1:

n = 5

硬币可排列成以下几行:
¤
¤ ¤
¤ ¤

因为第三行不完整，所以返回2.

示例 2:

n = 8

硬币可排列成以下几行:
¤
¤ ¤
¤ ¤ ¤
¤ ¤

因为第四行不完整，所以返回3.

---

20ms

class Solution {
    func arrangeCoins(_ n: Int) -> Int {
        return Int((-1 + sqrt(Double(1 + 8 * n))) / 2)
    }
}

---

28ms

class Solution {
    func arrangeCoins(_ n: Int) -> Int {
            guard n > 1 else {
        return n
    }
    var index = n, lhs = 0, rhs = n, mid = 0
    while lhs < rhs {
        mid = (rhs + lhs) / 2
        let result = (1 + mid) * mid / 2
        if result == n {
            return mid
        } else if result > n {
            rhs = mid
        } else {
            lhs = mid + 1
        }
    }
    return lhs - 1
    }
}

---

36ms

class Solution {
    func arrangeCoins(_ n: Int) -> Int {
        var left = 1
        var right = n

        while left <= right {
            let mid = left + (right - left) / 2
            if n * 2 < mid * (mid + 1) {
                right = mid - 1
            } else {
                left = mid + 1
            }
        }

        return left - 1
    }
}

---

52ms

class Solution {
    func arrangeCoins(_ n: Int) -> Int {
        var result = Int(sqrt(Double(n * 2))) - 1
        while result * (result + 1) / 2 <= n {
            result += 1
        }
        return result - 1
    }    
}

---

80ms

class Solution {
    func arrangeCoins(_ n: Int) -> Int {
        var row = 1
        var sum = row
        while true {
            if sum == n {
                return row
            } else if sum > n {
                return row - 1
            }
            row += 1
            sum += row
        }
    }
}

---

176ms

class Solution {
    func arrangeCoins(_ n: Int) -> Int {
    return self.lineCoins(n, 1)
    }
        func lineCoins(_ n: Int, _ line: Int) -> Int {
        if n<line {
            return line-1
        }
        return lineCoins(n-line, line+1);
    }
}

---

204ms

class Solution {
    func arrangeCoins(_ n: Int) -> Int {
        if n == 0 || n == 1 {
            return n
        }
        for value in 1...n {
            if Double((1 + value) * value) * 0.5 > Double(n) {
                return (value - 1)
            }
        }
        return 0
    }
}