[Swift]LeetCode483. 最小好进制 | Smallest Good Base

For an integer n,we call k>=2 a?good base?of n,if all digits of n base k are 1.

Now given a string representing n,you should return the smallest good base of n in string format.?

Example 1:

Input: "13"
Output: "3"
Explanation: 13 base 3 is 111.?

Example 2:

Input: "4681"
Output: "8"
Explanation: 4681 base 8 is 22222.?

Example 3:

Input: "1000000000000000000"
Output: "999999999999999999"
Explanation: 1000000000000000000 base 999999999999999999 is 11.?

Note:

1. The range of n is [3,10^18].
2. The string representing n is always valid and will not have leading zeros.

对于给定的整数 n,如果n的k（k>=2）进制数的所有数位全为1，则称?k（k>=2）是 n 的一个好进制。

以字符串的形式给出 n,以字符串的形式返回 n 的最小好进制。?

示例 1：

输入："13"
输出："3"
解释：13 的 3 进制是 111。

示例 2：

输入："4681"
输出："8"
解释：4681 的 8 进制是 22222。

示例 3：

输入："1000000000000000000"
输出："999999999999999999"
解释：1000000000000000000 的 999999999999999999 进制是 11。?

提示：

1. n的取值范围是?[3,10^18]。
2. 输入总是有效且没有前导 0。

12ms

 1 class Solution {
 2     func smallestGoodBase(_ n: String) -> String {
 3         var num:Int = Int(n)!
 4         for i in (2...(Int(log(Double(num + 1)) / log(2)))).reversed()
 5         {
 6             var left:Int = 2
 7             var right:Int = Int(pow(Double(num),1.0 / Double(i - 1))) + 1
 8             while (left < right)
 9             {
10                 var mid:Int = left + (right - left) / 2
11                 var sum:Int = 0
12                 for j in 0..<i
13                 {
14                     sum = sum * mid + 1
15                 }
16                 if sum == num {return String(mid)}
17                 else if sum < num {left = mid + 1}
18                 else {right = mid}
19             }
20         }
21         return String(num - 1)
22     }
23 }