[LeetCode] 483. Smallest Good Base

https://leetcode.com/problems/smallest-good-base

关于 base 的概念：

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

Input: "4681"
Output: "8"
Explanation: 4681 base 8 is 11111.

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

13 = (1 * 3 + 1) * 3 + 1

4681 = (((1 * 8 + 1) * 8 + 1) * 8 + 1) * 8 + 1

用 getResultOfBase 求出这个 base 所能构成的 good base，和目标值比较，二分查找。

 

public class Solution {
    
    public String smallestGoodBase(String n) {
        Long num = Long.parseLong(n);
        int times = (int)(Math.log(num) / Math.log(2) + 1);
        for (int i = times; i >= 2; i--) {
            Long start = 2L;
            Long end = (long)Math.pow(num, 1.0 / i); // was num/2, failed case: 2251799813685247
            while (start <= end) {
                Long mid = start + (end - start) / 2;
                Long target = getResultOfBase(mid, i);
                int retval = target.compareTo(num);
                if (retval == 0) { // was target == num, failed case: 3541
                    return Long.toString(mid);
                } else if (retval > 0) {
                    end = mid - 1;
                } else {
                    start = mid + 1;
                }
            }
        }
        return Long.toString(num - 1);
    }
    
    private Long getResultOfBase(Long base, int times) {
        Long current = 1L;
        for (int i = 0; i < times; i++) {
            current = current * base + 1;
        }
        return current;
    }
    
}