[leetcode]483. Smallest Good Base_xiaocong4681-优快云博客

本文链接：https://blog.youkuaiyun.com/xiaocong1990/article/details/77160066

本文介绍了一种算法，用于寻找一个给定整数n的最小良好进制，即找到最大的k，使得n在基k下的所有位都为1。通过解析LeetCode题目并提供解决方案，包括二分查找的方法来逼近答案。

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题目链接：https://leetcode.com/problems/smallest-good-base/description/

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 11111.

Example 3:

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

Note:

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

class Solution {
public:
    string smallestGoodBase(string n) {
        unsigned long long tn=(unsigned long long)stoll(n);
        unsigned long long x=1;
        for(int i=62;i>=1;i--)
        {
            if((x<<i)<tn)
            {
                unsigned long long cur=mysolve(tn,i);
                if(cur!=0) return to_string(cur);
            }
        }
        return to_string(tn-1);
    }
private:
    unsigned long long mysolve(unsigned long long n,int d)
    {
        
        unsigned long long right=(unsigned long long)(pow(n,1.0/d)+1);
        unsigned long long left=1;
        while(left<=right)
        {
            unsigned long long mid=left+(right-left)/2;
            unsigned long long sum=1,cur=1;
            for(int i=1;i<=d;i++)
            {
                cur*=mid;
                sum+=cur;
            }
            if(sum==n) return mid;
            if(sum>n) right=mid-1;
            else left=mid+1;
        }
        return 0;
    }
};