483. Smallest Good Base

本文介绍了一种寻找整数n的最小良好基数的算法实现。该算法通过计算确定能够表示给定整数n的最短良好基数。良好基数定义为一种基数表示法,使得整数n可以被表示为一系列1组成的数(例如,在基数k下,n表示为11...1)。文章提供了详细的Python代码实现,并解释了核心计算逻辑。

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http://blog.youkuaiyun.com/hanzheng992/article/details/54879692

class Solution(object):
    def smallestGoodBase(self, n):
        """
        :type n: str
        :rtype: str
        """        
        num = int(n)
        thisLen = int(math.log(num,2)) + 1
        while thisLen > 2:
            # from equation [3], we havve
            thisBase = int(num ** (1.0/(thisLen - 1)))
            # from equation [2], we have
            if num * (thisBase - 1) == thisBase ** thisLen - 1:
                return str(thisBase)
            thisLen -= 1
        return str(num - 1)

题目: Problem Statement There are N houses numbered from 1 to N on a number line. House i is located at coordinate X i ​ . Multiple houses may be located at the same coordinate. You place M base stations at arbitrary real coordinates on the number line. Then, you set a non-negative integer signal strength for each base station. When the signal strength of a base station is set to x, The signal from that base station reaches a house if and only if the distance between the base station and the house is at most 2 x ​ . Particularly, when x=0, the signal reaches only houses located at the same coordinate as the base station. Find the minimum possible sum of signal strengths when the positions and signal strengths of the base stations are set such that at least one base station's signal reaches every house. It can be proved that the answer is an integer for any input satisfying the constraints. Constraints 1≤M≤N≤5×10 5 1≤X i ​ ≤10 12 ( 1≤i≤N) All input values are integers. Input The input is given from Standard Input in the following format: N M X 1 ​ … X N ​ Output Output the answer as an integer in one line. Sample Input 1 Copy 7 3 5 10 15 20 8 14 15 Sample Output 1 Copy 6 By placing three base stations as follows, signals reach all houses. Place a base station with signal strength 5 at coordinate 7.5. This base station reaches houses 1,2,5. Place a base station with signal strength 1 at coordinate 14.5. This base station reaches houses 3,6,7. Place a base station with signal strength 0 at coordinate 20. This base station reaches house 4. The sum of signal strengths in this case is 6. It is impossible to satisfy the condition with an arrangement where the sum of signal strengths is smaller than 6, so output 6. 如何用c++在1s内解决
07-13
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