2017杭电多校联赛-Add More Zero 数学找公式_2017 muladd more zero-优快云博客

本文链接：https://blog.youkuaiyun.com/wang_heng199/article/details/76101599

Add More Zero

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 2245 Accepted Submission(s): 1053

Problem Description

There is a youngster known for amateur propositions concerning several mathematical hard problems.

Nowadays, he is preparing a thought-provoking problem on a specific type of supercomputer which has ability to support calculations of integers between

0 and

(2m−1) (inclusive).

As a young man born with ten fingers, he loves the powers of

10 so much, which results in his eccentricity that he always ranges integers he would like to use from

1 to

10k (inclusive).

For the sake of processing, all integers he would use possibly in this interesting problem ought to be as computable as this supercomputer could.

Given the positive integer

m , your task is to determine maximum possible integer

k that is suitable for the specific supercomputer.

Input

The input contains multiple test cases. Each test case in one line contains only one positive integer

m , satisfying

1≤m≤105 .

Output

For each test case, output " Case #

x :

y " in one line (without quotes), where

x indicates the case number starting from

1 and

y denotes the answer of corresponding case.

Sample Input

Sample Output

  
  
   
   Case #1: 0
Case #2: 19
  
  

题目大意：给你m，m满足有2^m-1>=10^k，询问最大k值为多少。

解题思路：有题，我们只需要求得最大k值，则可以列出下列公式：

因此代码就非常好写了。
#include <cstdio>
#include <iostream>
#include <cmath>
using namespace std;
int main()
{
	int m, k;
	int cas = 0;
	while(~scanf("%d", &m))
	{
         k = log10(2)*m;
		printf("Case #%d: %d\n", ++cas, k);
	}
	return 0;
}

题目链接：点击打开链接http://acm.hdu.edu.cn/contests/contest_showproblem.php?pid=1001&cid=759