Leftmost Digit

最新推荐文章于 2017-07-08 15:49:12 发布

原创最新推荐文章于 2017-07-08 15:49:12 发布 · 679 阅读

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Description

Given a positive integer N, you should output the leftmost digit of N^N.

Input

The input contains several test cases. The first line of the input is a single integer T which is the number of test cases. T test cases follow.
Each test case contains a single positive integer N(1<=N<=1,000,000,000).

Output

For each test case, you should output the leftmost digit of N^N.

Sample Input

2
3
4

Sample Output

2
2

思路：题目要求的是n^n的最左边的数字，因为n的范围很大，直接求是不可能的，那么就要用一下数学的思想来转化。假设我们要求的是1234的最左边的数字，我们可以先转化为求1.234的整数位，怎么转化呢？因为log10(1234)-log(1000)=log10(1234。0/1000)=log10(1.234),呵呵，发现问题了吗？其中log10(1000)=(int)log(1234)。那么就有log10(1.234)=log10(1234)-(int)log(1234),最后就只需要求pow(10,log10(1.234))的整数位就好了。把n^n换回去又有log10(n^n)=nlog10(n)。
 
#include <stdio.h>
#include <math.h>

int main()
{
    int n,x;

    scanf("%d",&n);
    while(n--)
    {
        scanf("%d",&x);

        printf("%d\n",(int)pow(10,x*log10(x)-(__int64)(x*log10(x))));//x*log10(x) int可能会存不下
    }

    return 0;
}