The Gate to Freedom （数学思维题）

ZOJ Problem Set - 2277
http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemCode=2277

Problem

There’re some words on the gate: “This gate will lead you to freedom. First, you have to open it. I have a problem for you to solve, if you answer it correctly, the gate will open!”

“Tell me, young boy, what is the leftmost digit of N^N?”

Input

This problem contains multiple test cases.

Each test case contains an integer N (N<=1,000,000,000).

Output

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

Sample Input

3
4

Sample Output

2
2

给你一个N，求N^N第一位数字是几。

这个题用lg10写。
比如5 = 10^lg5

首先：这个题可以换成所以 N^N = 10^N*lgN

其次：比如10^8.3 = 10⁸ * 10^0.3, 10⁸第一位就是1，所以第一位数是几取决于 10^0.3，算这个 10^0.3就行了。

代码如下：

#include <bits/stdc++.h>
#define ll long long
using namespace std;
int main()
{
    double n;
    while(scanf("%lf",&n)!=EOF)
    {
      double a = n*(log10(n));    如果对应上边那个例子，这个a = 5.8；
      ll b = (n*log10(n));                                b = 5;
      int x = (int)pow(10, a-b);                          10^0.8 就是结果了
      printf("%d\n",x);
    }
    return 0;
}