ZOJ.2277 The Gate to Freedom【数论-海伦】 2015/09/16-优快云博客

本文探讨了解开通往自由之门的数学谜题，并通过代码实现了解答过程。主要内容包括理解问题背景，分析输入输出规则，采用数学方法计算左数位数字，最后使用编程技巧实现解决方案。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

The Gate to Freedom

Time Limit: 2 Seconds Memory Limit: 32768 KB

Background

It is dark at night.
It is silence at night.
It is she in the dark.
It is she in the silence.

Then a light appeared. A huge gate came into our sights, called

The Gate to Freedom

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

Contest: A Great Beloved and My Gate to Freedom
There is a cx, there is a love_cx.

Author: JIANG, Yanyan

Source: JIANG, Yanyan's Contest #2

设n^n = x，两边同时取对数得n*log10(n) = log10(x)，取y=n*log10(n)，可知y的小数部分即为n^n最高位的对数。

#include<cstdio>
#include<cmath>

using namespace std;

int main(){
    long long n;
    while( ~scanf("%lld",&n) ){
        double ret = n*log10(n) - (int)(n*log10(n));
        ret = pow(10,ret);
        printf("%d\n",(int)ret);
    }
    return 0;
}