HDOJ-1060-Leftmost Digit(求n^n的最高位)

Leftmost Digit

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 2924    Accepted Submission(s): 1026


Problem 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


   
   
   
   
Hint
In the first case, 3 * 3 * 3 = 27, so the leftmost digit is 2. In the second case, 4 * 4 * 4 * 4 = 256, so the leftmost digit is 2.
对一个数num可写为 num=10 n + a, 即科学计数法,使a的整数部分即为num的最高位数字

num num =10 n + a 这里的n与上面的n不等

两边取对数: num*lg(num) = n + lg(a);

因为a<10,所以0<lg(a)<1

令x=n+lg(a); 则n为x的整数部分,lg(a)为x的小数部分

又x=num*lg(num);

a=10 (x-n) = 10 (x-int(x)))

再取a的整数部分即得num的最高位
#include <iostream> #include <math.h> using namespace std; int main() { int t; while(cin>>t) { while(t--) { unsigned long n; cin>>n; double x=n*log10(n*1.0); x-=(__int64)x; int a=pow(10.0, x); cout<<a<<endl; } } return 0; }

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