Leftmost Digit
Time Limit: 1000 ms
Memory Limit: 65535 kB
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
Source
對于任何一個數我們可以寫成這樣的形式:a*10^n
同樣對于n^n我們可以寫成10^m*a,即n^n = a*10^m,我們要求的n^n的Leftmost位即最高位,即a的最高位,即整數位。
兩邊同時取對數即nlogn = loga + m,即a要等于nlogn的小數部分。
那麼temp=loga = nlogn-(long long)nlogn,
是以a = 10^loga=10^temp,即為所求。
這裡能得到啟發:對于很大的數的處理,取對數往往能收到很不錯的效果。
#include <cstdio>
#include <cmath>
int main()
{
int t, n;
FILE * fin, * fout;
fin = fopen("1.std.in", "r");
fout = fopen("1.std.out", "w");
fscanf(fin, "%d", &t);
while ( t-- )
{
fscanf(fin, "%d", &n);
double temp = n * log10(1.0 * n);
double a = temp - (long long)temp;
a = pow(10.0, a);
fprintf(fout, "%d\n", (long long)a);
}
return 0;
}