HDU1060:Leftmost Digit(数论)
2017-02-13 11:13
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Leftmost Digit
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 17765 Accepted Submission(s): 6869
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.
Author
Ignatius.L
题意:求N^N的最高位数字。
思路:N^N用科学记数法表示,N^N = (double)a * 10^x,x为N^N的位数减一,用N去表示x显然有x = lg(N^N)向下取整;所以(double)a = N^N / 10^( (int)lg(N^N) ),a的整数部分就是答案,但直接计算会溢出,两边取对数有lg(a) = N*lg(N) - (int)N*lg(N),a = 10^( N*lg(N) -
(int)N*lg(N) ),这样就不会溢出了。
# include <stdio.h> # include <math.h> int main() { int t, n; scanf("%d",&t); while(t--) { scanf("%d",&n); double k = n*log10(n); k -= (long long)k; printf("%lld\n",(long long)pow(10, k)); } return 0; }
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