Leftmost Digit
2014-10-20 20:51
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Leftmost Digit
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 13438 Accepted Submission(s): 5159
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.
此题充分利用log来解题,n^n=x -> nlgn=lgx x=10^(nlgn) ->由此易有nlgn又小数部分和整数部分组成,及可以通过数值的转化来求题,考虑到此题数字较大,我们使用_int64和double来得到小数部分来解题,及通过10^小数得到最高位。
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.
#include <stdio.h> #include <math.h> int main() { int i; int Case; double num; int result; double reminder; double temp; scanf("%d",&Case); while(Case--) { scanf("%lf",&num); temp=num*log10(num); reminder=temp-(__int64)(temp); result=pow(10,reminder); printf("%d\n",result); } return 0;此题充分利用log来解题,n^n=x -> nlgn=lgx x=10^(nlgn) ->由此易有nlgn又小数部分和整数部分组成,及可以通过数值的转化来求题,考虑到此题数字较大,我们使用_int64和double来得到小数部分来解题,及通过10^小数得到最高位。
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