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Leftmost Digit(杭电1060)(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): 13574 Accepted Submission(s): 5216
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).
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 2HintIn 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
/*本题思路: 1,令M=N^N; 2,分别对等式两边取对数得 log10(M)=N*log10(N),得M=10^(N*log10(N)); 3,令N*log10(N)=a+b,a为整数,b为小数; 4,C函数:log10(),计算对数,pow(a,b)计算a^b 5,由于10的任何整数次幂首位一定为1,所以,M的首位只和N*log10(N)的小数部分有关, 即只用求10^b救可以了; 6,最后对10^b取整,输出取整的这个数就行了。(因为0<=b<1,所以1<=10^b<10对 其取整,那么的到的就是一个个位,也就是所求的数)。 */ //hdoj系统就是坑,各种CE,各种W,多亏康晓辉指点。 #include<stdio.h> #include<math.h> int main() { int test; double n,k,a; scanf("%d",&test); while(test--) { scanf("%lf",&n); a=n*log10(n); k=a-(__int64)a; //这里强制转换需要用int64才能A,否则会w或者CE!!! printf("%d\n",int(pow(10,k))); } return 0; }
Leftmost Digit(杭电1060)(求N^N的最高位)
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