Rightmost Digit

Time Limit: 2000/1000 MS
(Java/Others)    Memory Limit: 65536/32768 K
(Java/Others)
Total Submission(s): 30543    Accepted
Submission(s): 11624

Problem Description

Given a positive integer N, you should output the
most right 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 rightmost
digit of N^N.

Sample Input

2 3 4

Sample Output

7 6

本题的大意是输入一个1到1000000000的整数N，要求输出N^N次方后的最后一个数字.....

解题思路：因为数据很大，只需要输出最后一位，所以对每个数据先求余得到最后一位数字，然后找出其最后一位的周期即可....

 1 /**************************************************

 2 HDOJ 1061 已经AC

 3 ***************************************************/

 4 #include <iostream>

 5 using namespace std;

 6 int main()

 7 {

 8     int N,T;

 9     int round=0;

10     int r[100]={0};

11     int i=0;

12     cin>>T;

13     while(T--)

14     {

15         cin>>N;

16         r[1]=N%10;//一定要对其求余

17         r[2]=(N%10)*(N%10)%10;//求余后再相乘，然后再求余，因为如果直接相乘时碰到1000000000时会发生错误

18         for(i=3;;i++)

19         {

20             r[i]=r[i-1]*(N%10)%10;

21             if(r[i]==r[1])

22             {round=i-1;break;}

23         }

24         if(N%round==0)

25             cout<<r[round]<<endl;

26         else cout<<r[N%round]<<endl;

27     }

28     //while(1);

29     return 0;

30 }

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