hdu 1061 Rightmost Digit

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

 这个题给定的n范围很大，但我们只关心最后一位，于是很容易想到每次都对10取余，但这超时了。其实，对每一个数来说，N^N的个位数是呈周期性的。找出周期所有的问题就解决了。代码如下：

#include<stdio.h>
#include<math.h>
int a[11];
int main()
{
    int n,k,count,t,i;
    scanf("%d",&t);
    while(t--)
    {
        count=1;
        scanf("%d",&n);
        a[1]=n%10;
        k=n%10;
        for(i=2;;i++)//这里不要限定范围（i<=n），因为有可能还没找到周期，循环就已经结束了。
        {    
            k*=n%10;
            k%=10;
            if(k==a[1]) break;
            else{
                a[++count]=k;
            }

        }
        a[0]=a[count];
        printf("%d\n",a[(n)%(count)]);
    }
    return 0;
}