HDU Rightmost Digit

                                                 Rightmost Digit

Time Limit:1000MS     Memory Limit:32768KB     64bit IO Format:%I64d & %I64u

 

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

Hint

In the first case, 3 * 3 * 3 = 27, so the rightmost digit is 7.
In the second case, 4 * 4 * 4 * 4 = 256, so the rightmost digit is 6.

 普通的算法会超时，数据量比较大，到1亿了

优化算法，分治思想.

例如：( 5^5)%10  = ((5^2)^2*5)%10;

                             这个过程中要取余 ！

还有一种思想利用乘方尾数周期性的关系！

 

#include <stdio.h>
#include <string.h>

int mod(int a, int n)
{
    long long x;
	long long ans;
     if(n==1||n==0)
        return n==0?1:a;

	x = mod(a, n/2);
    ans = x * x % 10;

	if(n%2==1)
		ans=ans*a%10 ;
	return (int)ans;
}

int main()
{
	int t;
    int a;
    int dd;
	scanf("%d", &t);
	while(t--)
	{
		scanf("%d", &a );
	    dd = mod(a, a);
		printf("%d\n", dd );
	}
	return 0;
}