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;

}

巴特西

HDU Rightmost Digit

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