HDU1061——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

此题明显不能暴力求解N^N,显然数太大并且会超时。通过找规律可以知道数与数相乘其个位数至于两个乘数有关，所以只需提取每个乘数的个位数字即可。但提交过后发现报错TLE.再加思考很容易发现一个数连乘其个位数是几个数字的循环，所以只要找出此题的循环节即可。

AC代码：

#include<iostream>
#include<algorithm>
#include<memory.h>
using namespace std;
typedef long long ll;
int a[10],b[10];

int main()
{
    int T, i;
    ll n;
    cin >> T;
    while (T--)
    {
        for (int i = 0; i < 10; i++)
            a[i] = 0;
        int cnt = 0;
        cin >> n;
        int temp = n % 10, res=1;
        for (i = 0; i < 10; i++)
        {    
            res = res*temp%10;
            a[res] += 1;
            b[i] = res;
            if (a[res] == 2)
                break;
            cnt++;
        }
        if (n % cnt == 0)
            cout << b[cnt - 1] << endl;
        else
            cout << b[n%cnt - 1] << endl;
    }
    return 0;
}