HDU 1061 Rightmost Digit

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于 2017-08-17 20:17:59 发布

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本文介绍了一种解决特定数学问题的方法——快速幂取模算法。该算法用于求解正整数N的N次方的最右一位数字，通过输入多个测试用例，输出每个用例中N^N的最右一位数字。文中提供了Java代码实现，通过快速幂算法并结合取模运算高效解决了这一问题。

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Problem:

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.

Input Example:

2
3
4

Output Example:

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.

本题考取算法为：快速幂取模

Code:

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        while (n-- > 0) {
            int x = sc.nextInt();
            System.out.println(f(x, x, 10));
        }
        sc.close();
    }

    static int f(int a, int b, int c) {
        int ans = 1;
        a = a % c;
        while (b > 0) {
            if (b % 2 == 1) {
                ans = (ans * a) % c;
            }
            b = b / 2;
            a = (a * a) % c;
        }
        return ans;
    }
}