PAT 1015. Reversible Primes (20)

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最新推荐文章于 2024-06-08 10:35:18 发布

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本文深入探讨了ReversiblePrimes算法的实现细节，包括如何判断数字及其在特定进制下的反转数是否同时为素数。重点在于进制转换和素数判断，特别注意到了1和0作为非素数的特殊性。

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1015. Reversible Primes (20)

时间限制

400 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

A reversible prime in any number system is a prime whose "reverse" in that number system is also a prime. For example in the decimal system 73 is a reversible prime because its reverse 37 is also a prime.

Now given any two positive integers N (< 10⁵) and D (1 < D <= 10), you are supposed to tell if N is a reversible prime with radix D.

Input Specification:

The input file consists of several test cases. Each case occupies a line which contains two integers N and D. The input is finished by a negative N.

Output Specification:

For each test case, print in one line "Yes" if N is a reversible prime with radix D, or "No" if not.

Sample Input:

Sample Output:

Yes
Yes
No

题目解析：

1、本题需要做的事情就是将判断数字N以及N在D进制下的“反数”是否同时为素数。

所以要做的就是算出N在D进制下的数，得到其“反数”后重新转换回十进制数。再行判断N和得到的新数是否同时为素数。

2、考察重点：进制转换和素数判断。

3、注意点：1）0和1不是素数；2）输入结束由一个负数标识

import java.util.ArrayList;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		ArrayList<Integer> list = new ArrayList<Integer>();
		int num = scanner.nextInt();
		// check the end of input
		while (num > 0) {
			list.add(num);
			list.add(scanner.nextInt());
			num = scanner.nextInt();
		}
		scanner.close();
		for (int i = 0; i < list.size(); i += 2) {
			// prime judgment
			if (isPrimes(list.get(i)) && isPrimes(getNumInRadixAndReverse(list.get(i), list.get(i + 1))))
				System.out.println("Yes");
			else
				System.out.println("No");
		}
	}

	static int getNumInRadixAndReverse(int num, int radix) {
		int result = 0;
		String nums = "";
		while (num != 0) {
			nums += num % radix;
			num = num / radix;
		}
		for (int i = 0; i < nums.length(); i++) {
			result *= radix;
			result += (nums.charAt(i) - '0');
		}
		return result;
	}

	static boolean isPrimes(int num) {
		boolean result = true;
		if (num == 1 || num == 0)
			result = false;
		for (int i = 2; i <= Math.sqrt(num); i++) {
			if (num % i == 0) {
				result = false;
				break;
			}
		}
		return result;
	}
}