Butchering Farmer John’s cows always yields the best prime rib. You can tell prime ribs by looking at the digits lovingly stamped across them, one by one, by FJ and the USDA. Farmer John ensures that a purchaser of his prime ribs gets really prime ribs because when sliced from the right, the numbers on the ribs continue to stay prime right down to the last rib, e.g.:
7 3 3 1
The set of ribs denoted by 7331 is prime; the three ribs 733 are prime; the two ribs 73 are prime, and, of course, the last rib, 7, is prime. The number 7331 is called a superprime of length 4.
Write a program that accepts a number N 1 <=N<=8 of ribs and prints all the superprimes of that length.
The number 1 (by itself) is not a prime number.
A single line with the number N.
4
The superprime ribs of length N, printed in ascending order one per line.
2333
2339
2393
2399
2939
3119
3137
3733
3739
3793
3797
5939
7193
7331
7333
7393
This problem can be solved using recursion.
public class sprime {
public static void main(String[] args) throws IOException {
try (final BufferedReader f = new BufferedReader(new FileReader("sprime.in"));
final PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("sprime.out")))) {
final int N = Integer.parseInt(f.readLine());
// find min and max value ranges
int min = 1;
for (int n = 1; n < N; n++) {
min = min * 10;
}
int max = min * 10;
max -= 1;
// note1: use 'char' instead of 'int' to reduce memory usage
// note2: only store computed values up to (max/10) to reduce memory usage
final char[] sprimes = new char[max / 10];
// initialize default values to '2' where '0' = not super prime,
// '1' = super prime, and '2' = don't know if super prime or not
Arrays.fill(sprimes, '2');
// find all superprimes of length N
for (int i = min + 1; i <= max; i += 2) {
if (isSuperPrime(i, sprimes)) {
out.println(i);
}
}
}
}
private static boolean isSuperPrime(int number, char[] sprimes) {
if (number >= 10) {
int nextNumber = number / 10;
// optimization: check if slice is superprime (first check against known superprimes)
if (sprimes[nextNumber - 1] != '2') {
return sprimes[nextNumber - 1] == '1' && isPrime(number);
}
// otherwise check if slice is superprime by computing
final boolean result = isSuperPrime(nextNumber, sprimes);
if (sprimes[nextNumber - 1] == '2') {
sprimes[nextNumber - 1] = result ? '1' : '0';
} else {
sprimes[nextNumber - 1] = (result && (sprimes[nextNumber - 1] == '1')) ? '1' : '0';
}
return result && isPrime(number);
} else {
// no more slices; just check if number is prime
return isPrime(number);
}
}
private static boolean isPrime(int number) {
// special case: for numbers 3 and under, only 2 and 3 are prime
if (number <= 3) {
return number > 1;
}
// all primes greater than 3 are of the form 6k[+/-]1;
// eliminate numbers divisible by 2 or 3
if ((number % 2 == 0) || (number % 3 == 0)) {
return false;
}
// and only check for divisors up to sqrt(number)
for (int i = 5; i * i <= number; i += 6) {
if ((number % i == 0) || ((number % (i + 2)) == 0)) {
return false;
}
}
return true;
}
}
Link To: Java Source Code