Title: Group prime numbers

Prime numbers are numbers that can no longer be divided equally, such as 2, 3, 5, 7, 11, etc

9=3*3 means that it can be divided into three equal parts and is therefore not prime

Our country was founded in 1949. If you were given only four cards with numbers 1, 9, 4 and 9, you could place them in any order you wanted.

So how many 4-digit primes can you form?

For example, 1949 and 4919 meet the requirements

Please e submit the number of 4-digit primes you can form. Do not list them!

Note: do not submit the solution process, or other supporting text

Key points of investigation:

Recursive and backtracking algorithms for the full arrangement of elements, prime number judgment, repeated elements to the weight

In this problem we need to focus on master is recursion, and backtracking algorithm under the whole arrangement of elements, according to the thought of 1, 9, 4, 9 this four number from the whole arrangement, access to the array as a result, and then judge the result of the arrangement, whether it is prime number, after record meet the requirements of prime Numbers.

Answer source:

Package 2013 Provincial competition import java.util.HashSet; import java.util.Set; public class Year2013_t2 { static Set<Integer> set = new HashSet<Integer>(); // Define the hash set, Public static void arrange(int[] arr,int n) {public static void arrange(int[] arr,int n) { If (n==arr.length) {int num =arr [0]*1000 + arr[1]*100 + arr[2]*10 + arr[3]; If (check(num)==num) {set.add(num); }} for (int I = n; i < arr.length; Int t = arr[n]; int t = arr[n]; arr[n] = arr[i]; arr[i] = t; arrange(arr, n+1); T = arr[n]; arr[n] = arr[i]; arr[i] = t; Private static int check(int num) {for (int I = 2;} private static int check(int num) {for (int I = 2; i <= Math.sqrt(num); i++) { if (num % i == 0) { return 0; } } return num; } public static void main(String[] args) {int[] array = {1,9,4,9}; arrange(array, 0); System.out.println(set.size()); // Output the required length of data stored in the collection}}Copy the code

Example output:

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There are deficiencies or improvements, but also hope that small partners put forward messages, learn together!

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