在 JAVA 中打印一个素数三角形

Question

I am trying to print a triangle of 0s and 1s. You get a number N . If N was 5 the triangle should look like:

1
11
111
11101

I get wrong output with 27 for example

1
11
111
11101
11101010
11101010001
11101010001010
11101010001010001
11101010001010001010

Lines ending with non-prime numbers are not printed, the prime numbers are printed as 1s, non-prime as 0s. I have a problem because some lines ending with 0s are printed.

import java.util.Scanner;

public class PrimeTriangle {

    public static void main(String[] args) {
        // TODO Auto-generated method stub

        Scanner input = new Scanner (System.in);
        int n = Integer.parseInt(input.nextLine());
        boolean isPrime=false;
        boolean nums[]=new boolean[n];

        for (int i=0; i<=2; i++) {
            nums[i]=true;
        //  System.out.print(nums[i]);
        }

        for (int i=4; i<=n; i++) {
            int m=i/2;
            for (int j=2; j<=m; j++) {
                if (i%j==0) {
                isPrime=false;
                break;
                }
                else {
                isPrime=true;
                }

            }
            nums[i-1]=isPrime;

        }
char[] digits = new char[n];
        for (int i=0; i<n; i++) {
            if (nums[i]) {
                digits[i]='1';
            }
            else {
                digits[i]='0';
            }
        }
for (int i=0; i<n; i++) {
            if (digits[i]==1) {
                System.out.println (new String (digits, 0, i+1));
                /*for (int j=0; j<i; j++) {
                    System.out.print(digits[i]);
                }
                System.out.println(); */ 
            }
        }

    }

}

Answer 1

@kalina199 Here is my approach at it - I was able to reduce it to just one loop:)

package bg.Cholakov;

import java.util.Scanner;

public class PrimeTriangle {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = Integer.parseInt(scanner.nextLine());
        int[] array = new int[n];
        StringBuilder stringBuilder = new StringBuilder();

        for (int i = 0, j = 1; i < n; i++, j++) {
            array[i] = j;
            if (isPrime(array[i])) {
                array[i] = 1;
                stringBuilder.append(String.valueOf(array[i]));
                System.out.println(stringBuilder);

            } else {
                array[i] = 0;
                stringBuilder.append(String.valueOf(array[i]));

            }
        }
    }

    static boolean isPrime(int number) {
        for (int i = 2; i <= number / 2; i++) {
            if (number % i == 0) {
                return false;
            }
        }
        return true;
    }
}

Answer 2

Problems in your code:

1. You have set the value of isPrime to true within the loop. You can not tell if the number is prime until you have divided it with each counter of the loop and found that it is not divisible by any of the loop counters. Therefore, it should be done only when the loop is finished.
2. In the declaration, for (int i=4; i<=n; i++) , you have declared i=4 for the number 5 ie you want to set nums[4] to true if 5 is prime or false if 5 is not prime. It means that you want to test 5 (not 4 ) for the primality. In your code, you have tested 4 for primality.

Given below is the corrected code:

import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        System.out.print("Enter the limit: ");
        int n = Integer.parseInt(input.nextLine());
        boolean nums[] = new boolean[n];

        for (int i = 0; i <= 2; i++) {
            nums[i] = true;
        }

        for (int i = 3; i < n; i++) {
            int num = i + 1, m = num / 2, j;
            for (j = 2; j <= m; j++) {
                if (num % j == 0) {
                    nums[i] = false;
                    break;
                }
            }

            // If j>m, it means that the loop did not terminate because of `break`
            if (j > m) {
                nums[i] = true;
            }
        }

        // Display nums[] for testing
        System.out.println(Arrays.toString(nums));

        for (int j = 0; j < n; j++) {
            if (nums[j] == false) {
                continue;
            } else {
                for (int i = 0; i <= j; i++) {
                    if (nums[i] == true) {
                        System.out.print("1");
                    } else {
                        System.out.print("0");
                    }
                }
                System.out.println();
            }
        }
    }
}

A sample run:

Enter the limit: 15
[true, true, true, false, true, false, true, false, false, false, true, false, true, false, false]
1
11
111
11101
1110101
11101010001
1110101000101

Additional notes:

1. I have removed an unnecessary variable, boolean isPrime . The array, boolean nums[] is sufficient in itself. I've also printed nums[] so that you can actually see what values have been set in this array.
2. A boolean variable has only two values, true and false . Therefore, if you check one value of a boolean variable in if , the else part becomes true for the other value eg in the following code, else if (nums[j]==true) is unnecessary and it can simply be written as else .

if (nums[j]==false) {
    continue;
} else if (nums[j]==true) {
    //...
}

---

A better approach:

1. You can make your code much cleaner by using a separate function to determine if a number is prime.
2. You do not need to check prime by dividing the number by each integer up to half of its value; you just need to divide the number by integers up to its square root. Check this to learn more about it.
3. Notice how my code looks cleaner by using the ternary operator. Check this to learn more about the ternary operator.

public class Main {
    public static void main(String[] args) {
        final int N = 5;
        StringBuilder sb;
        for (int i = 1; i <= N; i++) {
            sb = new StringBuilder();
            for (int j = 1; j <= i; j++) {
                sb.append(j == 1 || isPrime(j) ? 1 : 0);
            }
            if (sb.charAt(sb.length() - 1) != '0') {
                System.out.println(sb);
            }
        }
    }

    static boolean isPrime(int n) {
        for (int i = 2; i <= Math.sqrt(n); i++) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }
}

Output:

1
11
111
11101

As per your requirement, even though 1 is not a prime number, a 1 should be printed for it. Also, as per this requirement, we do not need to test 0 or a negative integer for primality. Therefore, I have not put any check for 0 , or 1 or a negative number in the method, isPrime to keep it clean and just relevant for this requirement.

Answer 3

Use Sieve of Eratosthenes to build a char[] of 0's and 1's, then print all substrings ending in 1.

static void printPrimeTriangle(int n) {
    char[] primes = new char[n];
    Arrays.fill(primes, '1');
    for (int sqrt = (int) Math.sqrt(n) + 1, i = 1; i < sqrt; i++)
        if (primes[i] == '1')
            for (int prime = i + 1, j = prime * 2 - 1; j < n; j += prime)
                primes[j] = '0';
    for (int i = 0; i < n; i++)
        if (primes[i] == '1')
            System.out.println(new String(primes, 0, i + 1));
}

Test

printPrimeTriangle(80);

Output

1
11
111
11101
1110101
11101010001
1110101000101
11101010001010001
1110101000101000101
11101010001010001010001
11101010001010001010001000001
1110101000101000101000100000101
1110101000101000101000100000101000001
11101010001010001010001000001010000010001
1110101000101000101000100000101000001000101
11101010001010001010001000001010000010001010001
11101010001010001010001000001010000010001010001000001
11101010001010001010001000001010000010001010001000001000001
1110101000101000101000100000101000001000101000100000100000101
1110101000101000101000100000101000001000101000100000100000101000001
11101010001010001010001000001010000010001010001000001000001010000010001
1110101000101000101000100000101000001000101000100000100000101000001000101
1110101000101000101000100000101000001000101000100000100000101000001000101000001

....:....1....:....2....:....3....:....4....:....5....:....6....:....7....:....8

Answer 4

I created an int array containing 1s and 0s and printed the triangle with two nested for loops. The outer loops is i