C++·PAT Grade B 1007. Prime Pair Conjecture (20/20)

/*
1007. Prime Pair Conjecture (20)

Let us define dn as: dn = pn+1 - pn, where pi is the ith prime number. Obviously d1=1 and dn is even for n>1. The "prime pair conjecture" states that "there are infinitely many pairs of adjacent prime numbers that differ by 2".

Now given any positive integer N (< 10^5), please count the number of prime pairs that satisfy the conjecture not exceeding N.

Input format: Each test input contains 1 test case, giving a positive integer N.

Output format: The output of each test case occupies one line, and does not exceed the number of N prime pairs that satisfy the conjecture.

Input sample:
20
Sample output:
4
*/
/*
    Ideas:
        1. Enter a positive integer n;
        2. Create a prime-marked integer array prime_array[n+1], and initialize the element to 0;
        3. Starting from 2, that is, prime_array[2], traverse the elements of the array prime_array to n in turn (+1), and determine whether each element is a prime number. If the current element is a prime number, mark prime_array[i] as 1;
        4. Determine whether prime_array[i-2] is marked as a prime number, if so, count it, otherwise, execute the next bit.

    the complexity:
        O(n^2);
*/
#include<stdio.h>
#include<math.h>

bool isPrime(int n){
    int k;
    k = sqrt(n);
    for(int j=2;j<=k;j++){
        if(n%j==0)
            return false;
    }
    return true;
}

int main(){
    int n,prime_count = 0;
    int *prime_array;//Marked array with memory function.
    scanf("%d", &n);
    prime_array = new int [n+1];

    if(n>1){
        prime_array[0]=0;
        prime_array[1]=0;
    }
    for(int i=2;i<=n;i++){//Note: equal sign, details!
        prime_array[i]=0;//Initialize prime mark element
        if(isPrime(i) == true){
            prime_array[i] = 1;
            if(prime_array[i-2] == 1)
                prime_count++;
        }
    }

    //test
//    for(int i=0;i<n;i++){
//        printf("%d ", prime_array[i]);
//    }
//    printf("\n");

    printf("%d", prime_count);
}