Informatics Olympiad 1405: sum and product of prime numbers (thinking problem)

Information Science Olympiad all in one （C++ edition ） Online evaluation system (ssoier.cn)

【 Title Description 】

The sum of two prime numbers is S, What is the maximum product of them ？

【 Input 】

One is not greater than 10000 The positive integer S, Is the sum of two prime numbers .

【 Output 】

An integer , Is the maximum product of two prime numbers . The data is guaranteed to have a solution .

【 sample input 】

50

【 sample output 】

589

Ideas ：

A number is divided into two parts , How to maximize the product , for example ：50 Split into 1 and 49 as well as 50 Split into 25 and 25, Obviously, the closer these two numbers are to the middle , The bigger the product , The problem is that these two prime numbers can be the same , But the title doesn't say .

Code ：

#include<iostream>
#include<cstring>
#include<vector>
#include<algorithm>

using namespace std;

bool flag = false;

bool isprime(int x) {
    if(x == 1) return false;
    for(int i = 2; i <= x / i; i ++) {
        if(x % i == 0) return false;
    }
        return true;
}

int main() {
    ios::sync_with_stdio(false);
    cout.tie(nullptr);

    int x;
    cin >> x;

    int h = x / 2;
    for(int i = h; i <= x; i ++) {
        for(int j = i; j >= 0; j --) {
            if(isprime(i)  && isprime(j) && i + j == x) {
                cout << i * j;
                flag = true;
                break;
            }
        }
        if(flag) break;
    }

    return 0;
}