【构造】CF Edu 12 D

谁践踏了优雅 2024-03-08 08:06 122阅读 0赞

[Problem - D - Codeforces][]

题意：

![c938d4045d17475f9e3ed23edf020b4f.png][]

思路：

这种题一定要从小数据入手，不然很有可能走歪思路

先考虑n = 1的情况，直接输出即可

然后是n = 2的情况，如果相加是质数，就输出2个，否则就输出一个

然后是n = 3的情况

看这个集合能不能是3个数

2 3 5不行

4 5 8不行

注意到三个数一定是奇 偶 奇，只要没有1，就一定不行

想到这就很简单了，分类讨论即可

Code：

#include <bits/stdc++.h>
    
    #define int long long
    
    using i64 = long long;
    
    constexpr int N = 2e3 + 10;
    constexpr int M = 2e6 + 10;
    constexpr int P = 2600;
    constexpr i64 Inf = 1e18;
    constexpr int mod = 1e9 + 7;
    constexpr double eps = 1e-6;
    
    int n;
    int len = 0;
    int a[N];
    int vis[M], prime[M];
    
    void p_init(int n) {
        for (int i = 2; i <= n; i ++) {
            if (!vis[i]) prime[++len] = i;
            for (int j = 1; prime[j] <= n / i; j ++) {
                vis[i * prime[j]] = 1;
                if (i % prime[j] == 0) break;
            }
        }
    }
    void solve() {
        std::cin >> n;
        
        int cnt1 = 0;
        for (int i = 1; i <= n; i ++) {
            std::cin >> a[i];
            if (a[i] == 1) cnt1 ++;
        }
    
        std::sort(a + 1, a + 1 + n);
    
        if (cnt1) {
            for (int i = cnt1 + 1; i <= n; i ++) {
                if (!vis[a[i] + 1]) {
                    std::cout << cnt1 + 1 << "\n";
                    for (int i = 1; i <= cnt1; i ++) std::cout << 1 << " ";
                    std::cout << a[i] << "\n";
                    return;
                }
            }
    
            if (cnt1 >= 2) {
                std::cout << cnt1 << "\n";
                for (int i = 1; i <= cnt1; i ++) std::cout << 1 << " \n" [i == cnt1];
                return;
            }
        }
    
        for (int i = 1; i <= n; i ++) {
            for (int j = i + 1; j <= n; j ++) {
                if (!vis[a[i] + a[j]]) {
                    std::cout << 2 << "\n";
                    std::cout << a[i] << " " << a[j] << "\n";
                    return;
                }
            }
        }
    
        std::cout << 1 << "\n" << a[1] << "\n";
    }
    signed main() {
        std::ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
        
        int t = 1;
        p_init(2e6);
    
        while (t--) {
            solve();
        }
        
        return 0;
    }

[Problem - D - Codeforces]: https://codeforces.com/contest/665/problem/D
[c938d4045d17475f9e3ed23edf020b4f.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/03/08/c1756befb8d54f10b8d0415d1218138d.png