ICPC Primer S04: Prime Sieve Contest

Session Architecture

• Topic: Mathematics & Number Theory
• Focus: Prime Sieve Mock Contest
• Goal: Implement Number Theory algorithms (Sieve of Eratosthenes, Prime Factorization) efficiently under a two-hour competitive constraint.

Logistics Update

Please note the time change for this specific contest session:

• Time: Sunday, 5:30 PM - 7:30 PM
• Location: BYENG 210
• Format: 2-Hour Mock Contest (No live instruction, pure problem-solving)

---

Problem A: Design Tutorial: Learn from Math

• Source: Codeforces 472A

// Compilation & Execution Instructions:
// g++ main.cpp -o main
// .\main
// PowerShell: Get-Content input.txt | .\main.exe
// Bash: cat input.txt | .\main.exe

#include <bits/stdc++.h>

using namespace std;
using ll = long long;

void solve() {
    int n;
    cin >> n;
    
    if (n % 2 == 0) {
        cout << 4 << " " << n - 4 << "\n";
    } else {
        cout << 9 << " " << n - 9 << "\n";
    }
}

int main() {
    // Fast I/O Optimization
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int t = 1;
    // cin >> t; 
    while (t--) {
        solve();
    }

    return 0;
}

---

Problem B: T-primes

• Source: Codeforces 230B

// Compilation & Execution Instructions:
// g++ main.cpp -o main
// .\main
// PowerShell: Get-Content input.txt | .\main.exe
// Bash: cat input.txt | .\main.exe

#include <bits/stdc++.h>

using namespace std;
using ll = long long;

const int MAXN = 1000005;
bool is_prime[MAXN];

void solve() {
    fill(is_prime, is_prime + MAXN, true);
    is_prime[0] = is_prime[1] = false;
    for (int i = 2; i * i < MAXN; i++) {
        if (is_prime[i]) {
            for (int j = i * i; j < MAXN; j += i) {
                is_prime[j] = false;
            }
        }
    }

    int n;
    if (!(cin >> n)) return;
    
    for (int i = 0; i < n; i++) {
        ll x;
        cin >> x;
        ll root = round(sqrt(x));
        if (root * root == x && is_prime[root]) {
            cout << "YES\n";
        } else {
            cout << "NO\n";
        }
    }
}

int main() {
    // Fast I/O Optimization
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int t = 1;
    // cin >> t; 
    while (t--) {
        solve();
    }

    return 0;
}

---

Problem C: Sherlock and his girlfriend

• Source: Codeforces 776B

// Compilation & Execution Instructions:
// g++ main.cpp -o main
// .\main
// PowerShell: Get-Content input.txt | .\main.exe
// Bash: cat input.txt | .\main.exe

#include <bits/stdc++.h>

using namespace std;
using ll = long long;

void solve() {
    int n;
    cin >> n;
    
    vector<int> colors(n + 2, 0);
    int max_color = 1;
    
    for (int i = 2; i <= n + 1; i++) {
        if (colors[i] == 0) {
            colors[i] = 1;
            for (int j = i * 2; j <= n + 1; j += i) {
                colors[j] = 2;
                max_color = 2;
            }
        }
    }
    
    cout << max_color << "\n";
    for (int i = 2; i <= n + 1; i++) {
        cout << colors[i] << (i == n + 1 ? "" : " ");
    }
    cout << "\n";
}

int main() {
    // Fast I/O Optimization
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int t = 1;
    // cin >> t; 
    while (t--) {
        solve();
    }

    return 0;
}

---

Problem D: Almost Prime

• Source: Codeforces 26A

// Compilation & Execution Instructions:
// g++ main.cpp -o main
// .\main
// PowerShell: Get-Content input.txt | .\main.exe
// Bash: cat input.txt | .\main.exe

#include <bits/stdc++.h>

using namespace std;
using ll = long long;

void solve() {
    int n;
    cin >> n;
    
    vector<int> prime_factors(n + 1, 0);
    int almost_primes = 0;
    
    for (int i = 2; i <= n; i++) {
        if (prime_factors[i] == 0) {
            for (int j = i; j <= n; j += i) {
                prime_factors[j]++;
            }
        }
        if (prime_factors[i] == 2) {
            almost_primes++;
        }
    }
    
    cout << almost_primes << "\n";
}

int main() {
    // Fast I/O Optimization
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int t = 1;
    // cin >> t; 
    while (t--) {
        solve();
    }

    return 0;
}

---

Problem E: Noldbach problem

• Source: Codeforces 17A

// Compilation & Execution Instructions:
// g++ main.cpp -o main
// .\main
// PowerShell: Get-Content input.txt | .\main.exe
// Bash: cat input.txt | .\main.exe

#include <bits/stdc++.h>

using namespace std;
using ll = long long;

void solve() {
    int n, k;
    cin >> n >> k;
    
    vector<bool> is_prime(n + 1, true);
    vector<int> primes;
    is_prime[0] = is_prime[1] = false;
    
    for (int i = 2; i <= n; i++) {
        if (is_prime[i]) {
            primes.push_back(i);
            for (int j = i * i; j <= n; j += i) {
                is_prime[j] = false;
            }
        }
    }
    
    int count = 0;
    for (int p : primes) {
        for (size_t i = 0; i < primes.size() - 1; i++) {
            if (primes[i] + primes[i+1] + 1 == p) {
                count++;
                break;
            }
        }
    }
    
    if (count >= k) cout << "YES\n";
    else cout << "NO\n";
}

int main() {
    // Fast I/O Optimization
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int t = 1;
    // cin >> t; 
    while (t--) {
        solve();
    }

    return 0;
}

---

Problem F: Colliders

• Source: Codeforces 154B

// Compilation & Execution Instructions:
// g++ main.cpp -o main
// .\main
// PowerShell: Get-Content input.txt | .\main.exe
// Bash: cat input.txt | .\main.exe

#include <bits/stdc++.h>

using namespace std;
using ll = long long;

void solve() {
    int n, m;
    cin >> n >> m;
    
    vector<int> min_prime(n + 1, 0);
    for (int i = 2; i <= n; i++) {
        if (min_prime[i] == 0) {
            for (int j = i; j <= n; j += i) {
                if (min_prime[j] == 0) min_prime[j] = i;
            }
        }
    }
    
    vector<bool> active(n + 1, false);
    vector<int> factor_used_by(n + 1, 0);
    
    for (int i = 0; i < m; i++) {
        char op;
        int x;
        cin >> op >> x;
        
        if (op == '+') {
            if (active[x]) {
                cout << "Already on\n";
            } else {
                int temp = x;
                int conflict = 0;
                while (temp > 1) {
                    int p = min_prime[temp];
                    if (factor_used_by[p] != 0) {
                        conflict = factor_used_by[p];
                        break;
                    }
                    while (temp % p == 0) temp /= p;
                }
                
                if (conflict != 0) {
                    cout << "Conflict with " << conflict << "\n";
                } else {
                    active[x] = true;
                    temp = x;
                    while (temp > 1) {
                        int p = min_prime[temp];
                        factor_used_by[p] = x;
                        while (temp % p == 0) temp /= p;
                    }
                    cout << "Success\n";
                }
            }
        } else {
            if (!active[x]) {
                cout << "Already off\n";
            } else {
                active[x] = false;
                int temp = x;
                while (temp > 1) {
                    int p = min_prime[temp];
                    factor_used_by[p] = 0;
                    while (temp % p == 0) temp /= p;
                }
                cout << "Success\n";
            }
        }
    }
}

int main() {
    // Fast I/O Optimization
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int t = 1;
    // cin >> t; 
    while (t--) {
        solve();
    }

    return 0;
}