Submission #1311807

#	Time	Username	Problem	Language	Result	Execution time	Memory
1311807		Boycl07	Hack (APIO25_hack)	C++20	0 / 100	11 ms	1692 KiB

hack

#include <vector>
#include <numeric>
#include <algorithm>
#include <random>
#include <cmath>
#include <set>

// Declare the interactor provided by the judge
long long collisions(std::vector<long long> x);

namespace {
    // Helper to find all divisors of val that are strictly greater than limit
    std::vector<long long> get_divisors(long long val, long long limit) {
        std::vector<long long> divs;
        for (long long i = 1; i * i <= val; ++i) {
            if (val % i == 0) {
                if (i > limit) divs.push_back(i);
                if (val / i > limit && val / i != i) divs.push_back(val / i);
            }
        }
        return divs;
    }

    // Check if a candidate n is correct (Cost: 2)
    bool check_n(long long n) {
        if (n <= 0) return false;
        std::vector<long long> q = {1, n + 1};
        return collisions(q) > 0;
    }
}

int hack() {
    // --- Phase 1: Efficient check for small N ---
    // Cost: 2500
    const int SMALL_LIMIT = 2500;
    std::vector<long long> small_q(SMALL_LIMIT);
    std::iota(small_q.begin(), small_q.end(), 1);
    
    if (collisions(small_q) > 0) {
        // Binary search for small N
        int low = 2, high = SMALL_LIMIT;
        int ans = high;
        while (low <= high) {
            int mid = low + (high - low) / 2;
            std::vector<long long> q(mid);
            std::iota(q.begin(), q.end(), 1);
            if (collisions(q) > 0) {
                ans = mid;
                high = mid - 1;
            } else {
                low = mid + 1;
            }
        }
        return ans - 1;
    }

    // --- Phase 2: Large N with Optimized Birthday Attack ---
    // Use a reduced K to ensure Total Cost < 110,000
    // K=22000 => Isolation cost ~4*K = 88,000. Fits budget.
    int K = 22000;
    
    std::mt19937_64 rng(1337); 
    // Range limited to 2*10^10 to ensure fast factorization
    std::uniform_int_distribution<long long> dist(1, 20000000000LL);

    while (true) {
        std::vector<long long> current_set;
        current_set.reserve(K);
        std::set<long long> distinct_check;
        
        // Generate random set
        while (current_set.size() < K) {
            long long val = dist(rng);
            if (distinct_check.insert(val).second) {
                current_set.push_back(val);
            }
        }

        // Initial check (Cost: K)
        if (collisions(current_set) > 0) {
            
            // Isolation Phase (Divide & Conquer)
            while (true) {
                // Optimization: If set is small, brute force all pairs
                // 12 elements = 66 pairs. Factorizing 66 differences is cheap.
                if (current_set.size() <= 12) { 
                    for (size_t i = 0; i < current_set.size(); ++i) {
                        for (size_t j = i + 1; j < current_set.size(); ++j) {
                            long long diff = std::abs(current_set[i] - current_set[j]);
                            std::vector<long long> cands = get_divisors(diff, SMALL_LIMIT);
                            for (long long cand : cands) {
                                if (check_n(cand)) return (int)cand;
                            }
                        }
                    }
                    // Fallback: If no divisor worked (rare), break to retry outer loop
                    break; 
                }

                int sz = current_set.size();
                int mid = sz / 2;
                std::vector<long long> left_part(current_set.begin(), current_set.begin() + mid);
                std::vector<long long> right_part(current_set.begin() + mid, current_set.end());

                // Check Left (Cost: sz/2)
                if (collisions(left_part) > 0) {
                    current_set = left_part;
                } 
                // Check Right (Cost: sz/2)
                else if (collisions(right_part) > 0) {
                    current_set = right_part;
                } 
                // Crossing Collision
                else {
                    // Both 0, but total > 0. Collision is between Left and Right.
                    // We must shuffle to try a new split.
                    std::shuffle(current_set.begin(), current_set.end(), rng);
                    // Note: We do NOT query 'current_set' again here, we know it collides.
                    // We just loop back and split the shuffled set.
                }
            }
        }
        // If initial check failed, we loop again with a new random set.
    }
    
    return -1;
}

• Subtask 0: 0 / 0
• Subtask 1: 0 / 8
• Subtask 2: 0 / 17
• Subtask 3: 0 / 75