Submission #1010585

#	Time	Username	Problem	Language	Result	Execution time	Memory
1010585		sleepntsheep	Magic Show (APIO24_show)	C++17	0 / 100	2 ms	836 KiB

Alice

#include <vector>
#include "Alice.h"

std::vector<std::pair<int,int>> Alice(){
    long long x = setN(5000);
    std::vector<std::pair<int, int > > T = {};
    for (int i = 2; i <= 5000; ++i)
        T.emplace_back( (x % (i - 1) + 1), i);
    return T;
}

Bob

#include <vector>
#include <cstdio>
#include <algorithm>
#include <array>
#include "Bob.h"

using ii = __int128;

template <typename T>
std::array<T, 3> exgcd(T x, T y) {
    if (y == 0)
        return {x, 0, x};
    auto [s1, t1, d] = exgcd(y, x % y);
    T s, t;
    s = t1;
    t = s1 - t1 * (x / y);
    return {s, t, d};
}
ii lcm(long long x, long long y) {
    auto [_, __, d] = exgcd(x, y);
    return (x / d) * y;
}

/*
 *
 * CRT
 *
 *
 * x = a1 (mod n1)
 * x = a2 (mod n2)
 *
 * x = a1 + k1n1
 *   = a2 + k2n2
 *
 * k2n2 - k1n1 = a1 - a2
 *
 * d = gcd(n1, n2)
 * let e = (a1 - a2) / d
 *
 * find s, t
 * such that
 *
 * n1s + n2t = d
 *
 * then x = a1 + n1 (se)
 *        = a2 + n2 (te)
 *
 * and new equation x = (sth) (mod lcm(n1, n2))
 *
 */

inline long long normalize(long long x, long long mod) { x %= mod; if (x < 0) x += mod; return x; }

long long Bob(std::vector<std::pair<int,int>> T) {
    ii n1 = 1, a1 = 0;

    for (auto [u, v] : T) {
        if (u > v) std::swap(u, v);

        --u;
        --v;
        /* x = u (mod v) */

        ii n2 = v, a2 = u;

        auto [s1, _, d] = exgcd(n1, n2);

        a1 = normalize(a1 + s1 * (a2 - a1) / d % (n2 / d) * n1, n1 * n2 / d);

        n1 = lcm(n1, n2);

        if (n1 > 1e18)
            return a1;
    }

    return (long long)a1;
}

• Subtask 1: 0 / 5
• Subtask 2: 0 / 30
• Subtask 3: 0 / 65