Submission #893752

#	Time	Username	Problem	Language	Result	Execution time	Memory
893752		Alcabel	Remittance (JOI19_remittance)	C++17	100 / 100	241 ms	59996 KiB

remittance

#include <bits/stdc++.h>
using namespace std;
 
#ifdef LOCAL
const long long mod = 1e9 + 7;
#else
const long long mod = 2000000000000021ll;
#endif
 
#ifdef LOCAL
typedef long long __int128_t;
#endif
 
struct Modint {
    long long x;
    Modint() {
        x = 0ll;
    }
    Modint(long long _x) {
        while (_x >= mod) {
            _x -= mod;
        }
        while (_x < 0) {
            _x += mod;
        }
        x = _x;
    }
    Modint(__int128_t _x) {
        if (_x >= mod || _x <= -mod) {
            _x %= mod;
        }
        if (_x < 0) {
            _x += mod;
        }
        x = _x;
    }
    Modint operator+(const Modint& other) const {
        return Modint(x + other.x);
    }
    Modint operator-(const Modint& other) const {
        return Modint(x - other.x);
    }
    Modint operator*(const Modint& other) const {
        return Modint((__int128_t)x * other.x);
    }
    void operator+=(const Modint& other) {
        *this = *this + other;
    }
    void operator-=(const Modint& other) {
        *this = *this - other;
    }
    void operator*=(const Modint& other) {
        *this = *this * other;
    }
    Modint operator^(long long k) const {
        Modint tmp = x, res = 1ll;
        while (k > 0) {
            // cerr << k << '\n';
            if (k & 1ll) {
                res *= tmp;
            }
            tmp *= tmp;
            k >>= 1;
        }
        return res;
    }
    ~Modint() {}
};
 
void solve() {
    int n;
    cin >> n;
    vector<int> a(n), b(n);
    for (int i = 0; i < n; ++i) {
        cin >> a[i] >> b[i];
    }
    Modint denom = 1ll;
    for (int i = 0; i < n; ++i) {
        denom = denom + denom;
    }
    // cerr << denom.x << '\n';
    denom = (denom - 1ll) ^ (mod - 2);
    // cerr << (denom * ((1ll << n) - 1)).x << '\n';
    vector<Modint> two(n + 1);
    two[0] = 1ll;
    for (int i = 1; i <= n; ++i) {
        two[i] = two[i - 1] + two[i - 1];
        // cerr << "i: " << i << ", two: " << two[i].x << '\n';
    }
    vector<Modint> pref(n + 1), suf(n + 1);
    for (int i = 1; i <= n; ++i) {
        pref[i] = pref[i - 1] + two[i - 1] * (long long)(b[i - 1] - a[i - 1]);
    }
    for (int i = n - 1; i >= 0; --i) {
        suf[i] = suf[i + 1] + suf[i + 1] + (long long)(b[i] - a[i]);
        // cerr << "i: " << i << ", suf: " << suf[i].x << '\n';
    }
    vector<long long> x(n);
    for (int i = 0; i < n; ++i) {
        Modint xmod = pref[i + 1] * two[n - i - 1] + suf[i + 1];
        /*for (int j = i; j >= 0; --j) {
            xmod = xmod + xmod + (long long)(b[j] - a[j]);
        }
        for (int j = n - 1; j > i; --j) {
            xmod = xmod + xmod + (long long)(b[j] - a[j]);
        }*/
        xmod = (Modint(0ll) - xmod) * denom;
        if (xmod.x > mod / 2) {
            cout << "No\n";
            return;
        }
        x[i] = xmod.x;
    }
    for (int i = 0, prv = n - 1; i < n; ++i, ++prv) {
        if (prv == n) { prv = 0; }
        if (x[prv] - 2 * x[i] != b[i] - a[i]) {
            cout << "No\n";
            return;
        }
    }
    bool change = true;
    while (change) {
        change = false;
        for (int i = 0; i < n; ++i) {
            if (x[i] > 0 && a[i] >= 2) {
                change = true;
                long long trans = min(x[i], a[i] * 1ll / 2);
                x[i] -= trans;
                a[i] -= 2 * trans;
                int nxt = i + 1;
                if (nxt == n) {
                    nxt = 0;
                }
                a[nxt] += trans;
            }
        }
    }
    for (int i = 0; i < n; ++i) {
        if (x[i] != 0) {
            cout << "No\n";
            return;
        }
    }
    cout << "Yes\n";
}
 
int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
 
#ifdef LOCAL
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    int T = 1;
    cin >> T;
    while (T--) {
        solve();
        cerr << "-----------\n";
        cout << "-----------\n";
    }
#else
    int T = 1;
    // cin >> T;
    while (T--) {
        solve();
    }
#endif
 
    return 0;
}
 
/*
2000000000000021
2000000000000077
2000000000000081
*/

• Subtask 1: 15 / 15
• Subtask 2: 40 / 40
• Subtask 3: 45 / 45