Submission #676313

#	Time	Username	Problem	Language	Result	Execution time	Memory
676313		tengiz05	Tents (JOI18_tents)	C++17	100 / 100	285 ms	35776 KiB

tents

// solutions need to be proved and have general ideas

#include <bits/stdc++.h>

constexpr int P = 1E9 + 7;
using i64 = long long;
// assume -P <= x < 2P
int norm(int x) {
    if (x < 0) {
        x += P;
    }
    if (x >= P) {
        x -= P;
    }
    return x;
}
template<class T>
T power(T a, int b) {
    T res = 1;
    for (; b; b /= 2, a *= a) {
        if (b % 2) {
            res *= a;
        }
    }
    return res;
}
struct Z {
    int x;
    Z(int x = 0) : x(norm(x)) {}
    Z(i64 x) : x(norm(x % P)) {}
    int val() const {
        return x;
    }
    Z operator-() const {
        return Z(norm(P - x));
    }
    Z inv() const {
        assert(x != 0);
        return power(*this, P - 2);
    }
    Z &operator*=(const Z &rhs) {
        x = i64(x) * rhs.x % P;
        return *this;
    }
    Z &operator+=(const Z &rhs) {
        x = norm(x + rhs.x);
        return *this;
    }
    Z &operator-=(const Z &rhs) {
        x = norm(x - rhs.x);
        return *this;
    }
    Z &operator/=(const Z &rhs) {
        return *this *= rhs.inv();
    }
    friend Z operator*(const Z &lhs, const Z &rhs) {
        Z res = lhs;
        res *= rhs;
        return res;
    }
    friend Z operator+(const Z &lhs, const Z &rhs) {
        Z res = lhs;
        res += rhs;
        return res;
    }
    friend Z operator-(const Z &lhs, const Z &rhs) {
        Z res = lhs;
        res -= rhs;
        return res;
    }
    friend Z operator/(const Z &lhs, const Z &rhs) {
        Z res = lhs;
        res /= rhs;
        return res;
    }
};

constexpr int N = 10000;
Z fac[N + 1], inv[N + 1];
Z nCk(int n, int k) {
    if (n < k) {
        return 0;
    }
    return fac[n] * inv[k] * inv[n - k];
}

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    
    fac[0] = inv[0] = 1;
    for (int i = 1; i <= N; i++) {
        fac[i] = fac[i - 1] * i;
        inv[i] = 1 / fac[i];
    }
    
    int h, w;
    std::cin >> h >> w;
    
    std::vector dp(h + 3, std::vector<Z>(w + 3));
    
    for (int i = 0; i <= w; i++) {
        dp[0][i] = 1;
    }
    
    for (int i = 0; i <= h; i++) {
        for (int j = 0; j <= w; j++) {
            dp[i + 1][j] += dp[i][j];
            dp[i + 1][j + 1] += nCk(j + 1, 1) * 4 * dp[i][j];
            dp[i + 1][j + 2] += nCk(j + 2, 2) * dp[i][j];
            dp[i + 2][j + 1] += nCk(i + 1, 1) * nCk(j + 1, 1) * dp[i][j];
        }
    }
    
    std::cout << (dp[h][w] - 1).val() << "\n";
    
    return 0;
}

• Subtask 1: 48 / 48
• Subtask 2: 52 / 52