algorithm

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View the Project on GitHub satashun/algorithm

:warning: cpp_src/math/ModularOperation.hpp

Code

V<Mint> fact, ifact, inv;
VV<Mint> small_comb;

void mod_init() {
    const int maxv = 1000010;
    const int maxvv = 5000;

    fact.resize(maxv);
    ifact.resize(maxv);
    inv.resize(maxv);

    small_comb = make_vec<Mint>(maxvv, maxvv);

    fact[0] = 1;
    for (int i = 1; i < maxv; ++i) {
        fact[i] = fact[i - 1] * i;
    }

    ifact[maxv - 1] = fact[maxv - 1].inv();

    for (int i = maxv - 2; i >= 0; --i) {
        ifact[i] = ifact[i + 1] * (i + 1);
    }

    for (int i = 1; i < maxv; ++i) {
        inv[i] = ifact[i] * fact[i - 1];
    }

    for (int i = 0; i < maxvv; ++i) {
        small_comb[i][0] = small_comb[i][i] = 1;
        for (int j = 1; j < i; ++j) {
            small_comb[i][j] = small_comb[i - 1][j] + small_comb[i - 1][j - 1];
        }
    }
}

Mint comb(int n, int r) {
    if (n < 0 || r < 0 || r > n) return Mint(0);
    if (n < small_comb.size()) return small_comb[n][r];
    return fact[n] * ifact[r] * ifact[n - r];
}

Mint inv_comb(int n, int r) {
    if (n < 0 || r < 0 || r > n) return Mint(0);
    return ifact[n] * fact[r] * fact[n - r];
}

// O(k)
Mint comb_slow(ll n, ll k) {
    if (n < 0 || k < 0 || k > n) return Mint(0);
    Mint res = ifact[k];
    for (int i = 0; i < k; ++i) {
        res = res * (n - i);
    }
    return res;
}

// line up
// a 'o' + b 'x'
Mint comb2(int a, int b) {
    if (a < 0 || b < 0) return 0;
    return comb(a + b, a);
}

// divide a into b groups
Mint nhr(int a, int b) {
    if (b == 0) return Mint(a == 0);
    return comb(a + b - 1, a);
}

// O(p + log_p n)

Mint lucas(ll n, ll k, int p) {
    if (n < 0 || k < 0 || k > n) return Mint(0);
    Mint res = 1;
    while (n > 0) {
        res *= comb(n % p, k % p);
        n /= p;
        k /= p;
    }
    return res;
}

struct ModPrepare {
    ModPrepare() { mod_init(); }
} prep_mod;
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