模板 BSGS

Posted 2022-10-11 xyq0220

EXBSGS

用于求解形如\(a^x≡b~(mod~p)\)的方程

ll exbsgs(ll a, ll b, ll p)

    if (b == 1LL) return 0;
    ll t, d = 1, k = 0;
    while ((t = gcd(a, p)) != 1)
    
        if (b % t) return -1;
        ++k, b /= t, p /= t, d = d * (a / t) % p;
        if (b == d) return k;
    
    unordered_map<ll, ll> dic;
    ll m = ceil(sqrt(p));
    ll a_m = ksm(a, m, p), mul = b;
    for (ll j = 1; j <= m; ++j) mul = mul * a % p, dic[mul] = j;
    for (ll i = 1; i <= m; ++i)
    
        d = d * a_m % p;
        if (dic[d]) return i * m - dic[d] + k;
    
    return -1;