Trailing Loves (or L'oeufs?) CodeForces - 1114C (数论)

Posted 2021-02-12 uid001

大意: 求n!在b进制下末尾0的个数

 

等价于求n!中有多少因子b, 素数分解一下, 再对求出所有素数的最小因子数就好了

 

ll n, b;
vector<pli> A, res;

void factor(ll x) {
    int mx = sqrt(x+0.5);
    REP(i,2,mx) if (x%i==0) {
        int t = 0;
        while (x%i==0) x/=i,++t;
        A.pb(pli(i,t));
    }   
    if (x>1) A.pb(pli(x,1));
}

int main() {
    cin>>n>>b;
    factor(b);
    int sz = A.size();
    ll ans = 1e18;
    REP(i,0,sz-1) {
        ll t = 0, num = n/A[i].x;
        while (num) t+=num, num/=A[i].x;
        ans = min(ans, t/A[i].y);
    }   
    printf("%lld
", ans);
}