BSGS模版 a^x=b ( mod c)

Posted 2020-08-16 xjhz

kuangbin的BSGS：

c为素数；

#define MOD 76543
int hs[MOD],head[MOD],next[MOD],id[MOD],top;
void insert(int x,int y)
{
    int k = x%MOD;
    hs[top] = x, id[top] = y, next[top] = head[k], head[k] = top++;
}
int find(int x)
{
    int k = x%MOD;
    for(int i = head[k]; i != -1; i = next[i])
        if(hs[i] == x)
            return id[i];
    return -1;
}
int BSGS(int a,int b,int n)
{
    memset(head,-1,sizeof(head));
    top = 1;
    if(b == 1)return 0;
    int m = sqrt(n*1.0), j;
    long long x = 1, p = 1;
    for(int i = 0; i < m; ++i, p = p*a%n)insert(p*b%n,i);
    for(long long i = m; ;i += m)
    {
        if( (j = find(x = x*p%n)) != -1 )return i-j;
        if(i > n)break;
    }
    return -1;
}

扩展BSGS:

const int  MAXN= 99991 ;
struct LINK{
    ll data;
    ll j;
    ll next;
}HASH_LINK[1000000];
ll ad, head[MAXN];

ll Gcd(ll a, ll b){
return b ? Gcd(b, a % b) : a;
}

ll Ext_Gcd(ll a, ll b, ll &x, ll &y){
    if(!b){
       x = 1; y = 0;
       return a;
    }
    ll r = Ext_Gcd(b, a % b, x, y);
    ll t = x; x = y; y = t - a / b * y;
    return r;
}

ll POWER(ll a, ll b, ll c){
    ll ans = 1;
    while(b){
       if(b & 1) ans = ans * a % c;
       a = a * a % c;
       b >>= 1;
    }
    return ans;
}

void init(){
    memset(head, -1, sizeof(head));
    ad = 0;
}

ll Hash(ll a){
    return a % MAXN;
}

void INSERT_HASH(ll i, ll buf){
    ll hs = Hash(buf), tail;
    for(tail = head[hs]; ~tail; tail = HASH_LINK[tail]. next)
       if(buf == HASH_LINK[tail]. data) return;
    HASH_LINK[ad]. data = buf;
    HASH_LINK[ad]. j    = i;
    HASH_LINK[ad]. next = head[hs];
    head[hs] = ad ++;
}

ll BSGS(ll a, ll b, ll c){
    ll i, buf, m, temp, g, D, x, y, n = 0;
    for(i = 0, buf = 1; i < 100; i ++, buf = buf * a % c)
       if(buf == b) return i;
    D = 1;
    while((g = Gcd(a, c)) != 1){
       if(b % g) return -1; // g | b 不满足，则说明无解
       b /= g;
       c /= g;
       D = D * a / g % c;
       ++ n;
    }
    init();
    m = ceil(sqrt((long double) c));
    for(i = 0, buf = 1; i <= m; buf = buf * a % c, i ++) INSERT_HASH(i, buf);
    for(i = 0, temp = POWER(a, m, c), buf = D; i <= m; i ++, buf = temp * buf % c){
       Ext_Gcd(buf, c, x, y);
       x = ((x * b) % c + c) % c;
       for(ll tail = head[Hash(x)]; ~tail; tail = HASH_LINK[tail].next)
           if(HASH_LINK[tail]. data == x) return HASH_LINK[tail].j + n + i * m;
    }
    return -1;
}