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BSGS模版 a^x=b ( mod c)
kuangbin的BSGS:
c为素数;
#define MOD 76543int 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 =http://www.mamicode.com/= x) return HASH_LINK[tail].j + n + i * m; } return -1;}
BSGS模版 a^x=b ( mod c)
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