#include<stdio.h>
#include<map>
#include<math.h>
#define ll long long
using namespace std;
struct H {
static const int md=3999997;
bool vis[md]; int dt[md], foo[md], s[md], top;
void clr() { while(top) { int x=s[top--]; vis[x]=0, dt[x]=-1; } }
void add(int a, int b) {
int x=a%md;
while(1) { if(!vis[x] || dt[x]==a) { if(!vis[x]) s[++top]=x; vis[x]=1; dt[x]=a; foo[x]=b; break; } ++x; if(x==md) x=0; }
}
int find(int a) {
int x=a%md;
while(1) { if(!vis[x]) return -1; if(dt[x]==a) return foo[x]; ++x; if(x==md) x=0; }
}
}h;
int gcd(int a, int b) {return b ? gcd(b, a % b) : a;}
inline ll ksm(ll a, ll b, ll mod)
{
ll ret = 1, h = a;
while(b)
{
if(b & 1)
ret *= h, ret %= mod;
h *= h, h %= mod, b >>= 1;
}
return ret;
}
inline int exbsgs(int a, int b, int p)
{
a %= p, b %= p;
if(b == 1) return 0; //特判2
int g, d = 0;
ll c = 1;
while((g = gcd(a, p)) > 1)
{
if(b % g) return -1;
b /= g, p /= g, c = c * (a / g) % p, ++d;
if(c == b) return d; //特判3(其实等价于特判2)
}
// h.clear();
int t = int(sqrt(p * 1.0) + 1);
ll base = b;
h.clr(); //计算右半部分的值
for(int i = 0; i < t; i++)
h.add(base,i), base = base * a % p;
base = ksm(a, t, p); //用左半边的值验证
ll now = c;
for(int i = 1; i <= t + 1; i++)
{
now = now * base % p;
if(h.find(now)!=-1)
return i * t - h.find(now) + d; //返回解
}
return -1; //无解
}
int main()
{
int a, b, p;
while(~scanf("%d%d%d", &a, &p, &b) && a && b && p)
{
if(p == 1) {puts("0"); continue;} //特判1
int ans = exbsgs(a, b, p);
if(ans == -1) puts("No Solution");
else printf("%d\n", ans);
}
}
扩展bsgs
最新推荐文章于 2021-11-07 09:39:40 发布