算法笔记--BSGS && exBSGS 模板

https://www.cnblogs.com/sdzwyq/p/9900650.html

模板：

unordered_map<int, int> mp;
LL q_pow(LL n, LL k, LL p) {
    LL ans = 1;
    if(k == -1) return 0;
    while(k) {
        if(k&1) ans = (ans*n) % p;
        n = (n*n) % p;
        k >>= 1;
    }
    return ans;
}
int BSGS(int a, int b, int p){
    int m = sqrt(p)+1, s = b;
    mp.clear();
    for(int i = 0; i < m; ++i){
        mp[s]=i;
        s= (s*1LL*a)%p;
    }
    int t = q_pow(a, m, p);
    s = 1;
    for(int i = 1; i <= m; ++i){
        s = (s*1LL*t)%p;
        if(mp.find(s) != mp.end()) return i*m-mp[s];
    }
    return -1;
}
int exBSGS(int a, int b, int p) {
    int d = __gcd(a, p), k = 1, t = 0;
    while(d^1){
        if(b%d) return -1;
        ++t;
        b /= d;
        p /= d;
        k = (k*1LL*(a/d)) % p;
        if(b == k) return t;
        d = __gcd(a, p);
    }
    int s = b;
    mp.clear();
    int m = sqrt(p) + 1;
    for(int i = 0;i < m; ++i){
        mp[s] = i;
        s = (s*1LL*a) % p;
    }
    s = k;
    k = q_pow(a, m, p);
    for(int i = 1; i <= m; ++i){
        s = (s*1LL*k) % p;
        if(mp.find(s) != mp.end()) return i*m-mp[s]+t;
    }
    return -1;
}

例题：P4195 【模板】exBSGS/Spoj3105 Mod

代码：

#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize(4)
#include<bits/stdc++.h>
using namespace std;
#define y1 y11
#define fi first
#define se second
#define pi acos(-1.0)
#define LL long long
//#define mp make_pair
#define pb push_back
#define ls rt<<1, l, m
#define rs rt<<1|1, m+1, r
#define ULL unsigned LL
#define pll pair<LL, LL>
#define pli pair<LL, int>
#define pii pair<int, int>
#define piii pair<pii, int>
#define pdd pair<double, double>
#define mem(a, b) memset(a, b, sizeof(a))
#define debug(x) cerr << #x << " = " << x << "\n";
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
//head

unordered_map<int, int> mp;
LL q_pow(LL n, LL k, LL p) {
    LL ans = 1;
    if(k == -1) return 0;
    while(k) {
        if(k&1) ans = (ans*n) % p;
        n = (n*n) % p;
        k >>= 1;
    }
    return ans;
}
int exBSGS(int a, int b, int p) {
    int d = __gcd(a, p), k = 1, t = 0;
    while(d^1){
        if(b%d) return -1;
        ++t;
        b /= d;
        p /= d;
        k = (k*1LL*(a/d)) % p;
        if(b == k) return t;
        d = __gcd(a, p);
    }
    int s = b;
    mp.clear();
    int m = sqrt(p) + 1;
    for(int i = 0;i < m; ++i){
        mp[s] = i;
        s = (s*1LL*a) % p;
    }
    s = k;
    k = q_pow(a, m, p);
    for(int i = 1; i <= m; ++i){
        s = (s*1LL*k) % p;
        if(mp.find(s) != mp.end()) return i*m-mp[s]+t;
    }
    return -1;
}
int a, b, p;
int main() {
    while(~scanf("%d %d %d", &a, &p, &b)) {
    	if(!a && !b && !p) break;
		if(b == 1) {
			if(p == 1) printf("No Solution\n");
			else printf("0\n");
		}
		else {
			int x = exBSGS(a, b, p);
			if(~x) printf("%d\n", x);
			else printf("No Solution\n");
		}
	}
    return 0;
}