模板 BSGS

Posted 2020-12-19 hznumqf

BSGS存在的目的是求中x的解，BSGS算法要求A与C互质，且C为质数。

#pragma warning(disable:4996)

#include<iostream>
#include<algorithm>
#include<bitset>
#include<tuple>
#include<unordered_map>
#include<fstream>
#include<iomanip>
#include<string>
#include<cmath>
#include<cstring>
#include<vector>
#include<map>
#include<set>
#include<list>
#include<queue>
#include<stack>
#include<sstream>
#include<cstdio>
#include<ctime>
#include<cstdlib>
#define pb push_back
#define INF 0x3f3f3f3f
#define inf 0x7FFFFFFF
#define moD 1000000003
#define pii pair<ll,ll>
#define eps 1e-8
#define equals(a,b) (fabs(a-b)<eps)
#define bug puts("bug")
#define re  register
#define fi first
#define se second
typedef  long long ll;
typedef unsigned long long ull;
const ll MOD = 1e6 + 7;
const int maxn = 1e6 +5;
const double Inf = 10000.0;
const double PI = acos(-1.0);
using namespace std;

#define mod 75643
struct Hash{
    int ha;
    int id;
    int next;
}a[mod];

int head[mod];
int top;

void Insert(int x, int y){
    int k = x % mod;
    a[top].ha = x;
    a[top].id = y;
    a[top].next = head[k];
    head[k] = top++;
}

int Find(int x){
    int k = x % mod;
    for (int i = head[k]; i != -1; i = a[i].next)
        if (a[i].ha == x)
            return a[i].id;
    return -1;//表示没有找到
}

int BSGS(int a, int b, int c){
    if (b == 1)
        return 0;
    memset(head, -1, sizeof(head));
    top = 1;//一定要等于1
    int m = sqrt(c);
    ll p = 1, x = 1;
    for (int i = 0; i < m; ++i) {
        Insert(p * b % c, i);
        p = p * a % c;
    }
    for (ll i = m; ; i += m){
        x = x * p % c;//此时的p已经等于a^m
        int j = Find(x);
        if (j != -1)
            return i - j;//这里的i已经等于i*m了
        if (i > c)
            break;
    }
    return -1;
}


int main() {
    int a, b, c;
    while (~scanf("%d%d%d", &c, &a, &b)) {
        int ans = BSGS(a, b, c);
        if (ans == -1) puts("no solution");
        else printf("%d
", ans);
    }
}