SGU 200. Cracking RSA 高斯消元

比较裸的题了。分解因数后消元便行了，答案就是2的自由元数量次方减一（因为空集不算答案） \(2^k-1\)

 

//{HEADS
#define FILE_IN_OUT
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <ctime>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <vector>
#include <stack>
#include <queue>
#include <deque>
#include <map>
#include <set>
#include <bitset>
#include <complex>
#include <string>
#define REP(i, j) for (int i = 1; i <= j; ++i)
#define REPI(i, j, k) for (int i = j; i <= k; ++i)
#define REPD(i, j) for (int i = j; 0 < i; --i)
#define STLR(i, con) for (int i = 0, sz = con.size(); i < sz; ++i)
#define STLRD(i, con) for (int i = con.size() - 1; 0 <= i; --i)
#define CLR(s) memset(s, 0, sizeof s)
#define SET(s, v) memset(s, v, sizeof s)
#define mp make_pair
#define pb push_back
#define PL(k, n) for (int i = 1; i <= n; ++i) { cout << k[i] << ' '; } cout << endl
#define PS(k) STLR(i, k) { cout << k[i] << ' '; } cout << endl
using namespace std;
void FILE_INIT(string FILE_NAME) {
#ifdef FILE_IN_OUT
#ifndef ONLINE_JUDGE 
    freopen((FILE_NAME + ".in").c_str(), "r", stdin);
    freopen((FILE_NAME + ".out").c_str(), "w", stdout);
#endif
#endif
}
typedef long long LL;
typedef double DB;
typedef pair<int, int> i_pair;
const int INF = 0x3f3f3f3f;
//}

const int maxn = 1000 + 5;

bool is_prime[maxn];
int p[maxn], cnt;

void sieve() {
    memset(is_prime, true, sizeof is_prime);
    for(int i = 2; i < maxn; ++i) {
        if(is_prime[i]) {
            p[cnt++] = i;
            for(int j = i; j < maxn; j += i) {
                is_prime[j] = false;
            }
        }
    }
}

bitset<105> fac[105];
int t, m;
int d[maxn];

int guass() {
    int k = 0;
    for(int i = 0; k < m && i < t; ++i) {
        for(int j = k; j < m; ++j) {
            if(fac[j].test(i)) {
                if(j != k) {
                    swap(fac[j], fac[k]);
                }
                break;
            }
        }
        if(!fac[k].test(i)) {
            continue;
        }
        for(int j = i + 1; j < m; ++j) {
            if(fac[j].test(i)) {
                fac[j] ^= fac[i];
            }
        }
        ++k;
    }
    return m - k;
}

void divide(int num, int pos) {
    for(int i = 0; i < t; ++i) {
        while(num % p[i] == 0) {
            num /= p[i];
            fac[pos].flip(i);
        }
    }
}

int ans[100];
void answer(int index) {
    ans[0] = ans[1] = 1;
    for(int i = 1; i <= index; ++i) {
        for(int j = 1; j <= ans[0]; ++j) {
            ans[j] *= 2;
        }
        for(int j = 1; j <= ans[0]; ++j) {
            if(ans[j] > 9) {
                ans[j + 1] += ans[j] / 10;
                ans[j] %= 10;
            }
        }
        while(ans[ans[0] + 1] > 0) {
            ++ans[0];
        }
    }
    ans[1] -= 1;
    for(int i = 1; i <= ans[0]; ++i) {
        if(ans[i] < 0) {
            ans[i] += 10;
            ans[i + 1] -= 1;
        }
    }
    for(int i = ans[0]; 0 < i; --i) {
        printf("%d", ans[i]);
    }
    if(ans[0] == 0) {
        printf("0");
    }
    puts("");
}

int main() {
    FILE_INIT("200");

    sieve();
    scanf("%d%d", &t, &m);
    for(int i = 0; i < m; ++i) {
        scanf("%d", &d[i]);
        divide(d[i], i);
    }
    int num = guass();
    //printf("%d\n", num);
    answer(num);

    return 0;
}