高斯消元

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1 HDU 3364 Lanterns

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <vector>
#include <stack>
#include <map>
#include <set>
#include <cmath>
#include <cctype>
#include <ctime>
#include <bitset>

using namespace std;

#define REP(i, n) for (int i = 0; i < (n); ++i)
#define eps 1e-9

typedef long long ll;
typedef pair<int, int> pii;

const int INF = 0x7fffffff;
const int maxn = 55;
struct Matrix { int det[maxn][maxn]; };
int T, n, m, q, Case = 0;
Matrix A, A_t;

int solve(Matrix A, int m, int n) {
    int i = 0, j = 0, k, r, u;
    while (i < m && j < n) {
        r = i;
        for (k = i; k < m; ++k) {
            if (A.det[k][j]) { r = k; break; }
        }
        if (!A.det[r][j]) { ++j; continue; }
        if (r != i) {
            for (int k = 0; k <= n; ++k) { swap(A.det[r][k], A.det[i][k]); }
        }
        for (u = i + 1; u < m; ++u) if (A.det[u][j]) {
            for (k = i; k <= n; ++k) { A.det[u][k] ^= A.det[i][k]; }
        }
        ++i; ++j;
    }
    for (u = i; u < m; ++u) {
        if (A.det[u][n]) { return -1; }
    }
    return i;
}

int main() {
#ifdef __AiR_H
    freopen("in.txt", "r", stdin);
//    freopen("out.txt", "w", stdout);
#endif // __AiR_H
    scanf("%d", &T);
    while (T--) {
        scanf("%d %d", &n, &m); int k, x;
        memset(A_t.det, 0, sizeof(A_t.det));
        for (int i = 0; i < m; ++i) {
            scanf("%d", &k);
            for (int j = 0; j < k; ++j) {
                scanf("%d", &x); A_t.det[x - 1][i] = 1;
            }
        }
        scanf("%d", &q); printf("Case %d:
", ++Case);
        while (q--) {
            A = A_t;
            for (int i = 0; i < n; ++i) { scanf("%d", &A.det[i][m]); }
            int ans = solve(A, n, m); if (ans == -1) { printf("0
"); continue; }
            ans = m - ans; printf("%lld
", 1ll << ans);
        }
    }
    return 0;
}

2 HDU 5833 Zhu and 772002

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <vector>
#include <stack>
#include <map>
#include <set>
#include <cmath>
#include <cctype>
#include <ctime>
#include <bitset>

using namespace std;

#define REP(i, n) for (int i = 0; i < (n); ++i)
#define eps 1e-9

typedef long long ll;
typedef pair<int, int> pii;

const int INF = 0x7fffffff;
const int maxn = 2000 + 10;
const ll mod = 1e9 + 7;
int prime[maxn];
int prime_cnt = 0, T, n, Case = 0;
bool is_prime[maxn];

struct Matrix { int det[maxn][maxn]; };
Matrix A;

void init() {
    memset(is_prime, true, sizeof(is_prime));
    is_prime[0] = is_prime[1] = false;
    for (int i = 2; i < maxn; ++i) {
        if (is_prime[i]) { prime[prime_cnt++] = i; }
        for (int j = 0; j < prime_cnt; ++j) {
            if (i * prime[j] >= maxn) { break; }
            is_prime[i * prime[j]] = false;
            if (i % prime[j] == 0) { break; }
        }
    }
}
int solve(int m, int n) {
    int i = 0, j = 0, k, r, u;
    while (i < m && j < n) {  //当前正在处理第i个方程，第j个变量
        r = i;
        for (k = i; k < m; ++k) {
            if (A.det[k][j]) { r = k; break; }
        }
        if (!A.det[r][j]) { ++j; continue; }
        if (r != i) {
            for (k = 0; k <= n; ++k) { swap(A.det[r][k], A.det[i][k]); }
        }
        for (u = i + 1; u < m; ++u) if (A.det[u][j]) {
            for (k = i; k <= n; ++k) { A.det[u][k] ^= A.det[i][k]; }
        }
        ++i; ++j;
    }
    return i;
}
ll my_pow(ll x, ll y) {
    ll ret = 1, t = x;
    while (y) {
        if (y & 1) { ret *= t; ret %= mod; }
        y >>= 1; t *= t; t %= mod;
    }
    return ret;
}

int main() {
#ifdef __AiR_H
    freopen("in.txt", "r", stdin);
//    freopen("out.txt", "w", stdout);
#endif // __AiR_H
    scanf("%d", &T); init();
    while (T--) {
        scanf("%d", &n); memset(A.det, 0, sizeof(A.det));
        int maxp = 0; ll x;
        for (int i = 0; i < n; ++i) {
            scanf("%lld", &x);
            for (int j = 0; j < prime_cnt; ++j) {
                while (x % prime[j] == 0) {
                    maxp = max(maxp, j); x /= prime[j]; A.det[j][i] ^= 1;
                }
            }
        }
        printf("Case #%d:
", ++Case);
        int ans = solve(maxp + 1, n); ans = n - ans;
        ll ret = my_pow(2, ans); --ret;
        if (ret < 0) { ret += mod; } printf("%lld
", ret);
    }
    return 0;
}

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