DAY 14

高斯消元：

几个方程，每次消去一个未知数，最后判断有解，无解，多解

cur = 1;
    for (int i = 1; i <= n; i++) {
        id = cur;
        for (int j = cur; j <= m; j++) {
            if (fabs(a[j][i]) > fabs(a[id][i]))
                id = j;
        }
        if (fabs(a[id][i]) > 1e-10)
            for (int j = i; j <= n + 1; j++) swap(a[id][j], a[cur][j]);
        else
            continue;

        for (int j = n + 1; j >= i; j--) a[cur][j] /= a[cur][i];
        for (int j = 1; j <= m; j++) {
            for (int h = n + 1; h >= i; h--)
                if (j != cur)
                    a[j][h] -= a[j][i] * a[cur][h];
        }
        cur++;
    }
    int fl = 0;
    for (int i = cur; i <= m; i++) {
        if (fabs(a[i][n + 1]) >= 1e-10) {
            cout << "No solutions";
            return 0;
        }
    }
    for (int i = 1; i <= n; i++) {
        if (fabs(a[i][i]) < 1e-10 && fabs(a[i][n + 1]) < 1e-10) {
            cout << "Many solutions";
            return 0;
        }
    }
    for (int i = 1; i <= n; i++) {
        cout << int(a[i][n + 1] / a[i][i] + 0.5) << endl;
    }

线性基

不好说，直接放代码
建基：

void build(long long xx) {
    for (int i = 50; i >= 0; i--) {
        if ((xx >> i & 1) == 1) {
            if (d[i] != 0)
                xx = xx ^ d[i];
            else {
                d[i] = xx;
                break;
            }
        }
    }
}

查询第k小的位置：

void rebuild() {
    for (long long i = 62; i >= 0; i--) {
        for (long long j = i - 1; j >= 0; j--) {
            if (p[i] & (1ll << j))
                p[i] ^= p[j];
        }
    }
    for (long long i = 0; i <= 62; i++) {
        if (p[i] != 0) {
            top++;
            d[top] = p[i];
        }
    }
}
void work(long long kk) {
    if (kk >= (1ll << top)) {
        cout << "-1" << endl;
        return;
    }
    anss = 0;
    for (long long i = 1; i <= top; i++) {
        if (kk & (1ll << (i - 1)))
            anss ^= d[i];
    }
    cout << anss << endl;
}

查k的位置

void ist(int tmp) {
    for (int i = 30; i >= 0; --i) {
        if (!((1 << i) & tmp))
            continue;
        if (!b[i]) {
            b[i] = tmp;
            break;
        }
        tmp ^= b[i];
        if (tmp == 0) {
            (cnt <<= 1) %= mod;
            break;
        }
    }
}