题目链接：点击打开链接
题意：
给定n盏灯，m个开关
下面m行给出每个开关可以控制哪些灯（即按下此开关，这些灯的状态会改变）
下面q个询问：一行一个询问，一个询问n个数字表示灯的最终状态
问从全暗到这个状态的方案数（一个开关只能按一次）
n条方程，等式右边就是输入的灯的状态。
m个未知数，表示每个开关是否按下，系数就是这个开关能否影响到那盏灯
解完方程后首先判断系数矩阵的秩是否和增广矩阵的秩相同，若相同则必有解，否则则无解。
因为求的是方案数，所以求出解完方程后的自由元数量即可。
方案数=2^(自由元数量)
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.util.Queue;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
public class Main {
int[][] A = new int[N][N], init = new int[N][N];
int n, m;
long Gauss(int[][] mat, int row, int col){
int r, c, i, j;
for(r = c = 0; r < row && c < col; r++, c++){
for(i = r; i < row; i++)
if(mat[i][c]>0)break;
if(i == row){r--; continue;}
if(i!=r)
for(j = c; j <= col; j++){
int tmp = mat[r][j]; mat[r][j] = mat[i][j]; mat[i][j] = tmp;
}
for(i = r+1; i < row; i++)
if(mat[i][c]>0)
for(j = c; j <= col; j++)
mat[i][j] ^= mat[r][j];
}
for(i = r; i < row; i++)
if(mat[i][col]!=0)return 0L;
return 1L<<(col-r);
}
void work() throws Exception {
int T = Int(), Cas = 1;
while (T-->0){
n = Int(); m = Int();
for(int i = 0; i < n; i++)for(int j = 0; j < m; j++)init[i][j] = 0;
for(int i = 0, j, num; i < m; i++)
{
num = Int();
while(num-->0)init[Int()-1][i] = 1;
}
int q = Int();
out.println("Case "+(Cas++)+":");
while(q-->0){
for(int i = 0; i < n; i++)for(int j = 0; j < m; j++)A[i][j] = init[i][j];
for(int i = 0; i < n; i++)A[i][m] = Int();
out.println(Gauss(A, n, m));
}
}
}
public static void main(String[] args) throws Exception {
Main wo = new Main();
in = new BufferedReader(new InputStreamReader(System.in));
out = new PrintWriter(System.out);
// in = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
// out = new PrintWriter(new File("output.txt"));
wo.work();
out.close();
}
static int N = 56;
static int M = N * 2;
DecimalFormat df = new DecimalFormat("0.0000");
static int inf = (int) 1e9;
static long inf64 = (long) 1e18;
static double eps = 1e-8;
static double Pi = Math.PI;
static int mod = (int) 1e9 + 7;
private String Next() throws Exception {
while (str == null || !str.hasMoreElements())
str = new StringTokenizer(in.readLine());
return str.nextToken();
}
private int Int() throws Exception {
return Integer.parseInt(Next());
}
private long Long() throws Exception {
return Long.parseLong(Next());
}
private double Double() throws Exception {
return Double.parseDouble(Next());
}
StringTokenizer str;
static Scanner cin = new Scanner(System.in);
static BufferedReader in;
static PrintWriter out;
class Edge{
int from, to, dis, nex;
Edge(){}
Edge(int from, int to, int dis, int nex)
{
this.from = from; this.to = to; this.dis = dis; this.nex = nex;
}
}
Edge[] edge = new Edge[M<<1];
int[] head = new int[N]; int edgenum;
void init_edge(){ for(int i = 0; i < N; i++)head[i] = -1; edgenum = 0;}
void add(int u, int v, int dis){
edge[edgenum] = new Edge(u, v, dis, head[u]);
head[u] = edgenum++;
}
/*
*/
int upper_bound(int[] A, int l, int r, int val) {// upper_bound(A+l,A+r,val)-A;
int pos = r;
r--;
while (l <= r) {
int mid = (l + r) >> 1;
if (A[mid] <= val) {
l = mid + 1;
} else {
pos = mid;
r = mid - 1;
}
}
return pos;
}
int lower_bound(int[] A, int l, int r, int val) {// upper_bound(A+l,A+r,val)-A;
int pos = r;
r--;
while (l <= r) {
int mid = (l + r) >> 1;
if (A[mid] < val) {
l = mid + 1;
} else {
pos = mid;
r = mid - 1;
}
}
return pos;
}
int Pow(int x, int y) {
int ans = 1;
while (y > 0) {
if ((y & 1) > 0)
ans *= x;
y >>= 1;
x = x * x;
}
return ans;
}
double Pow(double x, int y) {
double ans = 1;
while (y > 0) {
if ((y & 1) > 0)
ans *= x;
y >>= 1;
x = x * x;
}
return ans;
}
int Pow_Mod(int x, int y, int mod) {
int ans = 1;
while (y > 0) {
if ((y & 1) > 0)
ans *= x;
ans %= mod;
y >>= 1;
x = x * x;
x %= mod;
}
return ans;
}
long Pow(long x, long y) {
long ans = 1;
while (y > 0) {
if ((y & 1) > 0)
ans *= x;
y >>= 1;
x = x * x;
}
return ans;
}
long Pow_Mod(long x, long y, long mod) {
long ans = 1;
while (y > 0) {
if ((y & 1) > 0)
ans *= x;
ans %= mod;
y >>= 1;
x = x * x;
x %= mod;
}
return ans;
}
int gcd(int x, int y) {
if (x > y) {
int tmp = x;
x = y;
y = tmp;
}
while (x > 0) {
y %= x;
int tmp = x;
x = y;
y = tmp;
}
return y;
}
int max(int x, int y) {
return x > y ? x : y;
}
int min(int x, int y) {
return x < y ? x : y;
}
double max(double x, double y) {
return x > y ? x : y;
}
double min(double x, double y) {
return x < y ? x : y;
}
long max(long x, long y) {
return x > y ? x : y;
}
long min(long x, long y) {
return x < y ? x : y;
}
int abs(int x) {
return x > 0 ? x : -x;
}
double abs(double x) {
return x > 0 ? x : -x;
}
long abs(long x) {
return x > 0 ? x : -x;
}
boolean zero(double x) {
return abs(x) < eps;
}
double sin(double x) {
return Math.sin(x);
}
double cos(double x) {
return Math.cos(x);
}
double tan(double x) {
return Math.tan(x);
}
double sqrt(double x) {
return Math.sqrt(x);
}
double fabs(double x){return x>0?x:-x;}
}
因为求的是方案数，所以求出解完方程后的自由元数量即可。
