HDU 5833 高斯消元

n个数，任选>=1个数相乘，使得乘积是完全平方数。

其实就是开关，控制灯泡。

数 ----第i个质因子p的个数%2  = {1 ， 0}

==

开关----第i个灯泡 = {开 ， 关}

最后使得所有灯泡都是灭着的方案数 = 2^自由变元个数  

全部关着的情况     ==   一个数也不选   应省去

import java.io.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
public static void main(String[] args){
new HDU5833().solve()  ;
}
}

class HDU5833{
InputReader in = new InputReader(System.in) ;
PrintWriter out = new PrintWriter(System.out) ;

final int N = 2000 ;
int[] prime = new int
;
int primeSize ;
boolean[] is = new boolean
;

{
Arrays.fill(is , false) ;
primeSize = 0 ;
for(int i = 2 ; i < N ; i++){
if(! is[i]) prime[primeSize++] = i ;
for(int j = 0 ; j < primeSize && prime[j] * i < N ; j++){
is[i * prime[j]] = true ;
if(i % prime[j] == 0) break ;
}
}
}

final int MAXN = 318 ;
int[][] A = new int[MAXN][MAXN] ;
int gauss(int n){
int col , cnt = 0 , row ;
for(col = 0  ; col < n ; col++){
for(row = cnt ; row < 303 ; row++){
if(A[row][col] != 0 ) break ;
}
if(row < 303){
if(row != cnt){
for(int i = 0 ; i < n ; i++){
int t = A[row][i] ;
A[row][i] = A[cnt][i] ;
A[cnt][i] = t ;
}
}
for(int i = cnt + 1 ; i < 303 ; i++){
if(A[i][col] != 0){
for(int j = col ; j < n ; j++)
A[i][j] ^= A[cnt][j] ;
}
}
cnt++ ;
}
}
return n - cnt ;
}

long[] a = new long[MAXN] ;
final long MOD = 1000000007L ;
void solve(){
int t = in.nextInt() ;
for(int ca = 1 ; ca <= t ; ca++){
int n = in.nextInt() ;
for(int i = 0 ; i < n ; i++) a[i] = in.nextLong() ;

for(int i = 0 ; i < 303 ; i++){
for(int j = 0 ; j < n ; j++){
int k = 0 ;
while(a[j] % prime[i] == 0){
k++ ;
a[j] /= prime[i] ;
}
A[i][j] = k % 2 ;
}
}

int res = gauss(n) ;
long ans = 1L ;
while(res-- > 0){
ans <<= 1 ;
ans %= MOD ;
}
ans = (ans - 1 + MOD) % MOD ;
out.println("Case #" + ca + ":") ;
out.println(ans) ;
}
out.flush() ;
}
}

class InputReader {
public BufferedReader reader;
public StringTokenizer tokenizer;

public InputReader(InputStream stream) {
reader = new BufferedReader(new InputStreamReader(stream), 32768);
tokenizer = new StringTokenizer("");
}

private void eat(String s) {
tokenizer = new StringTokenizer(s);
}

public String nextLine() {
try {
return reader.readLine();
} catch (Exception e) {
return null;
}
}

public boolean hasNext() {
while (!tokenizer.hasMoreTokens()) {
String s = nextLine();
if (s == null)
return false;
eat(s);
}
return true;
}

public String next() {
hasNext();
return tokenizer.nextToken();
}

public int nextInt() {
return Integer.parseInt(next());
}

public long nextLong() {
return Long.parseLong(next());
}

public double nextDouble() {
return Double.parseDouble(next());
}

public BigInteger nextBigInteger() {
return new BigInteger(next());
}

}