HDU 5833 高斯消元

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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[N] ;int primeSize ;boolean[] is = new boolean[N] ;{   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());      }    }

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