[UVA11542] Square 高斯消元

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显然我们需要将数唯一分解显然只有质因子质数为偶数才可能是完全平方数于是可以由此得出xor方程组高斯消元求出方程的秩（1 << 自由因子）-1即为答案（去掉0）

#include<cstdio>#include<algorithm>#include<cstdlib>#include<cstring>#include<cmath>using namespace std;#define MAXN 500#define MAXM 400int Prime[MAXN+10], P, used;bool isprime(int x){int t = sqrt(x) + 0.5;if(x == 1) return false;for(int i = 2; i <= t; i++) if(x % t == 0) return false;return true;}void get_prime(){for(int i = 1; i <= MAXN; i++)if(isprime(i))Prime[P++] = i;}template <int maxn, int maxm>struct I_Maxtrix{int N, M, rank;I_Maxtrix() {}I_Maxtrix(int x, int y) { N = x; M = y; }int A[maxn+10][maxm+10];void init() { memset(A, 0, sizeof(A)); }void read(){for(int i = 0; i < N; i++)for(int j = 0; j <= M; j++)scanf("%lf", &A[i][j]);}void Guss(){int i = 0, j = 0;//swap(N, M);while(i < N && j < M){int r = i;for(int k = i; k < N; k++) if(A[k][j]) { r = k; break; }if(A[r][j]){if(r != i) for(int k = 0; k <= M; k++) swap(A[r][k], A[i][k]);for(int u = i+1; u < N; u++)if(A[u][j])for(int k = i; k <= M; k++)A[u][k] ^= A[i][k];i++;}j++;}rank = i;}};I_Maxtrix <MAXN, MAXM> A;void Div(long long x, int pos){for(int i = 0; i < P; i++)while(x % Prime[i] == 0) {A.A[i][pos] ^= 1;x /= Prime[i];used = max(used, i);}}int main(){get_prime();int n, m, kase;scanf("%d", &kase);while(kase--){scanf("%d", &n);A.M = n;A.init();for(int i = 0; i < n; i++){long long x;scanf("%lld", &x);Div(x, i);}A.N = used+1;A.Guss();int ans = n-(A.rank);printf("%lld\n", (1LL << (ans))-1);}}

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