uva 11542 - Square(高斯消元)

题目链接：uva 11542 - Square

题目大意：给出n个整数，从中选出1个或多个，使得选出的整数乘积为完全平方数，一共有多少种选法。空集不算。

解题思路：大白数例题。

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;
const int maxn = 500;
typedef long long ll;
typedef int Matrix[maxn+5][maxn+5];

int np, pri[maxn+5], vis[maxn+5];

void prime_table (int n) {
    np = 0;
    memset(vis, 0, sizeof(vis));
    for (int i = 2; i <= n; i++) {
        if (vis[i])
            continue;

        pri[np++] = i;
        for (int j = i + i; j <= n; j += i)
            vis[j] = 1;
    }
}

Matrix A;

int solve (Matrix a, int m, int n) {
    int i = 0, j = 0, k, r, u;
    while (i < m && j < n) {
        r = i;
        for (k = i; k < m; k++)
            if (A[k][j]) {
                r = k;
                break;
            }

        if (A[r][j]) {
            if (r != i) {
                for (k = 0; k <= n; k++)
                    swap(A[r][k], A[i][k]);
            }

            for (u = i + 1; u < m; u++) {
                if (A[u][j])
                    for (k = i; k <= n; k++)
                        A[u][k] ^= A[i][k];
            }
            i++;
        }
        j++;
    }    
    return i;
}

int main () {
    prime_table(maxn);

    int cas;
    scanf("%d", &cas);

    while (cas--) {
        ll x;
        int n, maxp = 0;
        scanf("%d", &n);
        memset(A, 0, sizeof(A));

        for (int i = 0; i < n; i++) {
            scanf("%lld", &x);
            for (int j = 0; j < np; j++) {
                while (x % pri[j] == 0) {
                    maxp = max(maxp, j);
                    x /= pri[j];
                    A[j][i] ^= 1;
                }
            }
        }

        int ret = solve(A, maxp+1, n);
        printf("%lld\n", (1LL<<(n-ret))-1);
    }
    return 0;
}