uva 11542 - Square(高斯消元)

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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;}

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