hdu 4196（数论）

题意：问小于n的数的乘积能拼成的最大平方数是多少？

思路：给n!做质数分解在除去指数为奇数的那些质数，由于题目中需要模运算所以不能直接除，必须乘上摸逆。

代码如下：

/**************************************************
 * Author     : xiaohao Z
 * Blog     : http://www.cnblogs.com/shu-xiaohao/
 * Last modified : 2014-06-28 15:26
 * Filename     : hdu_4196.cpp
 * Description     : 
 * ************************************************/

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <queue>
#include <stack>
#include <vector>
#include <set>
#include <map>
#define MP(a, b) make_pair(a, b)
#define PB(a) push_back(a)

using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<unsigned int,unsigned int> puu;
typedef pair<int, double> pid;
typedef pair<ll, int> pli;
typedef pair<int, ll> pil;

const int INF = 0x3f3f3f3f;
const double eps = 1E-6;
const int MOD = 1e9+7;
const int MAXN = 10000000+1;
int prime[MAXN], n;
int f[MAXN];

void getPrime()
{
    memset(prime,0,sizeof(prime));
    for(int i = 2;i <= MAXN;i++)
    {
        if(!prime[i])prime[++prime[0]] = i;
        for(int j = 1;j <= prime[0] && prime[j] <= MAXN/i;j++)
        {
            prime[prime[j]*i] = 1;
            if(i % prime[j] == 0)break;
        }
    }
}

ll inv(ll a,ll m)
{
    if(a == 1)return 1;
    return inv(m%a,m)*(m-m/a)%m;
}

//求x！中p（素数）因子的个数
ll ff(ll x, ll p){
    ll tp = p, ret = 0;
    while(tp <= x){
        ret += (x/tp);
        tp = tp*p;
    }
    return ret;
}

int main()
{
    freopen("in.txt", "r", stdin);

    f[0] = 1;
    for(int i=1; i<=MAXN; i++) 
        f[i] = (ll)f[i-1] * i % MOD;
    getPrime();
    while(scanf("%d", &n)!=EOF && n){
        ll ans = 1;
        for(int i=1; i <= prime[0] && prime[i]<=n; i++){
            ll tp = ff(n, prime[i]);
            if(tp & 1) ans = (ll)ans * prime[i] % MOD;
        }
        ans = (f[n] * inv(ans, MOD))%MOD;
        printf("%I64d
", ans);
    }
    return 0;
}