（高斯消元）HDU2827 The Evaluation of Determinant

The determinant is quite important in Linear Algebras, but I think that almost everyone who has ever learnt Linear Algebras is tired of the complicated and tedious calculations of determinant. Actually, it’s not the job we should do, isn’t it? As an outstanding Geek, why don’t we just ask computers to do these? 


Give you a determinant D (it’s ensured that the result of it is an integer) and m, try to get the result of this determinant mod m, and m = p1 * p2 …… pn, all the pi are different. You can assume 1000 < pi < 10000, aij < 1000, and m can be fit in 32-bit signed integer. 

InputInput two integers n and m in the first line, n represents the scale of the determinant. (n <= 100) 
 Then comes an n * n matrix, the determinant’s component aij means the one in row i and column j. 
OutputOutput the result of the determinant D mod m.Sample Input

2 1009
1 2
3 4

Sample Output

1007

用高斯消元法化为对角线形式即可。

纯暴力进行过多swap的高斯消元会TLE

#include <iostream>
#include <string>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <cmath>
#include <queue>
#include <set>
#include <map>
#include <list>
#include <vector>
#include <stack>
#define mp make_pair
//#define P make_pair
#define MIN(a,b) (a>b?b:a)
//#define MAX(a,b) (a>b?a:b)
typedef long long ll;
typedef unsigned long long ull;
const int MAX=1e3+5;
const int MAX_V=1e3+5;
const int INF=1e9+5;
const ll INF2=4e18+5;
const double M=4e18;
using namespace std;
const int MOD=1e9+7;
typedef pair<ll,int> pii;
const double eps=0.000000001;
#define rank rankk
ll n,m;
ll a[MAX][MAX];
ll Gause()
{
    ll re=1;
    int st=0;
    for(ll i=1;i<=n;i++)
    {
        for(ll j=i+1;j<=n;j++)
        {
            ll x=i,y=j;
            while(a[y][i])
            {
                ll ex=a[x][i]/a[y][i];
                for(ll s=i;s<=n;s++)
                {
                    a[x][s]=((a[x][s]-ex*a[y][s]%m)%m+m)%m;
                }
                swap(x,y);
            }
            if(x!=i)
            {
                for(ll s=i;s<=n;s++)
                    swap(a[i][s],a[x][s]);
                st^=1;
            }
        }
        if(!a[i][i])
            return 0;
    }
    for(ll i=1;i<=n;i++)
        re=(re*a[i][i]%m+m)%m;
    if(st)
        re*=-1;
    if(re<0)
        re+=m;
    return re;
}
int main()
{
    while(~scanf("%I64d%I64d",&n,&m))
    {
        for(ll i=1;i<=n;i++)
            for(ll j=1;j<=n;j++)
            {
                scanf("%I64d",&a[i][j]);
                a[i][j]=(a[i][j]%m+m)%m;
            }
        printf("%I64d
",Gause());
    }
    return 0;
}