poj 2497 高斯消元解同余方程

#include<stdio.h>
#include<iostream>
#include<algorithm>
#include<string.h>
using namespace std;
const int nMax=305;
const int MOD=7;
int freex[nMax],x[nMax],a[nMax][nMax],N,M;
char week[7][10]={"MON","TUE","WED","THU","FRI","SAT","SUN"};
int getday(char s[])
{
for(int i=0;i<7;i++)
if(strcmp(week[i],s)==0)
return i;
}
int gcd(int a,int b)
{
return b==0?a:gcd(b,a%b);
}
int lcm(int a,int b)
{
return a/gcd(a,b)*b;//先除后乘防溢出
}

//欧几里得扩展，求得aX+bY=gcd（a，b） 的解，保存在x,y中
void exgcd(int a,int b,int &x,int &y)
{
b?(exgcd(b,a%b,y,x),y-=x*(a/b)):(x=1,y=0);
}
int guass(int n,int m)
{
memset(x,0,sizeof(x));
//0表示为不确定变元
memset(freex,0,sizeof(freex));
int row=0,col=0;
for(;row<n&&col<m;col++)
{
int maxr=row;
for(int i=row+1;i<n;i++)
if(abs(a[i][col])>abs(a[maxr][col]))maxr=i;
if(maxr!=row) for(int i=0;i<=m;i++) swap(a[maxr][i],a[row][i]);
if(a[row][col]==0) continue;
for(int i=row+1;i<n;i++)
if(a[i][col]!=0)
{
int g=lcm(abs(a[row][col]),abs(a[i][col]));
int ga=g/abs(a[row][col]),gb=g/abs(a[i][col]);
if(a[row][col]*a[i][col]<0) ga=-ga;
for(int j=col;j<=m;j++)
{
a[i][j]=(a[i][j]*gb-a[row][j]*ga)%MOD;
if(a[i][j]<0) a[i][j]+=MOD;
}
}
row++;
}
//判断无解
for(int i=row;i<n;i++) if(a[i][m]!=0) return -1;
//判断无穷多解
if(row<m) return m-row;
//唯一解情况
for(int i=m-1;i>=0;i--)
{
int tmp=0,tx,ty;
for(int j=i+1;j<m;j++)tmp+=x[j]*a[i][j];
tmp=(a[i][m]-tmp)%MOD;
if(tmp<MOD) tmp+=MOD;
exgcd(a[i][i],MOD,tx,ty),tx%=MOD;
x[i]=tx*tmp/gcd(a[i][i],MOD);
}
return 0;
}

int main()
{
//    freopen("test.txt","r",stdin);
while(scanf("%d%d",&N,&M) &&N)
{
memset(a,0,sizeof(a));
for(int i=0;i<M;i++)
{
int k,d[2],t;
scanf("%d",&k);
char s[10];
for(int j=0;j<2;j++)
{
scanf("%s",s);d[j]=getday(s);
}
a[i]
=(d[1]-d[0]+8)%7;
for(int j=0;j<k;j++)
{
scanf("%d",&t);
a[i][t-1]++;a[i][t-1]%=MOD;
}

}
int ans=guass(M,N);
if(ans==-1) printf("Inconsistent data.\n");
else if(ans>0) printf("Multiple solutions.\n");
else
{
for(int i=0;i<N;i++)
{
x[i]=(x[i]%MOD+MOD)%MOD;
if(x[i]<3) x[i]+=MOD;
printf("%d%c",x[i],i==N-1?'\n':' ');
}
}
}
return 0;
}