poj 2065 SETI 高斯消元解模线性方程

http://poj.org/problem?id=2065

思路：http://blog.csdn.net/winddreams/article/details/47260465

/*解模线性方程 */#include<cstdio>#include<cstring>#include<algorithm>using namespace std;const int maxn = 100;int a[maxn][maxn];int x[maxn],free_x[maxn];void print(int n){for(int i=0;i<n;i++){for(int j=0;j<=n;j++)printf("%d ",a[i][j]);printf("\n");}printf("\n");}int lcm(int a,int b){return (a/__gcd(a,b))*b;}int Pow(int a,int n,int MOD){int ans=1;int res=a%MOD;//while(n){if(n&1)ans=(ans*res)%MOD;res=(res*res)%MOD;n>>=1;}return ans;}int Gauss(int equ,int var,int MOD){int maxrow;int row=0,col=0,num=0;for(;row<equ&&col<var;row++,col++)//{maxrow=row;for(int k=row+1;k<equ;k++)if(abs(a[k][col])>abs(a[maxrow][col]))maxrow=k;if(maxrow!=row){for(int j=row;j<=var;j++)//swap(a[maxrow][j],a[row][j]);}if(a[row][col]==0){row--;continue;}for(int i=row+1;i<equ;i++){if(a[i][col]!=0){int LCM=lcm(a[row][col],a[i][col]);int tb=LCM/a[row][col];int ta=LCM/a[i][col];if(a[row][col]>0&&a[i][col]<0||a[row][col]<0&&a[i][col]>0)tb=-tb;for(int j=0;j<=var;j++)a[i][j]=((a[i][j]*ta-a[row][j]*tb)%MOD+MOD)%MOD;}}}//保证有解 printf("ssss\n");for(int i=var-1;i>=0;i--){int temp=a[i][var];for(int j=i+1;j<var;j++){if(a[i][j]!=0)temp= temp-a[i][j]*x[j];temp=(temp%MOD+MOD)%MOD;//}while(temp%a[i][i]!=0)temp+=MOD;x[i]=(temp/a[i][i])%MOD;}return 0;}int main(){int t;//freopen("in.txt","r",stdin);//freopen("out.txt","w",stdout);scanf("%d",&t);while(t--){int MOD;scanf("%d",&MOD);char s[100];scanf("%s",s);int n=strlen(s);memset(a,0,sizeof(a));for(int i=0;i<n;i++){if(s[i]=='*')a[i][n]=0;else a[i][n]=s[i]-'a'+1;for(int j=0;j<n;j++)a[i][j]=Pow(i+1,j,MOD);}//print(n);Gauss(n,n,MOD);for(int i=0;i<n;i++)if(i!=n-1)printf("%d ",x[i]);else printf("%d\n",x[i]);}}