103 lines
2.4 KiB
C++
103 lines
2.4 KiB
C++
#include<iostream>
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#include<cstdio>
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#include<cstring>
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#include<cstdlib>
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#include<cmath>
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using namespace std;
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#define maxn 102
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#define eps 1e-10
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double g[maxn][maxn];
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double x[maxn];
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int n,m,k;
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void add(int cnt,int i,int j,double val)
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{
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int t=i*n+j;
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if(i==m)
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{
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if(j==1)
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g[cnt][m*n+1]+=-1.0*val;
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return;
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}
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g[cnt][t]+=val;
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}
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void gauss(int n,int m)
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{
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int row,col,i,j,k;
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for(row=1,col=1;row<n,col<m;row++,col++)
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{
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k=row;
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for(i=row+1;i<=n;i++)
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if(fabs(g[i][col])>fabs(g[k][col]))
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k=i;
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if(k!=row)
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{
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for(i=col; i<=m; i++)
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swap(g[k][i],g[row][i]);
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}
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for(i=row+1; i<=n; i++)
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{
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if(fabs(g[i][col])<eps)
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continue;
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double t=g[i][col]/g[row][col];
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g[i][col]=0.0;
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for(j=col+1;j<=m;j++)
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g[i][j]-=t*g[row][j];
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}
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}
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for(i=n;i>=1;i--)
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{
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x[i]=g[i][m];
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for(j=i+1;j<=n;j++)
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x[i]-=x[j]*g[i][j];
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x[i]/=g[i][i];
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}
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}
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int main()
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{
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int i,j,cs,nn=0;
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scanf("%d",&cs);
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while(cs--){
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scanf("%d%d%d",&n,&m,&k);
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memset(g,0,sizeof(g));
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int cnt=0;
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for(i=0;i<m;i++)
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for(j=1;j<=n;j++)
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{
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cnt++;
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add(cnt,i,j,1.0);
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if(j==1)
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{
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add(cnt,i+1,j,-0.25);
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add(cnt,1,n-2,-0.75);
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}
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else if(j==2)
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{
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add(cnt,i+1,n-2,-0.25);
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add(cnt,1,1,-0.25);
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add(cnt,1,n-1,-0.5);
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}
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else if(j==3)
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{
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add(cnt,i+1,n-1,-0.25);
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add(cnt,1,1,-0.25);
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add(cnt,1,n-1,-0.25);
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add(cnt,1,n,-0.25);
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}
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else if(j==4)
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{
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add(cnt,i+1,n,-0.25);
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add(cnt,1,n,-0.5);
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add(cnt,1,1,-0.25);
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}
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else
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{
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add(cnt,i+1,j-3,-0.25);
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add(cnt,1,j-3,-0.75);
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}
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}
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gauss(cnt,cnt+1);
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printf("Case #%d: %.6lf\n",++nn,x[k]);
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}
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return 0;
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}
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