i have never met of this kind of matrix that is connecting with probablities..

подсмотренная ими у каких подвыпивших космонавтов
->
подсмотренная ими у каких-то подвыпивших космонавтов

This problem looks like a standart linear-programming problem. But it can be solved with O(n^3) complexity without simplex metod. What the difference between this problem and classical dual game problem in general form?

i use gauss with choice of maximum element in columns... type is double... to get the answer i had to
ceil(100000*x)/100000;
got WA 5.

Could anyone explain, what's the trick?

Can U give me some tricky tests to fail my program?
Thanks.

Var a:array[1..50,1..50] of Record ch,zn:longint; End;
    b:array[1..50] of real;
    n:integer;
    fl:boolean;
    ns:integer;

Procedure Input;
Var i,j:integer;
Begin
  Readln(n); inc(n);
  For j:=1 to n do Begin a[1,j].ch:=1; a[1,j].zn:=1; End; a[1,n].ch:=0;
  For i:=2 to n do
  Begin
    For j:=1 to n-1 do Begin Read(a[i,j].ch); a[i,j].zn:=1; End;
    a[i,n].ch:=-1; a[i,n].zn:=1;
    Readln;
  End;
  b[1]:=1;
End;

Function Nod(a,b:longint):longint; Begin If b=0 then Nod:=a else Nod:=Nod(b,a mod b); End;

Procedure Run(ns:integer);
Var d,c,z,i,j:longint;

Procedure Cor(i:integer);
Var j:integer;
Begin
  b[i]:=b[i]-(b[ns]*a[i,ns].ch/a[i,ns].zn);
  For j:=n downto ns do
  Begin
    c:=a[i,j].ch*a[i,ns].zn*a[ns,j].zn-a[i,j].zn*a[i,ns].ch*a[ns,j].ch;
    z:=a[i,j].zn*a[i,ns].zn*a[ns,j].zn;
    a[i,j].ch:=c; a[i,j].zn:=z;
    d:=Nod(a[i,j].ch,a[i,j].zn);
    a[i,j].ch:=a[i,j].ch div d; a[i,j].zn:=a[i,j].zn div d;
  End;
End;

Begin
  b[ns]:=b[ns]*a[ns,ns].zn/a[ns,ns].ch;
  For j:=n downto ns do
  Begin
    c:=a[ns,j].ch*a[ns,ns].zn; z:=a[ns,j].zn*a[ns,ns].ch;
    a[ns,j].ch:=c; a[ns,j].zn:=z;
    d:=Nod(a[ns,j].ch,a[ns,j].zn);
    a[ns,j].ch:=a[ns,j].ch div d; a[ns,j].zn:=a[ns,j].zn div d;
  End;
  If fl then For i:=1 to ns-1 do Cor(i)
        else For i:=ns+1 to n do Cor(i);
End;

Procedure Output;
Var i:integer;
Begin
  For i:=1 to n-1 do Writeln(b[i]:0:8);
End;

BEGIN
  Input;
  For ns:=1 to n do Run(ns);
  fl:=true;
  For ns:=n downto 1 do Run(ns);
  Output;
END.

I've writtan the program and it seems that I use correct solution. But the output for the sample is:

0.32985
0.33622
0.33390

Extended in Pascal doesn't help.
Should we use some specific things?

I can't submit this problem. Is it locked ?

Edited by author 10.02.2006 15:26