2102: [Usaco2010 Dec]The Trough Game

Time Limit: 10 Sec  Memory Limit: 64 MB
Submit: 117  Solved: 84
[Submit][Status]

Description

Farmer John and Bessie are playing games again. This one has to do with troughs of water. Farmer John has hidden N (1 <= N <= 20) troughs behind the barn, and has filled some of them with food. Bessie has asked M (1 <= M <= 100) questions of the form, "How many troughs from this list (which she recites) are filled?". Bessie needs your help to deduce which troughs are actually filled. Consider an example with four troughs where Bessie has asked these questions (and received the indicated answers): 1) "How many of these troughs are filled: trough 1" --> 1 trough is filled 2) "How many of these troughs are filled: troughs 2 and 3" --> 1 trough is filled 3) "How many of these troughs are filled: troughs 1 and 4" --> 1 trough is filled 4) "How many of these troughs are filled: troughs 3 and 4" --> 1 trough is filled From question 1, we know trough 1 is filled. From question 3, we then know trough 4 is empty. From question 4, we then know that trough 3 is filled. From question 2, we then know that trough 2 is empty. 求N位二进制数X，使得给定的M个数，满足X and Bi=Ci ,Bi ci分别是读入的两个数

Input

* Line 1: Two space-separated integers: N and M * Lines 2..M+1: A subset of troughs, specified as a sequence of contiguous N 0's and 1's, followed by a single integer that is the number of troughs in the specified subset that are filled.

Output

* Line 1: A single line with: * The string "IMPOSSIBLE" if there is no possible set of filled troughs compatible with Farmer John's answers. * The string "NOT UNIQUE" if Bessie cannot determine from the given data exactly what troughs are filled. * Otherwise, a sequence of contiguous N 0's and 1's specifying which troughs are filled.

Sample Input

4 4
1000 1
0110 1
1001 1
0011 1

Sample Output

1010

HINT

 

Source

Silver

题解：一上来居然没有别的想法——只有暴力。。。然后写了个纯粹的二进制穷举，然后，然后，然后，居然AC了？！？！44ms也是醉大了= =

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" alt="" />

 type

     point=^node;

     node=record

                g:longint;

                next:point;

     end;

 var

    i,j,k,l,m,n,t:longint;

    a:array[..] of point;

    b,c,d:array[..] of longint;

    c1,c2:char;

 procedure add(x,y:longint);inline;

           var p:point;

           begin

                new(p);p^.g:=y;

                p^.next:=a[x];a[x]:=p;

           end;

 procedure dfs(x:longint);inline;

           var i,j,k,l:longint;p:point;

           begin

                if x>n then

                   begin

                        for i:= to m do if b[i]> then exit;

                        if t= then

                           begin

                                for i:= to n do d[i]:=c[i];

                                t:=;

                           end

                        else

                            begin

                                 writeln('NOT UNIQUE');

                                 halt;

                            end;

                   end

                else

                    begin

                         p:=a[x];l:=;

                         while p<>nil do

                               begin

                                    if b[p^.g]= then

                                       begin

                                            l:=;

                                            break;

                                       end;

                                    p:=p^.next;

                               end;

                         if l= then

                            begin

                                 p:=a[x];

                                 while p<>nil do

                                       begin

                                            dec(b[p^.g]);

                                            p:=p^.next;

                                       end;

                                 c[x]:=;

                                 dfs(x+);

                                 p:=a[x];

                                 while p<>nil do

                                       begin

                                            inc(b[p^.g]);

                                            p:=p^.next;

                                       end;

                            end;

                         c[x]:=;

                         dfs(x+);

                    end;

           end;

 begin

      readln(n,m);

      for i:= to m do a[i]:=nil;

      for i:= to m do

          begin

               for j:= to n do

                   begin

                        read(c1);

                        if c1='' then add(j,i);

                   end;

               readln(b[i]);

          end;

      t:=;

      dfs();

      IF t= then write('IMPOSSIBLE') else for i:= to n do write(d[i]);

      writeln;

      readln;

 end.

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