2102: [Usaco2010 Dec]The Trough Game

时间:2024-10-24 22:02:50

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.