USACO 2.2 Party Lamps
类型：枚举
描述：
IOI 98
To brighten up the gala dinner of the IOI'98 we have a set of N(10 <= N <= 100) colored lamps numbered from 1 to N.
The lamps are connected to four buttons:
- Button 1: When this button is pressed, all the lamps change their state: those that are ON are turned OFF and those that are OFF are turned ON.
- Button 2: Changes the state of all the odd numbered lamps.
- Button 3: Changes the state of all the even numbered lamps.
- Button 4: Changes the state of the lamps whose number is of the form3xK+1 (with K>=0), i.e., 1,4,7,...
A counter C records the total number of button presses.
When the party starts, all the lamps are ON and the counter Cis set to zero.
You are given the value of counter C (0 <= C <= 10000) and thefinal state of some of the lamps after some operations have been executed.Write a program to determine all the possible final configurations ofthe N lamps that are consistent with the given information, withoutrepetitions.
PROGRAM NAME: lamps
INPUT FORMAT
No lamp will be listed twice in the input.
| Line 1: | N |
| Line 2: | Final value of C |
| Line 3: | Some lamp numbers ON in the final configuration, separated by one space and terminated by the integer -1. |
| Line 4: | Some lamp numbers OFF in the final configuration, separated by one space and terminated by the integer -1. |
SAMPLE INPUT (file lamps.in)
10
1
-1
7 -1
In this case, there are 10 lamps and only one button has been pressed.Lamp 7 is OFF in the final configuration.
OUTPUT FORMAT
Lines with all the possible final configurations (without repetitions)of all the lamps. Each line has N characters, where the first characterrepresents the state of lamp 1 and the last character represents thestate of lamp N. A 0 (zero) stands for a lamp that is OFF, and a 1(one) stands for a lamp that is ON. The lines must be ordered fromleast to largest (as binary numbers).
If there are no possible configurations, output a single line withthe single word `IMPOSSIBLE'
SAMPLE OUTPUT (file lamps.out)
0000000000
0101010101
0110110110
In this case, there are three possible final configurations:
- All lamps are OFF
- Lamps 1, 4, 7, 10 are OFF and lamps 2, 3, 5, 6, 8, 9 are ON.
- Lamps 1, 3, 5, 7, 9 are OFF and lamps 2, 4, 6, 8, 10 are ON.
思路：1.有4种操作，操作的顺序与结果无关，两次同样的操作=无操作，于是可以枚举24种操作；2.进一步的优化是，灯的状态可以压缩成6bit。
ps:请先自己实现，再参考标程。
标程
#include
<
stdio.h
>
#include
<
stdlib.h
>
#include
<
string
.h
>
#include
<
assert.h
>
#define
MAXLAMP 6
#define
LAMPMASK ((1<<MAXLAMP)-1)
int
nlamp;
int
nswitch;
int
ison;
int
known;
int
poss[
1
<<
MAXLAMP];
int
flip[
4
]
=
{
LAMPMASK,
/*
flip all lights
*/
LAMPMASK
&
0xAA
,
/*
flip odd lights
*/
LAMPMASK
&
0x55
,
/*
flip even lights
*/
LAMPMASK
&
((
1
<<
(MAXLAMP
-
1
))
|
(
1
<<
(MAXLAMP
-
4
)))
/*
lights 1, 4
*/
};
/*
* Starting with current light state ``lights'', flip exactly n switches
* with number >= i.
*/
void
search(
int
lights,
int
i,
int
n)
{
if
(n
==
0
) {
if
((lights
&
known)
==
ison)
poss[lights]
=
1
;
return
;
}
for
(; i
<
4
; i
++
)
search(lights
^
flip[i], i
+
1
, n
-
1
);
}
void
printseq(FILE
*
fout,
int
lights)
{
int
i;
char
s[
100
+
1
];
for
(i
=
0
; i
<
nlamp; i
++
)
s[i]
=
(lights
&
(
1
<<
(MAXLAMP
-
1
-
i
%
MAXLAMP)))
?
'
1
'
:
'
0
'
;
s[nlamp]
=
'
\0
'
;
fprintf(fout,
"
%s\n
"
, s);
}
void
main(
void
)
{
FILE
*
fin,
*
fout;
int
a, i, impossible;
fin
=
fopen(
"
lamps.in
"
,
"
r
"
);
fout
=
fopen(
"
lamps.out
"
,
"
w
"
);
assert(fin
!=
NULL
&&
fout
!=
NULL);
fscanf(fin,
"
%d %d
"
,
&
nlamp,
&
nswitch);
for
(;;) {
fscanf(fin,
"
%d
"
,
&
a);
if
(a
==
-
1
)
break
;
a
=
MAXLAMP
-
1
-
(a
-
1
)
%
MAXLAMP;
ison
|=
1
<<
a;
known
|=
1
<<
a;
}
for
(;;) {
fscanf(fin,
"
%d
"
,
&
a);
if
(a
==
-
1
)
break
;
a
=
MAXLAMP
-
1
-
(a
-
1
)
%
MAXLAMP;
assert((ison
&
(
1
<<
a))
==
0
);
known
|=
1
<<
a;
}
if
(nswitch
>
4
)
if
(nswitch
%
2
==
0
)
nswitch
=
4
;
else
nswitch
=
3
;
for
(; nswitch
>=
0
; nswitch
-=
2
)
search(LAMPMASK,
0
, nswitch);
impossible
=
1
;
for
(i
=
0
; i
<
(
1
<<
MAXLAMP); i
++
) {
if
(poss[i]) {
printseq(fout, i);
impossible
=
0
;
}
}
if
(impossible)
fprintf(fout,
"
IMPOSSIBLE\n
"
);
exit(
0
);
}