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algorithm/PuzzleCoding/src/Queen.java at master · wodgithub/algorithm · GitHub
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PuzzleCoding
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Queen.java
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126 lines (115 loc) · 3.66 KB
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algorithm
/
PuzzleCoding
/
src
/
Queen.java
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import
java
.
util
.
Arrays
;
/**
* Solve the 8 queens problem using recursion and backtracing.
* Prints out all solutions.
* <p/>
* Limitations: works for N <= 25, but slows down considerably
* for larger N.
* <p/>
* Remark: this program implicitly enumerates all N^N possible
* placements (instead of N!), but the backtracing prunes off
* most of them, so it's not necessarily worth the extra
* complication of enumerating only permutations.
* <p/>
* <p/>
* % java Queens 3
* <p/>
* % java Queens 4
* * Q * *
* * * * Q
* Q * * *
* * * Q *
* <p/>
* * * Q *
* Q * * *
* * * * Q
* * Q * *
* <p/>
* % java Queens 8
* Q * * * * * * *
* * * * * Q * * *
* * * * * * * * Q
* * * * * * Q * *
* * * Q * * * * *
* * * * * * * Q *
* * Q * * * * * *
* * * * Q * * * *
*/
public
class
Queen
{
/**
* ********************************************************************
* Return true if queen placement q[n] does not conflict with
* other queens q[0] through q[n-1]
* *********************************************************************
*/
public
static
boolean
isConsistent
(
int
[]
q
,
int
n
) {
for
(
int
i
=
0
;
i
<
n
;
i
++) {
if
(
q
[
i
] ==
q
[
n
])
return
false
;
// same column
if
((
q
[
i
] -
q
[
n
]) == (
n
-
i
))
return
false
;
// same major diagonal
if
((
q
[
n
] -
q
[
i
]) == (
n
-
i
))
return
false
;
// same minor diagonal
}
return
true
;
}
// since it is unique int array, there is no need to compare column/row
public
static
boolean
isConsistent
(
int
[]
q
) {
for
(
int
i
=
0
;
i
<
q
.
length
;
i
++) {
for
(
int
j
=
i
+
1
;
j
<
q
.
length
;
j
++) {
if
(
q
[
i
] ==
q
[
j
])
return
false
;
// same column
if
((
q
[
i
] -
q
[
j
]) == (
j
-
i
))
return
false
;
// same major diagonal
if
((
q
[
j
] -
q
[
i
]) == (
j
-
i
))
return
false
;
// same minor diagonal
}
}
return
true
;
}
/**
* ********************************************************************
* Print out N-by-N placement of queens from permutation q in ASCII.
* *********************************************************************
*/
public
static
void
printQueens
(
int
[]
q
) {
int
N
=
q
.
length
;
for
(
int
i
=
0
;
i
<
N
;
i
++) {
for
(
int
j
=
0
;
j
<
N
;
j
++) {
if
(
q
[
i
] ==
j
)
System
.
out
.
print
(
"Q "
);
else
System
.
out
.
print
(
"* "
);
}
System
.
out
.
println
();
}
System
.
out
.
println
();
}
public
static
void
permQueen
(
String
prefix
,
String
s
) {
int
N
=
s
.
length
();
if
(
N
==
0
) {
int
[]
tmp
=
new
int
[
prefix
.
length
()];
for
(
int
i
=
0
;
i
<
prefix
.
length
();
i
++)
tmp
[
i
] =
Integer
.
valueOf
(
prefix
.
substring
(
i
,
i
+
1
));
if
(
isConsistent
(
tmp
)) {
System
.
out
.
println
(
prefix
);
printQueens
(
tmp
);
}
return
;
}
for
(
int
i
=
0
;
i
<
N
;
i
++)
permQueen
(
prefix
+
s
.
charAt
(
i
),
s
.
substring
(
0
,
i
) +
s
.
substring
(
i
+
1
));
}
public
static
void
enumerate
(
int
[]
q
,
int
n
) {
int
N
=
q
.
length
;
if
(
n
==
N
) {
System
.
out
.
println
(
Arrays
.
toString
(
q
));
printQueens
(
q
);
}
else
{
for
(
int
i
=
0
;
i
<
N
;
i
++) {
q
[
n
] =
i
;
if
(
isConsistent
(
q
,
n
))
enumerate
(
q
,
n
+
1
);
}
}
}
public
static
void
main
(
String
[]
args
) {
int
N
=
4
;
enumerate
(
new
int
[
N
],
0
);
StringBuffer
sb
=
new
StringBuffer
();
for
(
int
i
=
0
;
i
<
N
;
i
++)
sb
.
append
(
String
.
valueOf
(
i
));
permQueen
(
""
,
sb
.
toString
());
}
}
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