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// Copyright ©2015 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package
plotter
import
(
"fmt"
"reflect"
"sort"
"testing"
)
func
linksTo
(
i
...
int
)
set
{
if
len
(
i
)
==
0
{
return
nil
}
s
:=
make
(
set
)
for
_
,
v
:=
range
i
{
s
[
v
]
=
struct
{}{}
}
return
s
}
func
(
s
set
)
String
()
string
{
a
:=
make
([]
int
,
0
,
len
(
s
))
for
v
:=
range
s
{
a
=
append
(
a
,
v
)
}
sort
.
Ints
(
a
)
return
fmt
.
Sprint
(
a
)
}
var
graphTests
=
[]
struct
{
path
path
g
graph
// Tarjan tests.
orderIsAmbiguous
bool
wantSCCs
[][]
int
wantAdj
graph
// Johnson tests.
wantCycles
[][]
int
wantCyclePaths
[]
path
}{
{
path
:
path
{{
0
,
0
}, {
1
,
1
}, {
2
,
2
}, {
3
,
3
}, {
4
,
4
}, {
5
,
5
}, {
6
,
6
}, {
7
,
7
}, {
8
,
8
}, {
9
,
9
}},
wantSCCs
: [][]
int
{{
9
}, {
8
}, {
7
}, {
6
}, {
5
}, {
4
}, {
3
}, {
2
}, {
1
}, {
0
}},
wantAdj
:
nil
,
wantCycles
:
nil
,
wantCyclePaths
:
nil
,
},
{
path
:
path
{{
0
,
0
}, {
1
,
1
}, {
2
,
2
}, {
3
,
3
}, {
4
,
4
}, {
5
,
5
}, {
6
,
6
}, {
4
,
4
}, {
7
,
7
}, {
8
,
8
}, {
9
,
9
}},
wantSCCs
: [][]
int
{
{
10
}, {
9
}, {
8
},
{
4
,
5
,
6
},
{
3
}, {
2
}, {
1
}, {
0
},
{
7
/*second point{4, 4}*/
},
},
wantAdj
:
graph
{
4
:
linksTo
(
5
),
5
:
linksTo
(
6
),
6
:
linksTo
(
4
),
10
:
nil
,
},
wantCycles
: [][]
int
{
{
4
,
5
,
6
,
4
},
},
wantCyclePaths
: []
path
{
{{
4
,
4
}, {
5
,
5
}, {
6
,
6
}, {
4
,
4
}},
},
},
{
path
:
path
{{
0
,
0
}, {
1
,
1
}, {
2
,
2
}, {
3
,
3
}, {
4
,
4
}, {
5
,
5
}, {
6
,
6
}, {
4
,
4
}, {
7
,
7
}, {
2
,
2
}, {
9
,
9
}},
wantSCCs
: [][]
int
{
{
10
},
{
2
,
3
,
4
,
5
,
6
,
8
},
{
1
}, {
0
},
{
7
/*second point{4, 4}*/
},
{
9
/*second point{2, 2}*/
},
},
wantAdj
:
graph
{
2
:
linksTo
(
3
),
3
:
linksTo
(
4
),
4
:
linksTo
(
5
,
8
),
5
:
linksTo
(
6
),
6
:
linksTo
(
4
),
8
:
linksTo
(
2
),
10
:
nil
,
},
wantCycles
: [][]
int
{
{
4
,
5
,
6
,
4
},
{
2
,
3
,
4
,
8
,
2
},
},
wantCyclePaths
: []
path
{
{{
4
,
4
}, {
5
,
5
}, {
6
,
6
}, {
4
,
4
}},
{{
2
,
2
}, {
3
,
3
}, {
4
,
4
}, {
7
,
7
}, {
2
,
2
}},
},
},
{
path
:
path
{{
0
,
0
}, {
1
,
1
}, {
2
,
2
}, {
3
,
3
}, {
4
,
4
}, {
5
,
5
}, {
2
,
2
}, {
7
,
7
}, {
2
,
2
}, {
9
,
9
}},
wantSCCs
: [][]
int
{{
9
},
{
2
,
3
,
4
,
5
,
7
},
{
1
}, {
0
},
{
6
/*second point{2, 2}*/
},
{
8
/*third point{2, 2}*/
},
},
wantAdj
:
graph
{
2
:
linksTo
(
3
,
7
),
3
:
linksTo
(
4
),
4
:
linksTo
(
5
),
5
:
linksTo
(
2
),
7
:
linksTo
(
2
),
9
:
nil
,
},
wantCycles
: [][]
int
{
{
2
,
7
,
2
},
{
2
,
3
,
4
,
5
,
2
},
},
wantCyclePaths
: []
path
{
{{
2
,
2
}, {
7
,
7
}, {
2
,
2
}},
{{
2
,
2
}, {
3
,
3
}, {
4
,
4
}, {
5
,
5
}, {
2
,
2
}},
},
},
{
path
:
path
{{
0
,
0
}, {
1
,
1
}, {
2
,
2
}, {
3
,
3
}, {
4
,
4
}, {
5
,
5
}, {
6
,
6
}, {
3
,
3
}, {
8
,
8
}, {
9
,
9
}, {
5
,
5
}, {
10
,
10
}},
wantSCCs
: [][]
int
{
{
11
},
{
3
,
4
,
5
,
6
,
8
,
9
},
{
2
}, {
1
}, {
0
},
{
7
/*second point{4, 4}*/
},
{
10
/*second point{2, 2}*/
},
},
wantAdj
:
graph
{
3
:
linksTo
(
4
,
8
),
4
:
linksTo
(
5
),
5
:
linksTo
(
6
),
6
:
linksTo
(
3
),
8
:
linksTo
(
9
),
9
:
linksTo
(
5
),
11
:
nil
,
},
wantCycles
: [][]
int
{
{
3
,
4
,
5
,
6
,
3
},
{
3
,
8
,
9
,
5
,
6
,
3
},
},
wantCyclePaths
: []
path
{
{{
3
,
3
}, {
4
,
4
}, {
5
,
5
}, {
6
,
6
}, {
3
,
3
}},
{{
3
,
3
}, {
8
,
8
}, {
9
,
9
}, {
5
,
5
}, {
6
,
6
}, {
3
,
3
}},
},
},
{
path
:
path
{{
0
,
0
}, {
1
,
1
}, {
2
,
2
}, {
3
,
3
}, {
0
,
0
}, {
5
,
5
}, {
6
,
6
}, {
7
,
7
}, {
5
,
5
}, {
9
,
9
}, {
10
,
10
}, {
9
,
9
}},
wantSCCs
: [][]
int
{
{
9
,
10
},
{
5
,
6
,
7
},
{
0
,
1
,
2
,
3
},
{
4
/*second point{0, 0}*/
},
{
8
/*second point{5, 5}*/
},
{
11
/*second point{9, 9}*/
},
},
wantAdj
:
graph
{
0
:
linksTo
(
1
),
1
:
linksTo
(
2
),
2
:
linksTo
(
3
),
3
:
linksTo
(
0
),
5
:
linksTo
(
6
),
6
:
linksTo
(
7
),
7
:
linksTo
(
5
),
9
:
linksTo
(
10
),
10
:
linksTo
(
9
),
11
:
nil
,
},
wantCycles
: [][]
int
{
{
9
,
10
,
9
},
{
5
,
6
,
7
,
5
},
{
0
,
1
,
2
,
3
,
0
},
},
wantCyclePaths
: []
path
{
{{
9
,
9
}, {
10
,
10
}, {
9
,
9
}},
{{
5
,
5
}, {
6
,
6
}, {
7
,
7
}, {
5
,
5
}},
{{
0
,
0
}, {
1
,
1
}, {
2
,
2
}, {
3
,
3
}, {
0
,
0
}},
},
},
{
g
:
graph
{
0
:
linksTo
(
1
),
1
:
linksTo
(
2
,
7
),
2
:
linksTo
(
3
,
6
),
3
:
linksTo
(
4
),
4
:
linksTo
(
2
,
5
),
6
:
linksTo
(
3
,
5
),
7
:
linksTo
(
0
,
6
),
},
wantSCCs
: [][]
int
{
{
5
},
{
2
,
3
,
4
,
6
},
{
0
,
1
,
7
},
},
wantAdj
:
graph
{
0
:
linksTo
(
1
),
1
:
linksTo
(
7
),
2
:
linksTo
(
3
,
6
),
3
:
linksTo
(
4
),
4
:
linksTo
(
2
),
6
:
linksTo
(
3
),
7
:
linksTo
(
0
),
},
wantCycles
: [][]
int
{
{
0
,
1
,
7
,
0
},
{
2
,
3
,
4
,
2
},
{
2
,
6
,
3
,
4
,
2
},
},
},
{
g
:
graph
{
0
:
linksTo
(
1
,
2
,
3
),
1
:
linksTo
(
2
),
2
:
linksTo
(
3
),
3
:
linksTo
(
1
),
},
wantSCCs
: [][]
int
{
{
1
,
2
,
3
},
{
0
},
},
wantAdj
:
graph
{
1
:
linksTo
(
2
),
2
:
linksTo
(
3
),
3
:
linksTo
(
1
),
},
wantCycles
: [][]
int
{
{
1
,
2
,
3
,
1
},
},
},
{
g
:
graph
{
0
:
linksTo
(
1
),
1
:
linksTo
(
0
,
2
),
2
:
linksTo
(
1
),
},
wantSCCs
: [][]
int
{
{
0
,
1
,
2
},
},
wantAdj
:
graph
{
0
:
linksTo
(
1
),
1
:
linksTo
(
0
,
2
),
2
:
linksTo
(
1
),
},
wantCycles
: [][]
int
{
{
0
,
1
,
0
},
{
1
,
2
,
1
},
},
},
{
g
:
graph
{
0
:
linksTo
(
1
),
1
:
linksTo
(
2
,
3
),
2
:
linksTo
(
4
,
5
),
3
:
linksTo
(
4
,
5
),
4
:
linksTo
(
6
),
5
:
nil
,
6
:
nil
,
},
orderIsAmbiguous
:
true
,
wantSCCs
: [][]
int
{
// Node pairs (2, 3) and (4, 5) are not
// relatively orderable within each pair.
{
6
}, {
5
}, {
4
}, {
3
}, {
2
}, {
1
}, {
0
},
},
wantAdj
:
nil
,
wantCycles
:
nil
,
},
{
g
:
graph
{
0
:
linksTo
(
1
),
1
:
linksTo
(
2
,
3
,
4
),
2
:
linksTo
(
0
,
3
),
3
:
linksTo
(
4
),
4
:
linksTo
(
3
),
},
orderIsAmbiguous
:
true
,
wantSCCs
: [][]
int
{
// SCCs are not relatively ordable.
{
3
,
4
}, {
0
,
1
,
2
},
},
wantAdj
:
graph
{
0
:
linksTo
(
1
),
1
:
linksTo
(
2
),
2
:
linksTo
(
0
),
3
:
linksTo
(
4
),
4
:
linksTo
(
3
),
},
wantCycles
: [][]
int
{
{
3
,
4
,
3
},
{
0
,
1
,
2
,
0
},
},
},
}
func
TestTarjan
(
t
*
testing.
T
) {
for
i
,
test
:=
range
graphTests
{
var
g
graph
if
test
.
path
!=
nil
{
g
=
graphFrom
(
test
.
path
)
}
else
{
g
=
test
.
g
}
tar
:=
newTarjan
(
g
)
gotSCCs
:=
tar
.
sccs
if
test
.
orderIsAmbiguous
{
// We lose topological order here, but that
// is not important for this use case.
sort
.
Sort
(
byComponentLengthOrStart
(
test
.
wantSCCs
))
sort
.
Sort
(
byComponentLengthOrStart
(
gotSCCs
))
}
// tarjan.strongconnect does range iteration over maps,
// so sort SCC members to ensure consistent ordering.
for
_
,
scc
:=
range
gotSCCs
{
sort
.
Ints
(
scc
)
}
if
!
reflect
.
DeepEqual
(
gotSCCs
,
test
.
wantSCCs
) {
t
.
Errorf
(
"unexpected tarjan scc result for %d:
\n
\t
got:%v
\n
\t
want:%v"
,
i
,
gotSCCs
,
test
.
wantSCCs
)
}
gotAdj
:=
tar
.
sccSubGraph
(
2
)
if
!
reflect
.
DeepEqual
(
gotAdj
,
test
.
wantAdj
) {
t
.
Errorf
(
"unexpected tarjan sccSubGraph(2) result for %d:
\n
\t
got:%#v
\n
\t
want:%#v"
,
i
,
gotAdj
,
test
.
wantAdj
)
}
}
}
func
TestJohnson
(
t
*
testing.
T
) {
for
i
,
test
:=
range
graphTests
{
var
g
graph
if
test
.
path
!=
nil
{
g
=
graphFrom
(
test
.
path
)
}
else
{
g
=
test
.
g
}
gotCycles
:=
cyclesIn
(
g
)
// johnson.circuit does range iteration over maps,
// so sort to ensure consistent ordering.
sort
.
Sort
(
byComponentLengthOrStart
(
gotCycles
))
if
!
reflect
.
DeepEqual
(
gotCycles
,
test
.
wantCycles
) {
t
.
Errorf
(
"unexpected johnson result for %d:
\n
\t
got:%#v
\n
\t
want:%#v"
,
i
,
gotCycles
,
test
.
wantCycles
)
}
// Don't do path reconstruction tests without a path definition.
if
test
.
path
==
nil
{
continue
}
// Test we reconstruct paths correctly from cycles.
var
gotPaths
[]
path
for
_
,
pi
:=
range
gotCycles
{
gotPaths
=
append
(
gotPaths
,
test
.
path
.
subpath
(
pi
))
}
if
!
reflect
.
DeepEqual
(
gotPaths
,
test
.
wantCyclePaths
) {
t
.
Errorf
(
"unexpected johnson path result for %d:
\n
\t
got:%#v
\n
\t
want:%#v"
,
i
,
gotPaths
,
test
.
wantCyclePaths
)
}
}
}
type
byComponentLengthOrStart
[][]
int
func
(
c
byComponentLengthOrStart
)
Len
()
int
{
return
len
(
c
) }
func
(
c
byComponentLengthOrStart
)
Less
(
i
,
j
int
)
bool
{
return
len
(
c
[
i
])
<
len
(
c
[
j
])
||
(
len
(
c
[
i
])
==
len
(
c
[
j
])
&&
c
[
i
][
0
]
<
c
[
j
][
0
])
}
func
(
c
byComponentLengthOrStart
)
Swap
(
i
,
j
int
) {
c
[
i
],
c
[
j
]
=
c
[
j
],
c
[
i
] }
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