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nqueens_test.go
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nqueens_test.go
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package gobdd
import (
"fmt"
"github.com/timbeurskens/gobdd/algorithm"
"github.com/timbeurskens/gobdd/bdd_test"
. "github.com/timbeurskens/gobdd/operators"
bdd2 "github.com/timbeurskens/gobdd/operators/bdd"
"log"
"testing"
)
func TestNQueensCDCL(t *testing.T) {
const n = 4
b := bdd_test.Bench{T: t}
expr := makeNQueensExpression(n)
nnf := algorithm.NNF(expr)
cnf := algorithm.TransformTseitin(nnf)
log.Println(cnf)
sat, solution := algorithm.CDCL(cnf)
b.Assert("n-queens cdcl is SAT", sat)
if model, ok := bdd2.FindModel(solution); ok {
queens_r := model.Variables(true)
queens := make([]Variable, 0, len(queens_r))
for _, q := range queens_r {
if _, ok := q.(*StringVariable); ok {
queens = append(queens, q)
}
}
b.AssertInfo("there are n queens", len(queens) == n, queens)
}
}
func TestNQueens(t *testing.T) {
const n = 4
b := bdd_test.Bench{T: t}
expr := makeNQueensExpression(n)
t.Log(PrintExpressiontree(expr))
// gobdd.DotExpressionTree(expr)
expr = algorithm.PruneUnary(expr)
t.Log("Size:", Size(expr))
bdd := algorithm.FromExpression(expr)
t.Log("Reduced size:", Size(bdd))
//DotExpressionTree(expr)
//DotSubtree(bdd)
b.AssertSat("n-queens is satisfiable", bdd)
if model, ok := bdd2.FindModel(bdd); ok {
t.Log(model)
queens := model.Variables(true)
b.AssertInfo("there are n queens", len(queens) == n, queens)
}
}
func makeNQueensExpression(n int) Expression {
field := make([][]Variable, n)
for i := range field {
field[i] = make([]Variable, n)
}
for i := range field {
for j := range field[i] {
field[i][j] = Var(fmt.Sprintf("p_%d_%d", i, j))
}
}
var expr Expression = Cons(true)
// every row must have at least one queen
for i := 0; i < n; i++ {
var disj Expression = Cons(false)
for j := 0; j < n; j++ {
disj = Or(disj, field[i][j])
}
expr = And(expr, disj)
}
// every column must have at least one queen
for i := 0; i < n; i++ {
var disj Expression = Cons(false)
for j := 0; j < n; j++ {
disj = Or(disj, field[j][i])
}
expr = And(expr, disj)
}
// every row must have at most one queen
for i := 0; i < n; i++ {
for j1 := 1; j1 < n; j1++ {
for j2 := 0; j2 < j1; j2++ {
expr = And(expr, Or(Not(field[i][j1]), Not(field[i][j2])))
}
}
}
// every column must have at most one queen
for i := 0; i < n; i++ {
for j1 := 1; j1 < n; j1++ {
for j2 := 0; j2 < j1; j2++ {
expr = And(expr, Or(Not(field[j1][i]), Not(field[j2][i])))
}
}
}
// no two queens on a single diagonal
for i := 1; i < n*n; i++ {
i1, j1 := i/n, i%n
for j := 0; j < i; j++ {
i2, j2 := j/n, j%n
if i1-j1 == i2-j2 || i1+j1 == i2+j2 {
expr = And(expr, Or(Not(field[i1][j1]), Not(field[i2][j2])))
}
}
}
return expr
}
func benchmarkNQueens(n int, b *testing.B) {
expr := makeNQueensExpression(n)
test := bdd_test.Bench{T: b}
for i := 0; i < b.N; i++ {
bdd := algorithm.FromExpression(expr)
test.AssertSat("n-queens is satisfiable", bdd)
}
}
func BenchmarkNQueens(b *testing.B) {
for i := 4; i <= 6; i++ {
b.Run(fmt.Sprintf("benchmarkNQueens:%d", i), func(b *testing.B) {
benchmarkNQueens(i, b)
})
}
}