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type TwoCNFSolver struct {
graph map[string][]string
revGraph map[string][]string
visited map[string]bool
finishOrder []string
sccId map[string]int
sccCount int
}
func solve2CNF(clauses [][]string) map[string]bool {
solver := &TwoCNFSolver{
graph: make(map[string][]string),
revGraph: make(map[string][]string),
visited: make(map[string]bool),
sccId: make(map[string]int),
}
// Build implication graph
solver.buildGraph(clauses)
// Find SCCs
solver.findSCCs()
// Check satisfiability
variables := extractVariables(clauses)
for _, variable := range variables {
if solver.sccId[variable] == solver.sccId[negate(variable)] {
return nil // Unsatisfiable
}
}
// Assign truth values
return solver.assignValues(variables)
}
func (s *TwoCNFSolver) buildGraph(clauses [][]string) {
for _, clause := range clauses {
a, b := clause[0], clause[1]
notA, notB := negate(a), negate(b)
// (A OR B) => (¬A → B) and (¬B → A)
s.graph[notA] = append(s.graph[notA], b)
s.graph[notB] = append(s.graph[notB], a)
s.revGraph[b] = append(s.revGraph[b], notA)
s.revGraph[a] = append(s.revGraph[a], notB)
}
}
func negate(lit string) string {
if strings.HasPrefix(lit, "¬") {
return lit[1:]
}
return "¬" + lit
}
func (s *TwoCNFSolver) findSCCs() {
// First DFS to get finish order
for node := range s.graph {
if !s.visited[node] {
s.dfs1(node)
}
}
// Second DFS on reverse graph
s.visited = make(map[string]bool)
s.sccCount = 0
// Reverse finish order
for i, j := 0, len(s.finishOrder)-1; i < j; i, j = i+1, j-1 {
s.finishOrder[i], s.finishOrder[j] = s.finishOrder[j], s.finishOrder[i]
}
for _, node := range s.finishOrder {
if !s.visited[node] {
s.dfs2(node, s.sccCount)
s.sccCount++
}
}
}
func (s *TwoCNFSolver) dfs1(node string) {
s.visited[node] = true
for _, neighbor := range s.graph[node] {
if !s.visited[neighbor] {
s.dfs1(neighbor)
}
}
s.finishOrder = append(s.finishOrder, node)
}
func (s *TwoCNFSolver) dfs2(node string, id int) {
s.visited[node] = true
s.sccId[node] = id
for _, neighbor := range s.revGraph[node] {
if !s.visited[neighbor] {
s.dfs2(neighbor, id)
}
}
}
func extractVariables(clauses [][]string) []string {
varSet := make(map[string]bool)
for _, clause := range clauses {
for _, lit := range clause {
var variable string
if strings.HasPrefix(lit, "¬") {
variable = lit[1:]
} else {
variable = lit
}
varSet[variable] = true
}
}
var variables []string
for variable := range varSet {
variables = append(variables, variable)
}
return variables
}
func (s *TwoCNFSolver) assignValues(variables []string) map[string]bool {
assignment := make(map[string]bool)
type sccLit struct {
id int
lit string
}
var sccOrder []sccLit
for _, variable := range variables {
sccOrder = append(sccOrder, sccLit{s.sccId[variable], variable})
sccOrder = append(sccOrder, sccLit{s.sccId["¬"+variable], "¬" + variable})
}
// Sort in reverse topological order
sort.Slice(sccOrder, func(i, j int) bool {
return sccOrder[i].id > sccOrder[j].id
})
for _, item := range sccOrder {
lit := item.lit
var variable string
if strings.HasPrefix(lit, "¬") {
variable = lit[1:]
} else {
variable = lit
}
if _, exists := assignment[variable]; !exists {
value := !strings.HasPrefix(lit, "¬")
assignment[variable] = value
}
}
return assignment
}
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