add nfa

Author: shellfly

README.md

@@ -78,6 +78,7 @@ To test each algorithm(data structure), instead of running the file directly, yo
   * [TrieST](algs4/trie_st.go)
   * [TST](algs4/tst.go)
   * [KMP](algs4/kmp.go)
+  * [NFA](algs4/nfa.go)
 
 
 ## License

algs4/nfa.go

@@ -0,0 +1,82 @@
+package algs4
+
+// NFA ...
+type NFA struct {
+	re string
+	g  *Digraph
+	m  int
+}
+
+// NewNFA ...
+func NewNFA(re string) *NFA {
+	m := len(re)
+	g := NewDigraphV(m + 1)
+	nfa := &NFA{re, g, m}
+	ops := NewStack()
+	for i := 0; i < m; i++ {
+		lp := i
+		c := string(re[i])
+		if c == "(" || c == "|" {
+			ops.Push(i)
+		} else if c == ")" {
+			op := ops.Pop().(int)
+			if string(re[op]) == "|" {
+				lp = ops.Pop().(int)
+				g.AddEdge(lp, op+1)
+				g.AddEdge(op, i)
+			} else {
+				lp = op
+			}
+		}
+		if i < m-1 && string(re[i+1]) == "*" {
+			g.AddEdge(lp, i+1)
+			g.AddEdge(i+1, lp)
+		}
+
+		if c == "(" || c == "*" || c == ")" {
+			g.AddEdge(i, i+1)
+		}
+	}
+	return nfa
+}
+
+// Recognizes ...
+func (n *NFA) Recognizes(txt string) bool {
+	pc := NewBag()
+	dfs := NewDirectedDFS(n.g, 0)
+	for v := 0; v < n.g.V(); v++ {
+		if dfs.Marked(v) {
+			pc.Add(v)
+		}
+	}
+
+	for i := 0; i < len(txt); i++ {
+		match := NewBag()
+		for _, v := range pc.Slice() {
+			if v.(int) < n.m {
+				if n.re[v.(int)] == txt[i] || string(n.re[v.(int)]) == "." {
+					match.Add(v.(int) + 1)
+				}
+			}
+		}
+
+		matches := []int{}
+		for _, m := range match.Slice() {
+			matches = append(matches, m.(int))
+		}
+		pc = NewBag()
+		dfs = NewDirectedDFSSources(n.g, matches)
+		for v := 0; v < n.g.V(); v++ {
+			if dfs.Marked(v) {
+				pc.Add(v)
+			}
+		}
+	}
+
+	for _, v := range pc.Slice() {
+		if v.(int) == n.m {
+			return true
+		}
+	}
+	return false
+}

cmd/nfa/main.go

@@ -0,0 +1,39 @@
+/******************************************************************************
+ *  Execution:    go run cmd/nfa/main.go regexp text
+ *
+ *  % go run cmd/nfa/main.go "(A*B|AC)D" AAAABD
+ *  true
+ *
+ *  % go run cmd/nfa/main.go "(A*B|AC)D" AAAAC
+ *  false
+ *
+ *  % go run cmd/nfa/main.go "(a|(bc)*d)*" abcbcd
+ *  true
+ *
+ *  % go run cmd/nfa/main.go "(a|(bc)*d)*" abcbcbcdaaaabcbcdaaaddd
+ *  true
+ *
+ *  Remarks
+ *  -----------
+ *  The following features are not supported:
+ *    - The + operator
+ *    - Multiway or
+ *    - Metacharacters in the text
+ *    - Character classes.
+ *
+ ******************************************************************************/
+
+package main
+
+import (
+	"fmt"
+	"os"
+
+	"github.com/shellfly/algo/algs4"
+)
+
+func main() {
+	pattern, txt := os.Args[1], os.Args[2]
+	nfa := algs4.NewNFA(pattern)
+	fmt.Println(nfa.Recognizes(txt))
+}