add nfa

README.md

@@ -85,7 +85,8 @@ Try to keep the interface and variable name consistent with the original book wh
   * [TrieST](algs4/trie_st.py)
   * [TST](algs4/tst.py)
   * [KMP](algs4/kmp.py)
-
+  * [NFA](algs4/nfa.py)
+
 ## License
 
 This code is released under MIT.

algs4/bag.py

@@ -19,7 +19,7 @@ def __init__(self):
         self.n = 0
 
     def __str__(self):
-        return " ".join(i for i in self)
+        return " ".join(str(i) for i in self)
 
     def __iter__(self):
         return LinkIterator(self.first)

algs4/nfa.py

@@ -0,0 +1,88 @@
+"""
+ *  Execution:    python nfa.py regexp text
+ *
+ *  % python nfa.py "(A*B|AC)D" AAAABD
+ *  true
+ *
+ *  % python nfa.py "(A*B|AC)D" AAAAC
+ *  false
+ *
+ *  % python nfa.py "(a|(bc)*d)*" abcbcd
+ *  true
+ *
+ *  % python nfa.py "(a|(bc)*d)*" abcbcbcdaaaabcbcdaaaddd
+ *  true
+ *
+ *  Remarks
+ *  -----------
+ *  The following features are not supported:
+ *    - The + operator
+ *    - Multiway or
+ *    - Metacharacters in the text
+ *    - Character classes.
+ *
+"""
+
+from algs4.bag import Bag
+from algs4.digraph import Digraph
+from algs4.directed_dfs import DirectedDFS
+from algs4.stack import Stack
+
+
+class NFA:
+    def __init__(self, regexp):
+        ops = Stack()
+        M = len(regexp)
+        G = Digraph(M+1)
+        for i in range(M):
+            lp = i
+            if regexp[i] == "(" or regexp[i] == "|":
+                ops.push(i)
+            elif regexp[i] == ")":
+                op = ops.pop()
+                if regexp[op] == "|":
+                    lp = ops.pop()
+                    G.add_edge(lp, op+1)
+                    G.add_edge(op, i)
+                else:
+                    lp = op
+            if i < M-1 and regexp[i+1] == "*":
+                G.add_edge(lp, i+1)
+                G.add_edge(i+1, lp)
+            if regexp[i] in ("(", "*", ")"):
+                G.add_edge(i, i+1)
+        self.M = M
+        self.G = G
+        self.re = regexp
+
+    def recognizes(self, txt):
+        pc = Bag()
+        dfs = DirectedDFS(self.G, [0])
+        for v in range(self.G.V):
+            if dfs.marked(v):
+                pc.add(v)
+        for i in range(len(txt)):
+            match = Bag()
+            for v in pc:
+                if v < self.M:
+                    if self.re[v] == txt[i] or self.re[v] == ".":
+                        match.add(v+1)
+            pc = Bag()
+            dfs = DirectedDFS(self.G, match)
+            for v in range(self.G.V):
+                if dfs.marked(v):
+                    pc.add(v)
+        for v in pc:
+            if v == self.M:
+                return True
+        return False
+
+    def char_at(self, s, d):
+        return ord(s[d])
+
+
+if __name__ == "__main__":
+    import sys
+    pattern, txt = sys.argv[1], sys.argv[2]
+    nfa = NFA(pattern)
+    print(nfa.recognizes(txt))