initial commit

cycles.py

@@ -0,0 +1,107 @@
+"""
+R. Tarjan, Enumeration of the elementary circuits of a directed graph, SIAM Journal on Computing, 2 (1973), pp. 211-216
+
+procedure circuit_enumeration;
+  begin
+    procedure BACKTRACK(integer value v, logical result f);
+      begin
+        logical g;
+        f := false;
+        place v on point stack;
+        mark(v) := true;
+        place v on marked stack;
+        for w in A(v) do
+          if w<s then delete w from A(v);
+          else if w=s then
+            begin
+              output circuit from s to v to s given by point stack
+              f:=true;
+            end;
+          else if not mark(w) then
+            begin
+              BACKTRACK(w,g);
+              f:=f or g;
+            end;
+          comment f=true if an elementary circuit continuing the
+            partial path on the stack has been found;
+        if f=true then
+          begin
+            while top of marked stack is not v do
+              begin
+                u:=top of marked stack;
+                delete u from marked stack;
+                mark(u):=false
+              end;
+            delete v from marked stack;
+            mar(v):=false;
+          end;
+        delete v from point stack;
+      end;
+    integer n;
+    for i:=1 until v do mark(i):=false;
+    for s:=1 until v do
+      begin
+        BACKTRACK(s,flag);
+        while marked stack not empty do
+          begin
+            u:=top of marked stack;
+            mark(u):=false;
+            delete u from marked stack;
+          end;
+      end;
+  end;
+"""
+
+A = [[] for a in range(5)]
+
+A[0].append(1)
+A[0].append(4)
+A[1].append(4)
+A[2].append(0)
+A[2].append(3)
+A[2].append(4)
+A[3].append(0)
+A[3].append(2)
+A[3].append(4)
+A[4].append(3)
+
+def print_point_stack():
+    for p in point_stack:
+        print p,
+    print
+
+point_stack = list()
+marked = dict()
+marked_stack = list()
+
+def backtrack(v, f):
+    g = [False]
+    f[0] = False
+    point_stack.append(v)
+    marked[v] = True
+    marked_stack.append(v)
+    for w in A[v]:
+        if w<s:
+            A[w] = 0
+        elif w==s:
+            print_point_stack()
+            f[0] = True
+        elif not marked[w]:
+            backtrack(w, g)
+            f[0] = f[0] or g[0]
+    if f:
+        while marked_stack[-1] != v:
+            u = marked_stack.pop()
+            marked[u] = False
+        marked_stack.pop()
+        marked[v] = False
+    point_stack.pop()
+
+for i in range(len(A)):
+    marked[i] = False
+
+for s in range(len(A)):
+    backtrack(s, [False])
+    while marked_stack:
+        u = marked_stack.pop()
+        marked[u] = False