Add example sent by Ganesh

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

examples/python/hamiltonian/hamiltonian.py

@@ -0,0 +1,88 @@
+############################################
+# Copyright (c) 2012 Ganesh Gopalakrishnan ganesh@cs.utah.edu
+# 
+# Hamiltonian
+#
+# Author: Ganesh Gopalakrishnan ganesh@cs.utah.edu
+############################################
+from z3 import *
+
+def gencon(gr):
+    """
+    Input a graph as an adjacency list, e.g. {0:[1,2], 1:[2], 2:[1,0]}.
+    Produces solver to check if the given graph has
+    a Hamiltonian cycle. Query the solver using s.check() and if sat,
+    then s.model() spells out the cycle. Two example graphs from
+    http://en.wikipedia.org/wiki/Hamiltonian_path are tested.
+
+    =======================================================
+    
+    Explanation:
+    
+    Generate a list of Int vars. Constrain the first Int var ("Node 0") to be 0.
+    Pick a node i, and attempt to number all nodes reachable from i to have a
+    number one higher (mod L) than assigned to node i (use an Or constraint).
+    
+    =======================================================
+    """
+    L = len(gr)
+    cv = [Int('cv%s'%i) for i in range(L)]
+    s = Solver()
+    s.add(cv[0]==0)
+    for i in range(L):
+        s.add(Or([cv[j]==(cv[i]+1)%L for j in gr[i]]))
+    return s
+
+def examples():
+    # Example Graphs: The Dodecahedral graph from http://en.wikipedia.org/wiki/Hamiltonian_path
+    grdodec = { 0: [1, 4, 5],
+                1: [0, 7, 2],
+                2: [1, 9, 3],
+                3: [2, 11, 4],
+                4: [3, 13, 0],
+                5: [0, 14, 6],
+                6: [5, 16, 7],
+                7: [6, 8, 1],
+                8: [7, 17, 9],
+                9: [8, 10, 2],
+                10: [9, 18, 11],
+                11: [10, 3, 12],
+                12: [11, 19, 13],
+                13: [12, 14, 4],
+                14: [13, 15, 5],
+                15: [14, 16, 19],
+                16: [6, 17, 15],
+                17: [16, 8, 18],
+                18: [10, 19, 17],
+                19: [18, 12, 15] }
+    import pprint
+    pp = pprint.PrettyPrinter(indent=4)
+    pp.pprint(grdodec)
+    
+    sdodec=gencon(grdodec)
+    print(sdodec.check())
+    print(sdodec.model())
+    # =======================================================
+    # See http://en.wikipedia.org/wiki/Hamiltonian_path for the Herschel graph
+    # being the smallest possible polyhdral graph that does not have a Hamiltonian
+    # cycle.
+    #
+    grherschel = { 0: [1, 9, 10, 7],
+                   1: [0, 8, 2],
+                   2: [1, 9, 3],
+                   3: [2, 8, 4],
+                   4: [3, 9, 10, 5],
+                   5: [4, 8, 6],
+                   6: [5, 10, 7],
+                   7: [6, 8, 0],
+                   8: [1, 3, 5, 7],
+                   9: [2, 0, 4],
+                   10: [6, 4, 0] }
+    pp.pprint(grherschel)
+    sherschel=gencon(grherschel)
+    print(sherschel.check())
+    # =======================================================
+
+if __name__ == "__main__":
+    examples()
+