Merge pull request #531 from sinAshish/patch-1

Create hamilton.py

Author: matthewsamuel95

BackTracking/Hamilton Path/hamilton.py

@@ -0,0 +1,96 @@
+
+class Graph(): 
+    def __init__(self, vertices): 
+        self.graph = [[0 for column in range(vertices)]\ 
+                            for row in range(vertices)] 
+        self.V = vertices 
+  
+    def isSafe(self, v, pos, path): 
+        # Check if current vertex and last vertex  
+        # in path are adjacent 
+        if self.graph[ path[pos-1] ][v] == 0: 
+            return False
+  
+        # Check if current vertex not already in path 
+        for vertex in path: 
+            if vertex == v: 
+                return False
+  
+        return True
+  
+    def hamCycleUtil(self, path, pos): 
+  
+        # base case: if all vertices are  
+        # included in the path 
+        if pos == self.V: 
+            # Last vertex must be adjacent to the  
+            # first vertex in path to make a cyle 
+            if self.graph[ path[pos-1] ][ path[0] ] == 1: 
+                return True
+            else: 
+                return False
+  
+        for v in range(1,self.V): 
+  
+            if self.isSafe(v, pos, path) == True: 
+  
+                path[pos] = v 
+  
+                if self.hamCycleUtil(path, pos+1) == True: 
+                    return True
+  
+                # Remove current vertex if it doesn't  
+                # lead to a solution 
+                path[pos] = -1
+  
+        return False
+  
+    def hamCycle(self): 
+        path = [-1] * self.V 
+  
+        ''' Let us put vertex 0 as the first vertex  
+            in the path. If there is a Hamiltonian Cycle,  
+            then the path can be started from any point 
+            of the cycle as the graph is undirected '''
+        path[0] = 0
+  
+        if self.hamCycleUtil(path,1) == False: 
+            print "Solution does not exist\n"
+            return False
+  
+        self.printSolution(path) 
+        return True
+  
+    def printSolution(self, path): 
+        print "Solution Exists: Following is one Hamiltonian Cycle"
+        for vertex in path: 
+            print vertex, 
+        print path[0], "\n"
+  
+''' Let us create the following graph 
+      (0)--(1)--(2) 
+       |   / \   | 
+       |  /   \  | 
+       | /     \ | 
+      (3)-------(4)    '''
+g1 = Graph(5) 
+g1.graph = [ [0, 1, 0, 1, 0], [1, 0, 1, 1, 1],  
+             [0, 1, 0, 0, 1,],[1, 1, 0, 0, 1],  
+             [0, 1, 1, 1, 0], ] 
+  
+# Print the solution 
+g1.hamCycle(); 
+  
+''' Let us create the following graph 
+      (0)--(1)--(2) 
+       |   / \   | 
+       |  /   \  | 
+       | /     \ | 
+      (3)       (4)    '''
+g2 = Graph(5) 
+g2.graph = [ [0, 1, 0, 1, 0], [1, 0, 1, 1, 1],  
+           [0, 1, 0, 0, 1,], [1, 1, 0, 0, 0],  
+           [0, 1, 1, 0, 0], ] 
+  
+# Print the solution 
+g2.hamCycle();