feat(travelling salesman): init dp soln, untested

Author: jessicayung

algorithms/travelling_salesman.py

@@ -0,0 +1,51 @@
+"""
+Travelling Salesman Problem:
+An Exact Dynamic Programming Solution in Python
+
+Jessica Yung
+Dec 2018
+"""
+
+class TravellingSalesman:
+
+    def __init__(self, graph, start):
+        """Initialise with graph and node you start from.
+        :param graph: takes the form of an adjacency matrix
+                      (suitable since we are given a fully connected graph).
+        :param start: an int (index in adj matrix).
+        Node you start from doesn't make a difference since this is a tour.
+        """
+        self.graph = graph
+        self.start = start
+        self.nodes = np.arange(len(graph))
+
+    def cost(self, nodes, end):
+        if (nodes, end) is in self.cost_dict.keys():
+            return self.cost_dict[(nodes, end)]
+        else:
+            self.cost_dict[nodes, end] = self.calc_cost(nodes, end)
+            return self.cost_dict[nodes, end]
+
+    def calc_cost(self, nodes, end):
+        if end not in nodes:
+            return Exception("Endpoint not in nodes to visit.")
+        if len(nodes) == 1:
+            return 0
+        if len(nodes) == 2:
+            return self.graph[nodes[0], nodes[1]]
+        non_end_nodes = nodes.copy().remove(end)
+        return min(self.cost(non_end_nodes, j) + self.graph[j, end] for j in non_end_nodes if j != self.start)
+
+    def dp(self):
+        """Dynamic programming solution to Travelling Salesman problem."""
+        return self.cost(self.nodes, self.start)
+
+
+# test case:
+def create_adj_matrix(dists):
+    """dists: (n-1)x(n-1) matrix with (n-1)*n/2 entries
+    dists from 0 to 1, 2,...n-1, then dists from 1 to 2,...,n-1.
+    cells that don't represent dists are left as zeroes.
+    """
+    pass
+