Combinations into pairs - combinations

Question

I'm working on a directed network problem and trying to compute all valid paths between two points. I need a way to look at paths up to 30 "trips" (represented by an [origin, destination] pair) in length. The full route is then composed of a series of these pairs:
route = [[start, city2], [city2, city3], [city3, city4], [city4, city5], [city5, city6], [city6, city7], [city7, city8], [city8, stop]]
So far my best solution is as follows:
def numRoutes(graph, start, stop, minStops, maxStops):
routes = []
route = [[start, stop]]
if distance(graph, route) != "NO SUCH ROUTE" and len(route) >= minStops and len(route) <= maxStops:
routes.append(route)
if maxStops >= 2:
for city2 in routesFromCity(graph, start):
route = [[start, city2],[city2, stop]]
if distance(graph, route) != "NO SUCH ROUTE" and len(route) >= minStops and len(route) <= maxStops:
routes.append(route)
if maxStops >= 3:
for city2 in routesFromCity(graph, start):
for city3 in routesFromCity(graph, city2):
route = [[start, city2], [city2, city3], [city3, stop]]
if distance(graph, route) != "NO SUCH ROUTE" and len(route) >= minStops and len(route) <= maxStops:
routes.append(route)
if maxStops >= 4:
for city2 in routesFromCity(graph, start):
for city3 in routesFromCity(graph, city2):
for city4 in routesFromCity(graph, city3):
route = [[start, city2], [city2, city3], [city3, city4], [city4, stop]]
if distance(graph, route) != "NO SUCH ROUTE" and len(route) >= minStops and len(route) <= maxStops:
routes.append(route)
if maxStops >= 5:
for city2 in routesFromCity(graph, start):
for city3 in routesFromCity(graph, city2):
for city4 in routesFromCity(graph, city3):
for city5 in routesFromCity(graph, city4):
route = [[start, city2], [city2, city3], [city3, city4], [city4, city5], [city5, stop]]
if distance(graph, route) != "NO SUCH ROUTE" and len(route) >= minStops and len(route) <= maxStops:
routes.append(route)
return routes
Where numRoutes is fed my network graph where numbers represent distances:
[[0, 5, 0, 5, 7], [0, 0, 4, 0, 0], [0, 0, 0, 8, 2], [0, 0, 8, 0, 6], [0, 3, 0, 0, 0]]
a start city, an end city and the parameters for the length of the routes.
distance checks if a route is viable and routesFromCity returns the attached nodes to each fed in city.
I have a feeling there's a far more efficient way to generate all of the routes especially as I move toward many more steps, but I can't seem to get anything else to work.

Answer 1

You could use a recursive function. Your maxStops can be a parameter and each time you call you decrease this by 1. When minStops is 0, you yield a result, When the maxStops is 0 you stop recursing.
Here is a code example:
def routesFromCity(x):
for i in range(2, 10):
yield x * i
def findRoutes(start, stop, minStops, maxStops):
if start == stop:
if minStops <= 0:
yield []
else:
if maxStops > 0:
for nextCity in routesFromCity(start):
for route in findRoutes(nextCity, stop, minStops - 1, maxStops - 1):
yield [(start, nextCity)] + route
for route in findRoutes(1, 12, 2, 5):
print route
Output:
[(1, 2), (2, 4), (4, 12)]
[(1, 2), (2, 6), (6, 12)]
[(1, 2), (2, 12)]
[(1, 3), (3, 6), (6, 12)]
[(1, 3), (3, 12)]
[(1, 4), (4, 12)]
[(1, 6), (6, 12)]