Sightseeing trip
There is a travel agency in Adelton town on Zanzibar island. It has decided to
offer its clients, besides many other attractions, sightseeing the town. To
earn as much as possible from this attraction, the agency has accepted a
shrewd decision: it is necessary to find the shortest route which begins and
ends at the same place. Your task is to write a program which finds such a
route.
In the town there are N crossing points numbered from 1 to N and M two-way
roads numbered from 1 to M. Two crossing points can be connected by multiple
roads, but no road connects a crossing point with itself. Each sightseeing
route is a sequence of road numbers y_1, ..., y_k, k>2. The road y_i
(1<=i<=k-1) connects crossing points x_i and x_{i+1}, the road y_k connects
crossing points x_k and x_1. All the numbers x_1,...,x_k should be different.
The length of the sightseeing route is the sum of the lengths of all roads on
the sightseeing route, i.e. L(y_1)+L(y_2)+...+L(y_k) where L(y_i) is the
length of the road y_i (1<=i<=k). Your program has to find such a sightseeing
route, the length of which is minimal, or to specify that it is not possible,
because there is no sightseeing route in the town.
Input:
The first line of input file TRIP.IN contains two positive integers: the
number of crossing points N<=100 and the number of roads M<=10000. Each of the
next M lines describes one road. It contains 3 positive integers: the number
of its first crossing point, the number of the second one, and the length of
the road (a positive integer less than 500).
Output:
There is only one line in output file TRIP.OUT. It contains either a string
`No solution.' in case there isn't any sightseeing route, or it contains the
numbers of all crossing points on the shortest sightseeing route in the order
how to pass them (i.e. the numbers x_1 to x_k from our definition of a
sightseeing route), separated by single spaces. If there are multiple
sightseeing routes of the minimal length, you can output any one of them.
Example 1:
TRIP.IN
5 7
1 4 1
1 3 300
3 1 10
1 2 16
2 3 100
2 5 15
5 3 20
TRIP.OUT (one of correct answers)
1 3 5 2
Example 2:
TRIP.IN
4 3
1 2 10
1 3 20
1 4 30
TRIP.OUT (the only correct answer)
No solution.