D :: Tour
Time Limit: 1 Second Memory Limit: 65536 KB
John Doe, a skilled pilot, enjoys traveling. While on vacation, he rents
a small plane and starts visiting beautiful places. To save money, John
must determine the shortest closed tour that connects his destinations.
Each destination is represented by a point in the plane pi = < xi,yi
>. John uses the following strategy: he starts from the leftmost
point, then he goes strictly left to right to the rightmost point, and
then he goes strictly right back to the starting point. It is known that
the points have distinct x-coordinates.
Write a program that, given a set of n points in the plane, computes
the shortest closed tour that connects the points according to John's
strategy.
Input
The program input is from a text file.
Each data set in the file stands for a particular set of points. For
each set of points the data set contains the number of points, and the
point coordinates in ascending order of the x coordinate. White spaces
can occur freely in input. The input data are correct.
Output
For each set of data, your program should
print the result to the standard output from the beginning of a line.
The tour length, a floating-point number with two fractional digits,
represents the result. An input/output sample is in the table below.
Here there are two data sets. The first one contains 3 points specified
by their x and y coordinates. The second point, for example, has the x
coordinate 2, and the y coordinate 3. The result for each data set is
the tour length, (6.47 for the first data set in the given example).
Sample Input
3 1 1 2 3 3 1 4 1 1 2 3 3 1 4 2
Sample Output
6.47 7.89Submit