TN's Kingdom II - Construction
Time Limit:10000MS Memory Limit:65536K
Total Submit:265 Accepted:9
Case Time Limit:6000MS
Description It
was the first anniversary of TN's coronation. After one year's
reconstruction, towns and cities were gradually rebuilt. There emerged
a call for a complete traffic system. Among all choices to solve the
problem, TN considered the construction of an expressway system the
best one. He followed his old way in planning - to build the fewest
number of expressways that would connect all the cities.
Though it was
a similar case to what had previously been done, differences existed.
The most significant one was that building expressways was costly. TN
wanted to minimize the cost to achieve the goal. It was known that the
cost of building an expressway between two cities was proportional to
the distance between the cities. What was more, the expressways were
straight and no two expressways could cross each other due to technical
limitations. Now TN was holding a map of his kingdom, fallen deep in
thinking. How should he make the plan?
Input The input consists of a single test case. The first line of input contains a positive integer N not exceeding 105 which is the number of cities in the kingdom. Then N lines follow. Each line contains a pair of non-negative integers within 50,000, giving in that order the x- and y-coordinates of a city in the Cartesian coordinate system. The distance between two cities was measured in the L2-metric, which means for two cities located at (x1, y1) and (x2, y2), the distance between them was
Output Your
solution should output a single number rounded to four decimal places
which is the minimum cost of building the expressways under the
assumption that building an expressway covering one unit of distance
required exactly one unit of cost.
Sample Input
2
0 0
1 1
Sample Output
1.4142
Hint It
is recommended that your solution uses standard C I/O interface to
achieve better efficiency and avoid unpredictable behaviours.
Source POJ Monthly--2006.04.28, frkstyc@PKU_RPWT
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