poj-1113-Wall(凸包问题)

Wall

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 26571 Accepted: 8843

Description

Once upon a time there was a greedy King who ordered his chief Architect to build a wall around the King's castle. The King was so greedy, that he would not listen to his

以前，                       有一个贪婪的国王                    命令他的首席建筑师    在城堡的周围建一堵墙。                                             国王很贪婪，                     他不听

Architect's proposals to build a beautiful brick wall with a perfect shape and nice tall towers. Instead, he ordered to build the wall around the whole castle using the

他建筑师的 提议  去建一个 美丽的 有完美的形状和不错的高塔的 砖墙。                                     相反，      他下令建一个墙，

least amount of stone and labor, but demanded that the wall should not come closer to the castle than a certain distance. If the King finds that the Architect has used

用最少的石头 和劳力，                         但是要求 墙与城堡的距离                                                                                                                         如果国王发现 建筑师建墙时

more resources to build the wall than it was absolutely necessary to satisfy those requirements, then the Architect will loose his head. Moreover, he demanded Architect

用了更多的资源                                                                                                                                                               

to introduce at once a plan of the wall listing the exact amount of resources that are needed to build the wall.

Your task is to help poor Architect to save his head, by writing a program that will find the minimum possible length of the wall that he could build around the castle to

                                                                                                                                                        尽可能长度最小的墙

satisfy King's requirements.

The task is somewhat simplified by the fact, that the King's castle has a polygonal shape and is situated on a flat ground. The Architect has already established a

                                                                                                                                   多边行                             坐落在平坦的地面

Cartesian coordinate system and has precisely measured the coordinates of all castle's vertices in feet.

笛卡尔坐标                                                        精确地测量                                                     城堡的顶点

Input

The first line of the input file contains two integer numbers N and L separated by a space. N (3 <= N <= 1000) is the number of vertices in the King's castle, and L (1 <= L <= 1000) is the minimal number of feet that King allows for the wall to come close to the castle.
 
Next N lines describe coordinates of castle's vertices in a clockwise order. Each line contains two integer numbers Xi and Yi separated by a space (-10000 <= Xi, Yi <=

                                                                                                         顺时针 顺序

10000) that represent the coordinates of ith vertex. All vertices are different and the sides of the castle do not intersect anywhere except for vertices.

                                                                                            所有的顶点都不相同                       

Output

Write to the output file the single number that represents the minimal possible length of the wall in feet that could be built around the castle to satisfy King's requirements. You must present the integer number of feet to the King, because the floating numbers are not invented yet. However, you must round the result in such a way, that it is accurate to 8 inches (1 foot is equal to 12 inches), since the King will not tolerate larger error in the estimates.

Sample Input

9 100200 400300 400300 300400 300400 400500 400500 200350 200200 200

Sample Output

1628

Hint

结果四舍五入就可以了

Source

Northeastern Europe 2001