P3033 [USACO11NOV]牛的障碍Cow Steeplechase

    • 112通过
    • 293提交
  • 题目提供者 FarmerJohn2
  • 评测方式 云端评测
  • 标签 二分图 最大匹配 USACO 2011
  • 难度 省选/NOI-
  • 时空限制 1000ms / 128MB

题解

  • 提示:收藏到任务计划后,可在首页查看。
  • 最新讨论 显示

    推荐的相关题目 显示

    题目描述

    Farmer John has a brilliant idea for the next great spectator sport: Cow Steeplechase! As everyone knows, regular steeplechase involves a group of horses that race around a course filled with obstacles they must jump over. FJ figures the same contest should work with highly-trained cows, as long as the obstacles are made short enough.

    In order to design his course, FJ makes a diagram of all the N (1 <= N <= 250) possible obstacles he could potentially build. Each one is represented by a line segment in the 2D plane that is parallel to the horizontal or vertical axis. Obstacle i has distinct endpoints (X1_i, Y1_i) and (X2_i, Y2_i) (1 <= X1_i, Y1_i, X2_i, Y2_i <= 1,000,000,000). An example is as follows:

    
       --+-------   
    -----+-----
      ---+---     |
         |     |  |
       --+-----+--+-   |
         |     |  |  | |
         |   --+--+--+-+-
               |  |  | |
                  |

    FJ would like to build as many of these obstacles as possible, subject to the constraint that no two of them intersect. Starting with the diagram above, FJ can build 7 obstacles:

    
       ----------   
    -----------
      -------     |
               |  |
               |  |    |
               |  |  | |
               |  |  | |
               |  |  | |
                  |
    

    Two segments are said to intersect if they share any point in common, even an endpoint of one or both of the segments. FJ is certain that no two horizontal segments in the original input diagram will intersect, and that similarly no two vertical segments in the input diagram will intersect.

    Please help FJ determine the maximum number of obstacles he can build.

    给出N平行于坐标轴的线段,要你选出尽量多的线段使得这些线段两两没有交点(顶点也算),横的与横的,竖的与竖的线段之间保证没有交点,输出最多能选出多少条线段。

    输入输出格式

    输入格式:

    * Line 1: A single integer: N.

    * Lines 2..N+1: Line i+1 contains four space-separated integers representing an obstacle: X1_i, Y1_i, X2_i, and Y2_i.

    输出格式:

    * Line 1: The maximum number of non-crossing segments FJ can choose.

    输入输出样例

    输入样例#1: 复制
    3 
    4 5 10 5 
    6 2 6 12 
    8 3 8 5 
    
    输出样例#1: 复制
    2 
    

    说明

    There are three potential obstacles. The first is a horizontal segment connecting (4, 5) to (10, 5); the second and third are vertical segments connecting (6, 2) to (6, 12) and (8, 3) to (8, 5).

    The optimal solution is to choose both vertical segments.

    提示
    标程仅供做题后或实在无思路时参考。
    请自觉、自律地使用该功能并请对自己的学习负责。
    如果发现恶意抄袭标程,将按照I类违反进行处理。