TZC Asteroids 【二分最大匹配做】

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此问题描述了一个名为Bessie的角色需要使用一种特殊武器清除NxN网格内的所有小行星的任务。该武器能够一次性清除整个行或列的小行星。挑战在于找出清除所有障碍所需的最少射击次数。

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Asteroids

时间限制(普通/Java):1000MS/10000MS 运行内存限制:65536KByte
总提交: 6 测试通过: 1

描述

Bessie wants to navigate her spaceship through a dangerous asteroid field in the shape of an N x N grid (1 <= N <= 500). The grid contains K asteroids (1 <= K <= 10,000), which are conveniently located at the lattice points of the grid.

Fortunately, Bessie has a powerful weapon that can vaporize all the asteroids in any given row or column of the grid with a single shot.This weapon is quite expensive, so she wishes to use it sparingly.Given the location of all the asteroids in the field, find the minimum number of shots Bessie needs to fire to eliminate all of the asteroids.

输入

* Line 1: Two integers N and K, separated by a single space.
* Lines 2..K+1: Each line contains two space-separated integers R and C (1 <= R, C <= N) denoting the row and column coordinates of an asteroid, respectively.

输出

* Line 1: The integer representing the minimum number of times Bessie must shoot.

样例输入

3 4 1 1 1 3 2 2 3 2

样例输出

2

提示

INPUT DETAILS:
The following diagram represents the data, where "X" is an asteroid and "." is empty space:
X.X .X. .X.

OUTPUT DETAILS:
Bessie may fire across row 1 to destroy the asteroids at (1,1) and (1,3), and then she may fire down column 2 to destroy the asteroids at (2,2) and (3,2).