[最大匹配]Pku3041--Asteroids

http://acm.pku.edu.cn/JudgeOnline/problem?id=3041

 

Asteroids

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 4643		Accepted: 2410

Description

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.

Input

* 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.

Output

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

Sample Input

3 4
1 1
1 3
2 2
3 2

Sample Output

2

Hint

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).

Source

USACO 2005 November Gold

题目大意：在一个n*n的矩阵中，有m个小行星，先可以用武器打掉一行或一列的行星，问最少要打多少次。

分析：经典的最大匹配题目。将每行每列抽出来作为节点，有行星的行列连边，则问题可以转化为一个最小顶点覆盖问题。最小顶点覆盖问题等价于最大匹配问题。问题得解。

 

codes:

 

var n,m,k:longint; a:array[1..500,1..500] of boolean; match,v:array[1..500] of longint; procedure init; var i,x,y:longint; begin readln(n,m); for i:=1 to m do begin readln(x,y); a[x,y]:=true; end; end; procedure main; function find(x:longint):boolean; var i,t:longint; begin for i:=1 to n do if a[x,i] and (v[i]<>k) then begin v[i]:=k; if (match[i]=0) or (find(match[i])) then begin match[i]:=x; exit(true); end; end; exit(false); end; var i:longint; begin k:=1; for i:=1 to n do if find(i) then inc(k); writeln(k-1); end; begin init; main; end.