poj3041[二分图最小点覆盖&König定理]

Asteroids

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 9515 Accepted: 5124

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 41 11 32 23 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

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二分图最大匹配的König定理：

最小点覆盖数 = 最大匹配数
然后，就不解释了~
Code：

program poj3041;varg:array[1..500,1..500] of boolean;cover:array[1..500] of boolean;from:array[1..500] of longint;n:longint;function Find(u:longint):boolean;var i,q:longint;begin     for i:=1 to n do     if (g[u,i])and(not cover[i])then begin        cover[i]:=true;        q:=from[i]; from[i]:=u;        if (q=0)or(Find(q))then exit(true);        from[i]:=q;     end;     exit(false);end;function Ed:longint;var i:longint;begin     Ed:=0;     fillchar(from,sizeof(from),0);     for i:=1 to n do begin         fillchar(cover,sizeof(cover),false);         if Find(i) then inc(Ed);     end;end;procedure Scan;var m,a,b:longint;begin     fillchar(g,sizeof(g),false);     readln(n,m);     while m>0 do begin           dec(m);           readln(a,b);           g[a,b]:=true;     end;end;procedure Main;begin     Scan;     write(Ed);end;begin     assign(input,'poj3041.in'); reset(input);     assign(output,'poj3041.out'); rewrite(output);     Main;     close(input); close(output);end.