poj3565Ants(KM-几何与图论的结合）

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可以看出蓝的之和一定比红的之和要大，也就是说符合条件的匹配一定是权值最小的，所以二分图的最佳完美匹配。。KM

  1 #include <iostream>

  2 #include<cstdio>

  3 #include<cstring>

  4 #include<algorithm>

  5 #include<stdlib.h>

  6 #include<vector>

  7 #include<cmath>

  8 #include<queue>

  9 #include<set>

 10 using namespace std;

 11 #define N 110

 12 #define LL long long

 13 #define INF 9999999999.0

 14 const double eps = 1e-8;

 15 const double pi = acos(-1.0);

 16 const double inf = ~0u>>2;

 17 struct point

 18 {

 19     int x,y;

 20     //point(int x=0,int y=0):x(x),y(y){}

 21 }p[N<<1];

 22 double dis(point a,point b)

 23 {

 24     return sqrt(1.0*(a.x-b.x)*(a.x-b.x)+1.0*(a.y-b.y)*(a.y-b.y));

 25 }

 26 double dcmp(double x)

 27 {

 28     if(fabs(x)<eps) return 0;

 29     return x<0?-1:1;

 30 }

 31 double w[N][N];

 32 int n,link[N],x[N],y[N];

 33 double lx[N],ly[N],slack[N],d;

 34 bool match(int u)

 35 {

 36     x[u] = 1;

 37     for(int i = 1; i <= n ; i++)

 38     {

 39         if(y[i]) continue;

 40         double o = lx[u]+ly[i]-w[u][i];

 41         if(dcmp(o)==0)

 42         {

 43             y[i] = 1;

 44             if(!link[i]||match(link[i]))

 45             {

 46                 link[i] = u;

 47                 return true;

 48             }

 49         }

 50         else if(slack[i]>o) slack[i] = o;

 51     }

 52     return false;

 53 }

 54 void km()

 55 {

 56     int i,j;

 57     for(i = 1 ;i <= n ;i++)

 58     lx[i] = -INF;

 59     memset(ly,0,sizeof(ly));

 60     memset(link,0,sizeof(link));

 61     for(i = 1; i <= n ;i++)

 62         for(j = 1; j <= n ;j++)

 63         lx[i] = max(lx[i],w[i][j]);

 64     for(i = 1; i <= n ;i++)

 65     {

 66         for(j = 1; j <= n;j++)

 67         slack[j] = INF;

 68         for(;;)

 69         {

 70              d = INF;

 71             memset(x,0,sizeof(x));

 72             memset(y,0,sizeof(y));

 73             if(match(i)) break;

 74             for(j =1 ; j <= n ;j++)

 75             if(!y[j]&&d>slack[j]) d =min(d,slack[j]);

 76             for(j =1 ;j <= n ;j++) if(x[j]){lx[j]-=d;}

 77             for(j =1 ;j <= n ;j++) if(y[j]){ly[j]+=d;}

 78            // else slack[j]-=d;

 79             //cout<<",";

 80         }

 81     }

 82 }

 83 

 84 int main()

 85 {

 86     int i,j;

 87     while(scanf("%d",&n)!=EOF)

 88     {

 89         //init();

 90         for(i = 1; i <=n+n; i++)

 91         scanf("%d%d",&p[i].x,&p[i].y);

 92         for(i  =1; i <= n ;i++)

 93             for(j = 1; j <= n ; j++)

 94             {

 95                 w[i][j] = -dis(p[i+n],p[j]);

 96             }

 97         km();

 98         for(i = 1; i <= n ;i++)

 99         printf("%d\n",link[i]);

100     }

101     return 0;

102 }

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