uva 1411（二分图最大权匹配）

题意：平面坐标系中有一堆白点与黑点，告诉你他们的坐标，然后让你把他们连接起来，每个白点恰好连接一个黑点。线段不能相交。最后输出每个白点匹配的黑点的序号。

思路：构造二分图每个白点对应一个x结点，黑点对应一个y结点权值是两者的欧氏距离相反数。之后最佳完全匹配就是解，原因是若存在(a,b)(c,d)两个匹配是相交的，那么必定存在(a,c)(b,d)比原来权值更大且不相交。

代码如下：

/**************************************************
 * Author     : xiaohao Z
 * Blog     : http://www.cnblogs.com/shu-xiaohao/
 * Last modified : 2014-02-20 20:29
 * Filename     : uva_1411.cpp
 * Description     : 
 * ************************************************/

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <queue>
#include <stack>
#include <vector>
#include <set>
#include <map>
#define MP(a, b) make_pair(a, b)
#define PB(a) push_back(a)
#define PF(a) ((a)*(a))

using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<unsigned int,unsigned int> puu;
typedef pair<int, double> pid;
typedef pair<ll, int> pli;
typedef pair<int, ll> pil;

const double INF = 1e30;
const double eps = 1E-6;
const int LEN = 1010;
double g[LEN][LEN], lx[LEN], ly[LEN], slack[LEN];
int linker[LEN], visx[LEN], visy[LEN], tlinker[LEN];
int nx, ny;
struct P {double x, y;};
P white[LEN], black[LEN];

double dis(P c, P d){return sqrt(PF(c.x - d.x) + PF(c.y - d.y));}

bool DFS(int x)
{
    visx[x] = 1;
    for(int y = 0; y < ny; y++)
    {
        if(visy[y])continue;
        double tmp = lx[x] + ly[y] - g[x][y];
        if(fabs(tmp) < eps)
        {
            visy[y] = 1;
            if(linker[y] == -1 || DFS(linker[y]))
            {
                linker[y] = x;
                tlinker[x] = y;
                return true;
            }
        }
        else if(slack[y] > tmp)
            slack[y] = tmp;
    }
    return false;
}
double KM()
{
    memset(linker,-1,sizeof(linker));
    memset(ly,0,sizeof(ly));
    for(int i = 0;i < nx;i++)
    {
        lx[i] = -INF;
        for(int j = 0;j < ny;j++)
            if(g[i][j] > lx[i])
                lx[i] = g[i][j];
    }
    for(int x = 0;x < nx;x++)
    {
        for(int i = 0;i < ny;i++)
            slack[i] = INF;
        while(1)
        {
            memset(visx,0,sizeof(visx));
            memset(visy,0,sizeof(visy));
            if(DFS(x))break;
            double d = INF;
            for(int i = 0;i < ny;i++)
                if(!visy[i] && d > slack[i])
                    d = slack[i];
            for(int i = 0;i < nx;i++)
                if(visx[i])
                    lx[i] -= d;
            for(int i = 0;i < ny;i++)
            {
                if(visy[i])ly[i] += d;
                else slack[i] -= d;
            }
        }
    }
    double res = 0;
    for(int i = 0;i < ny;i++)
        if(linker[i] != -1)
            res += g[linker[i]][i];
    return res;
}


int main()
{
//    freopen("in.txt", "r", stdin);

    int n, kase = 1;
    while(scanf("%d", &n)!=EOF){
        if(kase != 1) printf("
");
        kase ++;
        nx = ny = n;
        for(int i=0; i<n; i++)
            scanf("%lf%lf", &white[i].x, &white[i].y);
        for(int i=0; i<n; i++)
            scanf("%lf%lf", &black[i].x, &black[i].y);
        for(int i=0; i<n; i++)
            for(int j=0; j<n; j++)
                g[j][i] = -dis(white[i], black[j]);
        KM();
        for(int i=0; i<n; i++){
            printf("%d
", linker[i]+1);
        }
    }
    return 0;
}