[POJ 3565] Ant

Posted 2020-12-27 evenbao

[题目链接]

         http://poj.org/problem?id=3565

[算法]

        KM算法求最小匹配

[代码]

       

#include <algorithm>  
#include <bitset>  
#include <cctype>  
#include <cerrno>  
#include <clocale>  
#include <cmath>  
#include <complex>  
#include <cstdio>  
#include <cstdlib>  
#include <cstring>  
#include <ctime>  
#include <deque>  
#include <exception>  
#include <fstream>  
#include <functional>  
#include <limits>  
#include <list>  
#include <map>  
#include <iomanip>  
#include <ios>  
#include <iosfwd>  
#include <iostream>  
#include <istream>  
#include <ostream>  
#include <queue>  
#include <set>  
#include <sstream>  
#include <stdexcept>  
#include <streambuf>  
#include <string>  
#include <utility>  
#include <vector>  
#include <cwchar>  
#include <cwctype>  
#include <stack>  
#include <limits.h>
using namespace std;
#define MAXN 110
const double INF    = 1e12;
const double eps = 1e-5;

int i,j,n;
pair<double,double> a[MAXN],b[MAXN];
double w[MAXN][MAXN];
double la[MAXN],lb[MAXN];
double delta;
int ans[MAXN],match[MAXN];
bool visiteda[MAXN],visitedb[MAXN];

inline double dist(pair<double,double> a,pair<double,double> b)
{
        return 1.0 * sqrt((a.first - b.first) * (a.first - b.first) + (a.second - b.second) * (a.second - b.second));        
}
inline bool dfs(int u)
{
        int v;
        visiteda[u] = true;
        for (v = 1; v <= n; v++)
        {
                if (!visitedb[v])
                {
                        if (fabs(la[u] + lb[v] - w[u][v]) < eps)
                        {
                                visitedb[v] = true;
                                if (!match[v] || dfs(match[v]))
                                {
                                        match[v] = u;
                                        return true;
                                }
                        } 
                }
        }
        return false;
}
inline void KM()
{
        int i,j,k;
        memset(match,0,sizeof(match));
        for (i = 1; i <= n; i++) 
        {
                la[i] = -INF;
                lb[i] = 0;
                for (j = 1; j <= n; j++) la[i] = max(la[i],w[i][j]);
        }
        for (i = 1; i <= n; i++)
        {
                while (true)
                {
                        delta = INF;
                        for (j = 1; j <= n; j++) visiteda[j] = visitedb[j] = false;
                        if (dfs(i)) break;
                        for (j = 1; j <= n; j++)
                        {
                                if (visiteda[j])
                                {
                                        for (k = 1; k <= n; k++)
                                        {
                                                if (!visitedb[k])
                                                        delta = min(delta,la[j] + lb[k] - w[j][k]); 
                                        } 
                                }
                        }
                        for (j = 1; j <= n; j++)
                        {
                                if (visiteda[j]) la[j] -= delta;
                                if (visitedb[j]) lb[j] += delta;
                        }
                }
        }
}

int main()  
{
        
        scanf("%d",&n);
        for (i = 1; i <= n; i++) scanf("%lf%lf",&a[i].first,&a[i].second);
        for (i = 1; i <= n; i++) scanf("%lf%lf",&b[i].first,&b[i].second);
        for (i = 1; i <= n; i++)
        {
                for (j = 1; j <= n; j++)
                {
                        w[i][j] = -dist(a[i],b[j]);    
                }         
        }
        KM(); 
        for (i = 1; i <= n; i++) ans[match[i]] = i;
        for (i = 1; i <= n; i++) printf("%d
",ans[i]);
        
        return 0;
    
}