二分图最大权最小权完美匹配模板KM

在网上找了一份挺好的模板，先标一下哦~链接君：http://blog.csdn.net/abcjennifer/article/details/5844579

#include <iostream>
#include <string.h>
#include <algorithm>
#include <iostream>
using namespace std;
int max(int a,int b)
{return a<b?b:a;}
 
int min(int a,int b)
{return a<b?a:b;}
 
const int size = ;
const int INF = ;
 
bool map[size][size];         // 二分图的相等子图, map[i][j] = true 代表Xi与Yj有边
bool sx[size], sy[size]; // 标记在一次DFS中，Xi与Yi是否在交错树上
int match[size];             // 保存匹配信息，其中i为Y中的顶点标号，match[i]为X中顶点标号
 
bool DFS(int, const int);
void KM_Perfect_Match(const int n, const int edge[][size])
{
    int i, j;
    int lx[size], ly[size];   // KM算法中Xi与Yi的标号
    for(i = ; i < n; i++)
    {
        lx[i] = -INF;
        ly[i] = ;
        for(j = ; j < n; j++)
        {
            lx[i] = max(lx[i], edge[i][j]);
        }
    }
    bool perfect = false;
    while(!perfect)
    {
        // 初始化邻接矩阵
        for(i = ; i < n; i++)
        {
            for(j = ; j < n; j++)
            {
                if(lx[i]+ly[j] == edge[i][j])
                    map[i][j] = true;
                else map[i][j] = false;
            }
        }
        // 匹配过程
        int live = ;
        memset(match, -, sizeof(match));
        for(i = ; i < n; i++) {
            memset(sx, false, sizeof(sx));
            memset(sy, false, sizeof(sy));
            if(DFS(i, n)) live++;
            else {
                sx[i] = true;
                break;
            }
        }
        if(live == n) perfect = true;
        else {
            // 修改标号过程
            int ex = INF;
            for(i = ; i < n; i++)
            {
                for(j = ; sx[i] && j < n; j++)
                {
                    if(!sy[j])
                        ex = min(ex, lx[i]+ly[j]-edge[i][j]);
                }
            }
            for(i = ; i < n; i++)
            {
                if(sx[i]) lx[i] -= ex;
                if(sy[i]) ly[i] += ex;
            }
        }
    }
}
 
bool DFS(int p, const int n)//find augment path from X[p]
{
    int i;
    for(i = ; i < n; i++)
    {
        if(!sy[i] && map[p][i])
        {
            sy[i] = true;
            int t = match[i];
            match[i] = p;
            if(t == - || DFS(t, n))
            {
                return true;
            }
            match[i] = t;
            if(t != -) sx[t] = true;
        }
    }
    return false;
}
 
int main()
{
    int n, edge[size][size]; // edge[i][j]为连接Xi与Yj的边的权值
    int i;
    int m;
    /***************************************************
    *       record edge[i][j] as edge value between vertex i in X and vertex j in Y
    *       save n as vertexs need to be match (used in KM_Perfect_Match(n, edge);)
    ***************************************************/
    int s,d,pow;
 
    while(scanf("%d%d",&n,&m)!=EOF)
    {
        if(n== && m==) break;
        memset(edge,,sizeof(edge));
        /*最小权: 去掉memset(edge,0,sizeof(edge));改为如下：
        for(i=0;i<n;i++)
            for(int j=0;j<n;j++)
                edge[i][j]=-INF;
        */
        memset(sx,,sizeof(sx));
        memset(sy,,sizeof(sy));
        memset(match,,sizeof());
        while(m--)
        {
            scanf("%d%d%d",&s,&d,&pow);
            s--;d--;
            /*最小权：edge[s][d]=pow; 改为edge[s][d]= - pow;*/
            edge[s][d]=pow;
        }
        KM_Perfect_Match(n, edge);
        int cost = ;
        for(i=;i<n;i++)
        {
            cost += edge[match[i]][i];
        }
        /*最小权：output 改为 -cost*/
        cout<<cost<<endl;
    }
    // cost 为最大匹配的总和, match[]中保存匹配信息
    return ;
}

感觉这个模板也不错，比较符合审美。。。

#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
 
using namespace std;
const int maxn = ;
const int inf = 0x3f3f3f3f;
 
int N, L[maxn], Lx[maxn], Ly[maxn], W[maxn][maxn], slack[maxn];
bool S[maxn], T[maxn];
 
int match (int u) {
    S[u] = true;
    for (int i = ; i <= N; i++) if (!T[i]) {
        if (Lx[u] + Ly[i] == W[u][i]) {
            T[i] = true;
            if (!L[i] || match(L[i])) {
                L[i] = u;
                return true;
            }
        } else
            slack[i] = min(slack[i], Lx[u]+Ly[i]-W[u][i]);
    }
    return false;
}
 
void update () {
    int a = inf;
    for (int i = ; i <= N; i++) if (!T[i])
        a = min(a, slack[i]);
 
    for (int i = ; i <= N; i++) {
        if (S[i]) Lx[i] -= a;
        if (T[i]) Ly[i] += a;
    }
}
 
void KM () {
    for (int i = ; i <= N; i++) {
        L[i] = Lx[i] = Ly[i] = ;
        for (int j = ; j <= N; j++)
            Lx[i] = max(Lx[i], W[i][j]);
    }
 
    for (int i = ; i <= N; i++) {
        for (int j = ; j <= N; j++) slack[j] = inf;
        while (true) {
            for (int j = ; j <= N; j++) S[j] = T[j] = false;
            if (match(i)) break;
            else update();
        }
    }
}
 
void init () {
    for (int i = ; i <= N; i++)
        for (int j = ; j <= N; j++)
            W[i][j] = -inf;
    int u, v;
    for (int i = ; i <= N; i++) {
        while (scanf("%d", &u) ==  && u) {
            scanf("%d", &v);
            W[i][u] = max(W[i][u], -v);
        }
    }
}
 
int main () {
    while (scanf("%d", &N) ==  && N) {
        init();
        KM();
        bool flag = false;
        for (int i = ; i <= N; i++) {
            if (L[i] && W[L[i]][i] == -inf)
                flag = true;
        }
 
        if (flag) printf("N\n");
        else {
            int ans = ;
            for (int i = ; i <= N; i++)
                ans += (Lx[i] + Ly[i]);
            printf("%d\n", -ans);
        }
    }
    return ;
}