二分图匹配学习——匈牙利算法模板

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DFS(邻接矩阵)

const int MAXN=1000;int p,n;  //u,v数目int g[MAXN][MAXN];//左右集合连接情况int linker[MAXN];bool used[MAXN];bool dfs(int u){    int v;    for(v=1; v<=n; v++)        if(g[u][v]&&!used[v])        {            used[v]=true;            if(linker[v]==-1||dfs(linker[v]))            {                linker[v]=u;                return true;            }        }    return false;}int hungary(){    int res=0;    int u;    memset(linker,-1,sizeof(linker));    for(u=1; u<=p; u++)    {        memset(used,0,sizeof(used));        if(dfs(u))            res++;    }    return res;}

DFS(邻接表)

const int MAXN=10050;int linker[MAXN];bool used[MAXN];vector<int>g[MAXN];int n;bool dfs(int u){    for(int i=0; i<g[u].size(); i++)    {        if(!used[g[u][i]])        {            used[g[u][i]]=true;            if(linker[g[u][i]]==-1||dfs(linker[g[u][i]]))            {                linker[g[u][i]]=u;                return true;            }        }    }    return false;}int hungary(){    int u;    int res=0;    memset(linker,-1,sizeof(linker));    for(u=1; u<=n; u++)    {        memset(used,false,sizeof(used));        if(dfs(u))            res++;    }    return res;}

BFS

const int MAXN = 1000;int g[MAXN][MAXN];int Mx[MAXN], My[MAXN], p, n;int chk[MAXN];int Q[MAXN];int pre[MAXN];int hungary(){    int res = 0;    int qs, qe;    memset(Mx, -1, sizeof(Mx));    memset(My, -1, sizeof(My));    memset(chk, -1, sizeof(chk));    for (int i = 1; i <= p; i++)    {        if (Mx[i] == -1)  //对于x集合中的每个没有匹配的点i进行一次bfs找交错轨        {            qs = qe = 0;            Q[qe++] = i;            pre[i] = -1;            bool flag = 0;//判断是否找到            while (qs < qe && !flag)            {                int u = Q[qs];                for (int v = 1; v <= n && !flag; v++)                    if (g[u][v]//如果u和v相连                            && chk[v] != i)//并且v没有被u check过                    {                        chk[v] = i;                        Q[qe++] = My[v];//放进                        if (My[v] >= 0)//如果v和其他的相连,则修改之                            pre[My[v]] = u;                        else  //直到找到一个u和v都没有用过的                        {                            flag = 1;                            int d = u, e = v;                            while (d != -1)  //确保回到最初                            {                                int t = Mx[d];                                Mx[d] = e;                                My[e] = d;                                d = pre[d];                                e = t;                            }                        }                    }                qs++;            }            if (Mx[i] != -1)                res++;        }    }    return res;}

Hopcroft-Carp算法

#define MAXN 128const int INF = 1 << 28;int g[MAXN][MAXN], Mx[MAXN], My[MAXN], Nx, Ny;int dx[MAXN], dy[MAXN], dis;bool vst[MAXN];bool searchP(void){queue<int> Q;dis = INF;memset(dx, -1, sizeof(dx));memset(dy, -1, sizeof(dy));for (int i = 0; i < Nx; i++){if (Mx[i] == -1){Q.push(i);dx[i] = 0;}}while (!Q.empty()){int u = Q.front(); Q.pop();if (dx[u] > dis)break;for (int v = 0; v < Ny; v++){if (g[u][v] && dy[v] == -1){dy[v] = dx[u]+1;if (My[v] == -1)dis = dy[v];else{dx[My[v]] = dy[v]+1;Q.push(My[v]);}}}}return dis != INF;}bool DFS(int u){for (int v = 0; v < Ny; v++){if (!vst[v] && g[u][v] && dy[v] == dx[u]+1){vst[v] = 1;if (My[v] != -1 && dy[v] == dis)continue;if (My[v] == -1 || DFS(My[v])){My[v] = u;Mx[u] = v;return 1;}} }return 0;}int MaxMatch(void){int res = 0;memset(Mx, -1, sizeof(Mx));memset(My, -1, sizeof(My));while (searchP()){memset(vst, 0, sizeof(vst));for (int i = 0; i < Nx; i++){if (Mx[i] == -1 && DFS(i))//if (dx[i] == 0 && DFS(i))res++;}}return res;}

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