二分图最大匹配 Hopcroft-Karp算法模板

#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <queue>
#include <cmath>
using namespace std;

const int MAXN = 3010;//左边节点数量、右边节点数量
const int MAXM = 3010*3010;//边的数量
const int INF = 0x7FFFFFFF;

struct Edge
{
int v;
int next;
}edge[MAXM];

int nx, ny;
int cnt;int dis;

int first[MAXN];
int xlink[MAXN], ylink[MAXN];
/*xlink[i]表示左集合顶点所匹配的右集合顶点序号，ylink[i]表示右集合i顶点匹配到的左集合顶点序号。*/
int dx[MAXN], dy[MAXN];
/*dx[i]表示左集合i顶点的距离编号，dy[i]表示右集合i顶点的距离编号*/
int vis[MAXN]; //寻找增广路的标记数组

void init()
{
cnt = 0;
memset(first, -1, sizeof(first));
memset(xlink, -1, sizeof(xlink));
memset(ylink, -1, sizeof(ylink));
}

void read_graph(int u, int v)
{
edge[cnt].v = v;
edge[cnt].next = first[u], first[u] = cnt++;
}

int bfs()
{
queue<int> q;
dis = INF;
memset(dx, -1, sizeof(dx));
memset(dy, -1, sizeof(dy));
for(int i = 0; i < nx; i++)
{
if(xlink[i] == -1)
{
q.push(i);
dx[i] = 0;
}
}
while(!q.empty())
{
int u = q.front(); q.pop();
if(dx[u] > dis) break;
for(int e = first[u]; e != -1; e = edge[e].next)
{
int v = edge[e].v;
if(dy[v] == -1)
{
dy[v] = dx[u] + 1;
if(ylink[v] == -1) dis = dy[v];
else
{
dx[ylink[v]] = dy[v]+1;
q.push(ylink[v]);
}
}
}
}
return dis != INF;
}

int find(int u)
{
for(int e = first[u]; e != -1; e = edge[e].next)
{
int v = edge[e].v;
if(!vis[v] && dy[v] == dx[u]+1)
{
vis[v] = 1;
if(ylink[v] != -1 && dy[v] == dis) continue;
if(ylink[v] == -1 || find(ylink[v]))
{
xlink[u] = v, ylink[v] = u;
return 1;
}
}
}
return 0;
}

int MaxMatch()
{
int ans = 0;
while(bfs())
{
memset(vis, 0, sizeof(vis));
for(int i = 0; i < nx; i++) if(xlink[i] == -1)
{
ans += find(i);
}
}
return ans;
}

int main()
{
init();
nx=0,ny=0;//左边顶点数量，右边顶点数量
//加边的格式，左边的i和右边的j相连
read_graph(i, j);
int ans = MaxMatch();
printf("%d\n\n", ans);
return 0;
}