题目链接
这不是裸的二分图匹配吗?
而且匈牙利算法自带记录方案。。
但既然是网络流24题,那就用网络流来做吧。
具体就是从源点向左边每个点连一条流量为1的边,两边正常连边,流量都是一,右边所有点向汇点连一条流量为1的边,然后跑(Dinic)就行了。
怎么记录方案?枚举左边所有点连的所有边,如果剩余流量为0就是和这条边那边的点匹配了咯。
在家直接用在线IDE写的,一遍过了。
#include <cstdio>
#include <queue>
using namespace std;
#define INF 2147483647
inline int read(){
int s = 0, w = 1;
char ch = getchar();
while(ch < '0' || ch > '9'){if(ch == '-')w = -1;ch = getchar();}
while(ch >= '0' && ch <= '9') s = s * 10 + ch - '0',ch = getchar();
return s * w;
}
const int MAXN = 1000010;
struct Edge{
int next, from, to, rest;
}e[MAXN];
int head[MAXN], num = 1;
inline void Add(int from, int to, int flow){
//printf("%d %d
", from, to);
e[++num] = (Edge){ head[from], from, to, flow }; head[from] = num;
e[++num] = (Edge){ head[to], to, from, 0 }; head[to] = num;
}
int flow[MAXN], pre[MAXN], dfn[MAXN];
int h[MAXN], p[MAXN], f[100][100];
int n, m, s, t, a, b, now, Time, ans;
queue <int> q;
int RoadExist(){
while(q.size()) q.pop();
flow[s] = INF; pre[t] = 0; q.push(s); dfn[s] = ++Time;
while(q.size()){
now = q.front(); q.pop();
for(int i = head[now]; i; i = e[i].next)
if(e[i].rest && dfn[e[i].to] != Time)
dfn[e[i].to] = Time, flow[e[i].to] = min(flow[now], e[i].rest), q.push(e[i].to), pre[e[i].to] = i;
}
return pre[t];
}
int dinic(){
int ans = 0;
while(RoadExist()){
ans += flow[t];
now = t;
while(now != s){
e[pre[now]].rest -= flow[t];
e[pre[now] ^ 1].rest += flow[t];
now = e[pre[now]].from;
}
}
return ans;
}
int main(){
s = 99999; t = 100000;
n = read(); m = read();
while(233){
a = read(); b = read();
if(a == -1) break;
Add(a, b, 1);
}
for(int i = 1; i <= n; ++i)
Add(s, i, 1);
for(int i = n + 1; i <= m; ++i)
Add(i, t, 1);
ans = dinic();
printf("%d
", ans);
for(int i = 1; i <= n; ++i)
for(int j = head[i]; j; j = e[j].next)
if(!e[j].rest && e[j].to != s)
printf("%d %d
", i, e[j].to);
return 0;
}