最大流 （洛谷 3376）
#include<cstdio>
#include<algorithm>
#include<vector>
#include<queue>
#include<map>
#include<set>
#include<iostream>
#include<cstring>
#include<cmath>
using namespace std;
#define rep(i,f_start,f_end) for (int i=f_start;i<=f_end;++i)
#define per(i,n,a) for (int i=n;i>=a;i--)
#define MT(x,i) memset(x,i,sizeof(x) )
#define rev(i,start,end) for (int i=start;i<end;i++)
#define inf 0x3f3f3f3f
#define mp(x,y) make_pair(x,y)
#define lowbit(x) (x&-x)
#define MOD 1000000007
#define exp 1e-8
#define N 1000005
#define fi first
#define se second
#define pb push_back
typedef long long ll;
typedef pair<int ,int> PII;
ll gcd (ll a,ll b) {return b?gcd (b,a%b):a; }
const int maxn=520010;
const ll INF=2005020600;
int head[maxn];
int n,m,s,t,u,v;
int now[maxn],cnt=1;
ll dis[maxn],ans,w;
struct edge {
int v,next;
ll val;
// edge (int v=0,int next=0,ll val=0): v(v), next(next), val(val) {}
}e[maxn];
inline void add (int u,int v,ll w) {
e[++cnt].v=v;
e[cnt].val=w; //加正反两条边
e[cnt].next=head[u];
head[u]=cnt;
e[++cnt].v=u;
e[cnt].val=0;
e[cnt].next=head[v];
head[v]=cnt;
}
inline int bfs () { //求分层图
rep (i,1,n) dis[i]=INF;
queue <int > q;
dis[s]=0;
now[s]=head[s];
q.push (s);
while (q.size ()) {
int x=q.front (); q.pop();
for (int i=head[x];i;i=e[i].next) {
int v=e[i].v;
if (e[i].val>0&&dis[v]==INF) { //直接遍历邻边判断即可
q.push (v);
now[v]=head[v];
dis[v]=dis[x]+1;
if (v==t) return 1;
}
}
}
return 0;
}
inline ll dfs (int x,ll sum) {
if (x==t) return sum;
ll k,res=0;
for (int i=now[x];i&∑i=e[i].next) {
now[x]=i;
int v=e[i].v;
if (e[i].val>0&&(dis[v]==dis[x]+1)) {
k=dfs (v,min (sum,e[i].val)); //剩余流量最小值
if (k==0) dis[v]=INF;
e[i].val-=k; //更新残量网络
e[i^1].val+=k;
res+=k; //更新当前答案和剩余流量
sum-=k;
}
}
return res;
}
int main () {
// freopen ("data.in","r",stdin);
scanf ("%d%d%d%d",&n,&m,&s,&t);
rep (i,1,m) {
scanf ("%d%d%lld",&u,&v,&w);
add (u,v,w);
}
while (bfs ()) { //如果还存在合法分层图，累加答案
ans+=dfs (s,INF);
}
printf ("%lld",ans);
// fclose (stdin);
return 0;
}
最小费用最大流
#include<cstdio>
#include<algorithm>
#include<vector>
#include<queue>
#include<map>
#include<iostream>
#include<cstring>
#include<cmath>
using namespace std;
#define rep(i,f_start,f_end) for (int i=f_start;i<=f_end;++i)
#define per(i,n,a) for (int i=n;i>=a;i--)
#define MT(x,i) memset(x,i,sizeof(x) )
#define rev(i,start,end) for (int i=start;i<end;i++)
#define inf 0x3f3f3f3f
#define mp(x,y) make_pair(x,y)
#define lowbit(x) (x&-x)
#define MOD 1000000007
#define exp 1e-8
#define N 1000005
#define fi first
#define se second
#define pb push_back
typedef long long ll;
typedef vector <int> VI;
typedef pair<int ,int> PII;
typedef pair<int ,PII> PIII;
ll gcd (ll a,ll b) {return b?gcd (b,a%b):a; }
inline int read() {
char ch=getchar(); int x=0, f=1;
while(ch<'0'||ch>'9') {
if(ch=='-') f = -1;
ch=getchar();
}
while('0'<=ch&&ch<='9') {
x=x*10+ch-'0';
ch=getchar();
} return x*f;
}
const int maxn=5e4+10;
const int M=5e3+10;
int n,m,s,t,cnt=1;
int head[maxn],dis[maxn],pre[maxn],incf[maxn];
int maxflow,mincost;
bool vis[maxn];
struct edge {
int v,next,flow,cost;
}e[M<<1];
inline void add (int u,int v,int flow,int cost) {
e[++cnt]= (edge) {v,head[u],flow,cost};
head[u]=cnt;
}
inline void add_edge (int u,int v,int flow,int cost) {
add (u,v,flow,cost);
add (v,u,0,-cost);
}
inline bool spfa () {
queue <int > q;
MT (dis,0x3f);
MT (vis,0);
q.push (s);
dis[s]=0;
vis[s]=1;
incf[s]=1<<30;
while (q.size ()) {
int x=q.front (); q.pop ();
vis[x]=0;
for (int i=head[x];i;i=e[i].next) {
if (!e[i].flow) continue;
int v=e[i].v;
if (dis[v]>dis[x]+e[i].cost) {
dis[v]=dis[x]+e[i].cost;
incf[v]=min (incf[x],e[i].flow);
pre[v]=i;
if (!vis[v]) vis[v]=1,q.push (v);
}
}
}
if (dis[t]==inf) return 0;
return dis[t];
}
inline void mcmf () {
while (spfa ()) {
int x=t;
maxflow+=incf[t];
mincost+=dis[t]*incf[t];
int i;
while (x!=s) {
i=pre[x];
e[i].flow-=incf[t];
e[i^1].flow+=incf[t];
x=e[i^1].v;
}
}
}
int main () {
scanf ("%d%d%d%d",&n,&m,&s,&t);
rep (i,1,m) {
int u,v,w,c;
scanf ("%d%d%d%d",&u,&v,&w,&c);
add_edge (u,v,w,c);
}
mcmf ();
printf ("%d %d\n",maxflow,mincost);
return 0;
}
卡Dinic毒瘤题专用ISAP （hdu 4280）
#include<cstdio>
#include<algorithm>
#include<vector>
#include<queue>
#include<map>
#include<iostream>
#include<cstring>
#include<cmath>
using namespace std;
#define rep(i,f_start,f_end) for (int i=f_start;i<=f_end;++i)
#define per(i,n,a) for (int i=n;i>=a;i--)
#define MT(x,i) memset(x,i,sizeof(x) )
#define rev(i,start,end) for (int i=start;i<end;i++)
#define inf 0x3f3f3f3f
#define mp(x,y) make_pair(x,y)
#define lowbit(x) (x&-x)
#define MOD 1000000007
#define exp 1e-8
#define N 1000005
#define fi first
#define se second
#define pb push_back
typedef long long ll;
const ll INF=0x3f3f3f3f3f3f3f3f;
typedef vector <int> VI;
typedef pair<int ,int> PII;
typedef pair<int ,PII> PIII;
ll gcd (ll a,ll b) {return b?gcd (b,a%b):a; }
inline int read() {
char ch=getchar(); int x=0, f=1;
while(ch<'0'||ch>'9') {
if(ch=='-') f=-1;
ch=getchar();
} while('0'<=ch&&ch<='9') {
x=x*10+ch-'0';
ch=getchar();
} return x*f;
}
const int maxn=1e5+10;
struct Edge {
int u,v;
ll cap;
Edge (int u=0,int v=0,ll cap=0) :u (u),v (v),cap (cap) {}
}edge[maxn*4];
vector <int> G[maxn];
int dis[maxn],cur[maxn],num[maxn],pre[maxn],cnt,s,t;
void add_edge (int u,int v,int w) {
edge[cnt]=Edge (u,v,w);
G[u].pb (cnt++);
edge[cnt]=Edge (v,u,w);
G[v].pb (cnt++);
}
int bfs () {
MT (dis,-1);
queue <int> q; q.push (t);
dis[t]=0;
while (q.size ()) {
int u=q.front (); q.pop ();
for (auto it:G[u]) {
Edge &e=edge[it];
if (dis[e.v]==-1) {
dis[e.v]=dis[u]+1;
q.push (e.v);
}
}
}
return ~dis[s];
}
int dfs () {
int u=t; int flow=inf;
while (u!=s) {
Edge &e=edge[pre[u]];
if (e.cap<flow) flow=e.cap;
u=e.u;
} u=t;
while (u!=s) {
Edge &e1=edge[pre[u]];
Edge &e2=edge[pre[u]^1];
e1.cap-=flow; e2.cap+=flow;
u=e1.u;
}
return flow;
}
int isap (int n) {
if (!bfs ()) return 0;
MT (num,0);
MT (cur,0);
rep (i,1,n) if (~dis[i]) num[dis[i]]++;
int ans=0,u=s;
while (dis[s]<n) {
if (u==t) ans+=dfs (),u=s;
int flag=0;
for (auto it:G[u]) {
Edge &e=edge[it];
if (dis[e.v]+1==dis[u]&&e.cap>0) {
pre[e.v]=it; cur[u]=it;
flag=1; u=e.v;
break;
}
}
if (!flag) {
if (--num[dis[u]]==0) break;
int md=n;
for (auto it:G[u]) {
Edge &e=edge[it];
if (e.cap>0&&dis[e.v]<md) {
md=dis[e.v]; cur[u]=it;
}
}
num[dis[u]=md+1]++;
if (u!=s) u=edge[pre[u]].u;
}
}
return ans;
}
int main () {
int tt;
scanf ("%d",&tt);
while (tt--) {
int n,m;
scanf ("%d%d",&n,&m);
cnt=0; rep (i,0,n) G[i].clear ();
int u,v,c,west=inf,east=-inf;
rep (i,1,n) {
scanf ("%d%d",&u,&v);
if (west>u) west=u,s=i;
if (east<u) east=u,t=i;
}
rep (i,1,m) {
scanf ("%d%d%d",&u,&v,&c);
add_edge (u,v,c);
}
printf ("%d\n",isap (n));
}
return 0;
}
