省选_简单图论
这里是一些简单的图论模板，没有编译过.（编译过的话会做特殊说明）
目录：
1.Dijkstra
2.SPFA
3.Tarjan + toposort
4.Dinic
5.MCMF(最小费用流）
1.Dijkstra（Accepted)
namespace Dijkstra{
#define maxn 1000000
#define inf 2000000000
int n,m,s;
int cnt;
int head[maxn],nex[maxn<<1],to[maxn<<1],val[maxn<<1];
void addedge(int u,int v,int c){
nex[++cnt] = head[u];
head[u]=cnt;
to[cnt] = v;
val[cnt] = c;
}
struct Node{
int dist,u;
Node(int dist,int u):dist(dist),u(u){}
bool operator < (Node v)const{
return v.dist < dist;
}
};
priority_queue<Node>Q;
int done[maxn],d[maxn];
void dijkstra(){
memset(done,0,sizeof(done));
memset(d,0,sizeof(d));
for(int i=0;i<maxn;++i) d[i]=inf;
d[0]=d[s]=0;
Q.push(Node(d[0],s));
while(!Q.empty()){
int u=Q.top().u; Q.pop();
if(done[u]) continue;
done[u]=1;
for(int v=head[u];v;v=nex[v]){
if(d[u]+val[v]<d[to[v]]){
d[to[v]] = d[u]+val[v];
Q.push(Node(d[to[v]],to[v]));
}
}
}
}
int main(){
scanf("%d%d%d",&n,&m,&s);
for(int i=1;i<=m;++i) {
int a,b,c;
scanf("%d%d%d",&a,&b,&c);
addedge(a,b,c);
}
dijkstra();
for(int i=1;i<=n;++i) printf("%d ",d[i]);
return 0;
}
};
2.SPFA(Accepted)
namespace SPFA{
#define maxn 1000000
#define inf 2147483647
int head[maxn],to[maxn<<1],nex[maxn<<1],val[maxn<<1];
int cnt;
int n,m,s;
int inq[maxn],d[maxn];
deque<int>Q;
void addedge(int u,int v,int c){
nex[++cnt] = head[u], head[u] = cnt,to[cnt] = v,val[cnt] = c;
}
void spfa(){
for(int i=0;i<maxn;++i) d[i] = inf;
memset(inq,0,sizeof(inq));
Q.push_back(s);
inq[s] = 1;
d[s] = 0;
while(!Q.empty()){
int u=Q.front(); Q.pop_front();
inq[u] = 0;
for(int v=head[u];v;v=nex[v])
if(d[to[v]] > d[u] + val[v]) {
d[to[v]] = d[u] + val[v];
if(!inq[to[v]]) {
inq[to[v]] = 1;
if(Q.empty() || d[Q.front()] >= d[to[v]] - 2000)
Q.push_front(to[v]);
else
Q.push_back(to[v]);
}
}
}
}
int main(){
scanf("%d%d%d",&n,&m,&s);
for(int i=1;i<=m;++i) {
int a,b,c;
scanf("%d%d%d",&a,&b,&c);
addedge(a,b,c);
}
spfa();
for(int i=1;i<=n;++i) printf("%d ",d[i]);
return 0;
}
};
3.tarjan + toposort（Accepted）
namespace Tarjan{
#define maxn 1000000
#define ll long long
map<int,int>ed[maxn];
int scc,sig;
int vis[maxn];
int du[maxn];
int idx[maxn];
int pre[maxn],low[maxn];
int val[maxn];
long long value[maxn];
long long ans[maxn];
stack<int>S;
queue<int>Q;
struct graph{
int cnt;
int head[maxn],to[maxn<<1],nex[maxn<<1];
void addedge(int u,int v){
nex[++cnt] = head[u],head[u]=cnt,to[cnt] = v;
}
}G1,G2;
void tarjan(int u){
S.push(u);
vis[u] = 1;
pre[u] = low[u] = ++scc;
for(int v=G1.head[u];v;v=G1.nex[v]){
if(!vis[G1.to[v]]) {
tarjan(G1.to[v]);
low[u] = min(low[u],low[G1.to[v]]);
}
else if(vis[G1.to[v]] == 1) low[u] = min(low[u],pre[G1.to[v]]);
}
if(pre[u] == low[u]) {
++sig;
for(;;){
int a=S.top(); S.pop();
vis[a] = -1,idx[a] = sig;
value[sig] += (ll)val[a];
if(a==u) break;
}
}
}
void toposort(){
for(int i=1;i<=sig;++i)
for(int j=G2.head[i];j;j=G2.nex[j]) ++du[G2.to[j]];
for(int i=1;i<=sig;++i) if(du[i]==0) Q.push(i),ans[i] = value[i];
while(!Q.empty()){
int u=Q.front(); Q.pop();
for(int v=G2.head[u];v;v=G2.nex[v]){
ans[G2.to[v]] = max(ans[G2.to[v]],ans[u] + value[G2.to[v]]);
--du[G2.to[v]];
if(du[G2.to[v]]==0) Q.push(G2.to[v]);
}
}
long long fin=0;
for(int i=1;i<=sig;++i)
fin=max(fin,ans[i]);
printf("%lld",fin);
}
int main(){
int n,m,a,b;
scanf("%d%d",&n,&m);
for(int i=1;i<=n;++i) scanf("%d",&val[i]);
for(int i=1;i<=m;++i) {
scanf("%d%d",&a,&b);
G1.addedge(a,b);
}
for(int i=1;i<=n;++i) if(!vis[i]) tarjan(i);
for(int i=1;i<=n;++i)
for(int v=G1.head[i];v;v=G1.nex[v])
if(idx[i]!=idx[G1.to[v]] && !ed[idx[i]][idx[G1.to[v]]])
G2.addedge(idx[i],idx[G1.to[v]]),ed[idx[i]][idx[G1.to[v]]]=1;
toposort();
return 0;
}
};
4.Dinic(Accepted)
namespace Dinic{
#define maxn 200000
#define inf 10000000
int N,M,S,T;
struct Edge{
int from,to,cap;
Edge(int u,int v,int c):from(u),to(v),cap(c){}
};
vector<int>G[maxn];
vector<Edge>edges;
queue<int>Q;
void addedge(int u,int v,int c){
edges.push_back(Edge(u,v,c));
edges.push_back(Edge(v,u,0));
int m=edges.size();
G[u].push_back(m-2);
G[v].push_back(m-1);
}
int d[maxn],vis[maxn];
int current[maxn];
int BFS(){
memset(d,0,sizeof(d));
memset(vis,0,sizeof(vis));
d[S] = 0,vis[S] = 1; Q.push(S);
while(!Q.empty()){
int u=Q.front(); Q.pop();
int m=G[u].size();
for(int i=0;i<m;++i) {
Edge r = edges[G[u][i]];
if(!vis[r.to] && r.cap > 0) {
d[r.to] = d[u] + 1;
vis[r.to] = 1;
Q.push(r.to);
}
}
}
return vis[T];
}
int dfs(int x,int cur){
if(x == T) return cur;
int flow=0,f;
int m=G[x].size();
for(int i=current[x];i<m;++i) {
current[x] = i;
int u=G[x][i];
Edge r = edges[u];
if(d[r.to] == d[x] + 1 && r.cap >0) {
f = dfs(r.to,min(cur,r.cap));
if(f > 0) {
flow += f,cur -= f;
edges[u].cap -= f,edges[u ^ 1].cap += f;
}
}
if(cur == 0) break;
}
return flow;
}
int maxflow(){
int flow = 0;
while(BFS()){
memset(current,0,sizeof(current));
flow += dfs(S,inf);
}
return flow;
}
};
5.最小费用流（Accepted)
namespace MCMF{
#define inf 2000000
#define maxn 50004
#define ll long long
struct Edge{
int from,to,cap,cost;
Edge(int u,int v,int c,int f):from(u),to(v),cap(c),cost(f){}
};
long long ans;
int flow;
int n,m,s,t;
queue<int>Q;
vector<int>G[maxn];
vector<Edge>edges;
void addedge(int u,int v,int c,int f){
edges.push_back(Edge(u,v,c,f));
edges.push_back(Edge(v,u,0,-f));
int m = edges.size();
G[u].push_back(m-2);
G[v].push_back(m-1);
}
int d[maxn],inq[maxn],a[maxn],flow2[maxn];
int SPFA(){
for(int i=1;i<maxn;++i) d[i] = flow2[i] = inf;
memset(inq,0,sizeof(inq));
inq[s] = 1,d[s] = 0; Q.push(s);
int f;
while(!Q.empty()){
int u = Q.front(); Q.pop(); inq[u] = 0;
int sz = G[u].size();
for(int i=0;i<sz;++i) {
Edge r = edges[G[u][i]];
if(r.cap > 0 && d[r.to] > d[u] + r.cost) {
d[r.to] = d[u] + r.cost;
a[r.to] = G[u][i];
flow2[r.to] = min(r.cap,flow2[u]);
if(!inq[r.to]) {
inq[r.to] = 1;
Q.push(r.to);
}
}
}
}
if(d[t] == inf) return 0;
f = flow2[t];
flow += f;
int u = edges[a[t]].from;
edges[a[t]].cap -= f;
edges[a[t] ^ 1].cap += f;
while(u != s){
edges[a[u]].cap -= f;
edges[a[u] ^ 1].cap += f;
u = edges[a[u]].from;
}
ans += (ll) (d[t] * f);
return 1;
}
int maxflow(){
while(SPFA());
return flow;
}
long long getcost() { return ans; }
int main(){
scanf("%d%d%d%d",&n,&m,&s,&t);
for(int i=1;i<=m;++i) {
int a,b,c,d;
scanf("%d%d%d%d",&a,&b,&c,&d);
addedge(a,b,c,d);
}
printf("%d ",maxflow());
printf("%lld",getcost());
return 0;
}
};
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