最大流(Dinic法)
(graph_tree/dinic.hpp)
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Code
#pragma once
#include<vector>
#include<queue>
#include<cmath>
#include<limits>
#include<cassert>
#include<iostream>
#include<map>
#include<list>
/**
* @brief 最大流(Dinic法)
*/
template<typename T>
struct dinic {
struct edge {
int to;
typename std::list<edge>::iterator rev;
T cap,flow;
edge(int to,T cap):to(to),cap(cap),flow(T()){}
};
int n,src,dst;
T ret=T();
std::vector<std::list<edge>> g;
std::vector<typename std::list<edge>::iterator>itr;
std::vector<int>level,seen;
std::map<std::pair<int,int>,bool>exist;
std::map<std::pair<int,int>,typename std::list<edge>::iterator>m;
dinic(int n,int s,int t):n(n),src(s),dst(t){g.assign(n,std::list<edge>());itr.resize(n);}
void add_edge(int from, int to, T cap) {
g[from].push_back(edge(to,cap));
g[to].push_back(edge(from,0));
m[std::make_pair(from,to)]=prev(g[from].end());
m[std::make_pair(to,from)]=prev(g[to].end());
g[from].back().rev=prev(g[to].end());
g[to].back().rev=prev(g[from].end());
exist[std::make_pair(from,to)]=1;
exist[std::make_pair(to,from)]=1;
}
bool update_edge(int from, int to, T cap){
if(cap>0){
if(exist[std::make_pair(from,to)]){
auto e=m[std::make_pair(from,to)];
e->cap+=cap;
}else{
add_edge(from,to,cap);
}
return 1;
}else{
cap*=-1;
if(exist[std::make_pair(from,to)]){
auto e=m[std::make_pair(from,to)];
if(e->cap-e->flow>=cap){
e->cap-=cap;
}else{
e->cap-=cap;
T req=e->flow-e->cap;
e->flow-=req;
e->rev->flow+=req;
ret-=req;
assert(cancel(dst,to,req));
assert(cancel(from,src,req));
if(e->cap==0&&e->rev->cap==0){
g[from].erase(e);
g[to].erase(e->rev);
exist[std::make_pair(from,to)]=0;
exist[std::make_pair(to,from)]=0;
}
}
return 1;
}else{
return 0;
}
}
}
void bfs(int s) {
level.assign(n,-1);
std::queue<int> q;
level[s] = 0; q.push(s);
while (!q.empty()) {
int v = q.front(); q.pop();
for(edge e: g[v]){
if (e.cap-e.flow > 0 and level[e.to] < 0) {
level[e.to] = level[v] + 1;
q.push(e.to);
}
}
}
}
T dfs(int v, int t,T f) {
if (v == t) return f;
for(auto &e=itr[v];e!=g[v].end();++e){
if (e->cap-e->flow > 0 and level[v] < level[e->to]) {
T d = dfs(e->to, t, std::min(f, e->cap-e->flow));
if (d > 0) {
e->flow+=d;
e->rev->flow -= d;
return d;
}
}
}
return 0;
}
T __cancel(int v,int t,T f){
if (v == t) return f;
seen[v]=1;
for (edge& e: g[v]){
if (e.rev->flow > 0&&!seen[e.to]) {
T d = __cancel(e.to, t, std::min(f,e.rev->flow));
if (d > 0) {
e.flow+=d;
e.rev->flow-=d;
return d;
}
}
}
return 0;
}
T run() {
T f;
while (bfs(src), level[dst] >= 0) {
for(int i=0;i<n;++i)itr[i]=g[i].begin();
while ((f = dfs(src, dst, std::numeric_limits<T>::max())) > 0) {
ret += f;
}
}
return ret;
}
T cancel(int s,int t,T mx){
T f;
while(seen.assign(n,0),seen[s]=1,(f=__cancel(s, t, mx))>0)mx-=f;
return mx==0;
}
T cap(int s,int t){
if(exist[std::make_pair(s,t)]){
return m[std::make_pair(s,t)]->cap;
}else{
return 0;
}
}
T flow(int s,int t){
if(exist[std::make_pair(s,t)]){
return m[std::make_pair(s,t)]->flow;
}else{
return 0;
}
}
void debug(){
for(int i=0;i<n;++i)for(int j=0;j<n;++j){
if(i==j)continue;
if(flow(i,j)>0)std::cerr<<"("<<i<<","<<j<<")";
}
std::cerr<<'\n';
}
};
#line 2 "graph_tree/dinic.hpp"
#include<vector>
#include<queue>
#include<cmath>
#include<limits>
#include<cassert>
#include<iostream>
#include<map>
#include<list>
/**
* @brief 最大流(Dinic法)
*/
template<typename T>
struct dinic {
struct edge {
int to;
typename std::list<edge>::iterator rev;
T cap,flow;
edge(int to,T cap):to(to),cap(cap),flow(T()){}
};
int n,src,dst;
T ret=T();
std::vector<std::list<edge>> g;
std::vector<typename std::list<edge>::iterator>itr;
std::vector<int>level,seen;
std::map<std::pair<int,int>,bool>exist;
std::map<std::pair<int,int>,typename std::list<edge>::iterator>m;
dinic(int n,int s,int t):n(n),src(s),dst(t){g.assign(n,std::list<edge>());itr.resize(n);}
void add_edge(int from, int to, T cap) {
g[from].push_back(edge(to,cap));
g[to].push_back(edge(from,0));
m[std::make_pair(from,to)]=prev(g[from].end());
m[std::make_pair(to,from)]=prev(g[to].end());
g[from].back().rev=prev(g[to].end());
g[to].back().rev=prev(g[from].end());
exist[std::make_pair(from,to)]=1;
exist[std::make_pair(to,from)]=1;
}
bool update_edge(int from, int to, T cap){
if(cap>0){
if(exist[std::make_pair(from,to)]){
auto e=m[std::make_pair(from,to)];
e->cap+=cap;
}else{
add_edge(from,to,cap);
}
return 1;
}else{
cap*=-1;
if(exist[std::make_pair(from,to)]){
auto e=m[std::make_pair(from,to)];
if(e->cap-e->flow>=cap){
e->cap-=cap;
}else{
e->cap-=cap;
T req=e->flow-e->cap;
e->flow-=req;
e->rev->flow+=req;
ret-=req;
assert(cancel(dst,to,req));
assert(cancel(from,src,req));
if(e->cap==0&&e->rev->cap==0){
g[from].erase(e);
g[to].erase(e->rev);
exist[std::make_pair(from,to)]=0;
exist[std::make_pair(to,from)]=0;
}
}
return 1;
}else{
return 0;
}
}
}
void bfs(int s) {
level.assign(n,-1);
std::queue<int> q;
level[s] = 0; q.push(s);
while (!q.empty()) {
int v = q.front(); q.pop();
for(edge e: g[v]){
if (e.cap-e.flow > 0 and level[e.to] < 0) {
level[e.to] = level[v] + 1;
q.push(e.to);
}
}
}
}
T dfs(int v, int t,T f) {
if (v == t) return f;
for(auto &e=itr[v];e!=g[v].end();++e){
if (e->cap-e->flow > 0 and level[v] < level[e->to]) {
T d = dfs(e->to, t, std::min(f, e->cap-e->flow));
if (d > 0) {
e->flow+=d;
e->rev->flow -= d;
return d;
}
}
}
return 0;
}
T __cancel(int v,int t,T f){
if (v == t) return f;
seen[v]=1;
for (edge& e: g[v]){
if (e.rev->flow > 0&&!seen[e.to]) {
T d = __cancel(e.to, t, std::min(f,e.rev->flow));
if (d > 0) {
e.flow+=d;
e.rev->flow-=d;
return d;
}
}
}
return 0;
}
T run() {
T f;
while (bfs(src), level[dst] >= 0) {
for(int i=0;i<n;++i)itr[i]=g[i].begin();
while ((f = dfs(src, dst, std::numeric_limits<T>::max())) > 0) {
ret += f;
}
}
return ret;
}
T cancel(int s,int t,T mx){
T f;
while(seen.assign(n,0),seen[s]=1,(f=__cancel(s, t, mx))>0)mx-=f;
return mx==0;
}
T cap(int s,int t){
if(exist[std::make_pair(s,t)]){
return m[std::make_pair(s,t)]->cap;
}else{
return 0;
}
}
T flow(int s,int t){
if(exist[std::make_pair(s,t)]){
return m[std::make_pair(s,t)]->flow;
}else{
return 0;
}
}
void debug(){
for(int i=0;i<n;++i)for(int j=0;j<n;++j){
if(i==j)continue;
if(flow(i,j)>0)std::cerr<<"("<<i<<","<<j<<")";
}
std::cerr<<'\n';
}
};
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