标签：add flow return ret out 删除 sha c++ can
http://acm.hdu.edu.cn/search.php?field=problem&key=2019+Multi-University+Training+Contest+1&source=1&searchmode=source
删除某些边，让$1$到$n$的最短路径发生变化
删除某条边的费用是边的长度
先用迪杰斯特拉跑一遍整个图，满足$dis[a]+w=dis[b]$的边，肯定是最短路径上的边
选出这些边，找到一个最小割集，Dinic比EK快很多，虽然渐进复杂度相同，都是$O(nm^2)$
Dinic加上弧优化后速度更快
#include<bits/stdc++.h>
#define ll long long
#define ull unsigned long long
#define pa pair<ll,ll>
using namespace std;
const ll maxn=1e4+5;
const ll maxm=1e7+10;
const ll mod=1e9+7;
vector<pair<int,int>>ve[maxn];
ll dis[maxn];
int n,m,edge_num=-1,head[maxn],dep[maxn];
bool vis[maxn];
struct Edge{
int to,nex,v;
}edge[maxn*2];//maxn=1e4
void add_edge(int a,int b,int c)//边数从0开始，每次加上反向边，这样奇偶交替加边，重边无所谓
{
edge[++edge_num].to=b;
edge[edge_num].nex=head[a];
edge[edge_num].v=c;
head[a]=edge_num;
}
bool bfs()
{
for(int i=1;i<=n;i++)dep[i]=1e9;
dep[1]=0;
queue<int>que;
que.push(1);
while(que.size()){
int now=que.front();
que.pop();
for(int i=head[now];i!=-1;i=edge[i].nex){
int to=edge[i].to;
int v=edge[i].v;
if(v&&dep[to]>dep[now]+1){
dep[to]=dep[now]+1;
que.push(to);
}
}
}
if(dep[n]==1e9)return false;
else return true;
}
int dfs(int x,int lowflow)
{
if(x==n||lowflow==0)return lowflow;
int reslow=0;
int used=0;
for(int i=head[x];i!=-1;i=edge[i].nex){
int to=edge[i].to;
if(edge[i].v&&dep[x]+1==dep[to]){
if(reslow=dfs(to,min(lowflow,edge[i].v))){
edge[i].v-=reslow;
edge[i^1].v+=reslow;
used+=reslow;
lowflow-=reslow;
if(lowflow<=0)break;
}
}
}
return used;
}
void Dinic()
{
ll maxflow=0;
int lowflow;
while(bfs()){
while(lowflow=dfs(1,1e9)){
maxflow+=lowflow;
}
}
printf("%lld\n",maxflow);
}
void dj()
{
for(int i=1;i<=n;i++)dis[i]=1e18,vis[i]=false;
dis[1]=0;
priority_queue<pair<ll,int>>que;
que.push(make_pair(0,1));
while(que.size()){
pair<ll,int>now=que.top();
que.pop();
if(vis[now.second])continue;
vis[now.second]=true;
for(int i=0;i<ve[now.second].size();i++){
int to=ve[now.second][i].first;
int w=ve[now.second][i].second;
if(dis[to]>dis[now.second]+w){
dis[to]=dis[now.second]+w;
que.push(make_pair(-dis[to],to));
}
}
}
}
int main()
{
// freopen("D:/a.txt","w",stdout);
// freopen("D:/2.txt","r",stdin);
int T;
scanf("%d",&T);
while(T--){
scanf("%d %d",&n,&m);
for(int i=1;i<=m;i++){
int a,b,c;
scanf("%d %d %d",&a,&b,&c);
ve[a].push_back(make_pair(b,c));
}
dj();
if(dis[n]==1e18){
printf("0\n");
continue;
}
for(int i=1;i<=n;i++)head[i]=-1;
edge_num=-1;
for(int i=1;i<=n;i++){
for(int j=0;j<ve[i].size();j++){
int a=i,b=ve[i][j].first,c=ve[i][j].second;
if(dis[a]+c==dis[b])add_edge(a,b,c),add_edge(b,a,0);
}
}
Dinic();
for(int i=1;i<=n;i++)ve[i].clear();
}
return 0;
}
#include<bits/stdc++.h>
#define ll long long
#define ull unsigned long long
#define pa pair<ll,ll>
using namespace std;
const ll maxn=1e4+5;
const ll maxm=1e7+10;
const ll mod=1e9+7;
vector<pair<int,int>>ve[maxn];
ll dis[maxn];
int n,m,edge_num=-1,head[maxn],dep[maxn],cur[maxn];
bool vis[maxn];
struct Edge{
int to,nex,v;
}edge[maxn*2];//maxn=1e4
void add_edge(int a,int b,int c)//边数从0开始，每次加上反向边，这样奇偶交替加边，重边无所谓
{
edge[++edge_num].to=b;
edge[edge_num].nex=head[a];
edge[edge_num].v=c;
head[a]=edge_num;
}
bool bfs()//分层
{
for(int i=1;i<=n;i++)dep[i]=1e9;
dep[1]=0;
queue<int>que;
que.push(1);
while(que.size()){
int now=que.front();
que.pop();
for(int i=head[now];i!=-1;i=edge[i].nex){
int to=edge[i].to;
int v=edge[i].v;
if(v&&dep[to]>dep[now]+1){
dep[to]=dep[now]+1;
que.push(to);
}
}
}
if(dep[n]==1e9)return false;
else return true;
}
int dfs(int x,int lowflow)
{
if(x==n||lowflow==0)return lowflow;
int reslow=0;
int used=0;
for(int &i=cur[x];i!=-1;i=edge[i].nex){
int to=edge[i].to;
if(edge[i].v&&dep[x]+1==dep[to]){
if(reslow=dfs(to,min(lowflow,edge[i].v))){
edge[i].v-=reslow;
edge[i^1].v+=reslow;
used+=reslow;
lowflow-=reslow;
if(lowflow<=0)break;
}
}
}
return used;
}
void Dinic()
{
ll maxflow=0;
int lowflow;
while(bfs()){
for(int i=1;i<=n;i++)cur[i]=head[i];
while(lowflow=dfs(1,1e9)){
maxflow+=lowflow;
}
}
printf("%lld\n",maxflow);
}
void dj()
{
for(int i=1;i<=n;i++)dis[i]=1e18,vis[i]=false;
dis[1]=0;
priority_queue<pair<ll,int>>que;
que.push(make_pair(0,1));
while(que.size()){
pair<ll,int>now=que.top();
que.pop();
if(vis[now.second])continue;
vis[now.second]=true;
for(int i=0;i<ve[now.second].size();i++){
int to=ve[now.second][i].first;
int w=ve[now.second][i].second;
if(dis[to]>dis[now.second]+w){
dis[to]=dis[now.second]+w;
que.push(make_pair(-dis[to],to));
}
}
}
}
int main()
{
// freopen("D:/a.txt","w",stdout);
// freopen("D:/2.txt","r",stdin);
int T;
scanf("%d",&T);
while(T--){
scanf("%d %d",&n,&m);
for(int i=1;i<=m;i++){
int a,b,c;
scanf("%d %d %d",&a,&b,&c);
ve[a].push_back(make_pair(b,c));
}
dj();
if(dis[n]==1e18){
printf("0\n");
continue;
}
for(int i=1;i<=n;i++)head[i]=-1;
edge_num=-1;
for(int i=1;i<=n;i++){
for(int j=0;j<ve[i].size();j++){
int a=i,b=ve[i][j].first,c=ve[i][j].second;
if(dis[a]+c==dis[b])add_edge(a,b,c),add_edge(b,a,0);
}
}
Dinic();
for(int i=1;i<=n;i++)ve[i].clear();
}
return 0;
}
标签：add flow return ret out 删除 sha c++ can
原文地址：https://www.cnblogs.com/carcar/p/11231075.html
