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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#744197 | #602. 最小费用最大流(随机数据) | dreamjoker | 100 ✓ | 5ms | 7952kb | C++23 | 7.9kb | 2024-11-13 21:07:53 | 2024-11-13 21:08:01 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
template<typename T>
struct Dinic {
int n;
struct edge {
int to,nxt;
T cap;
T cost;
};
std::vector<edge> e;
std::vector<int> head,now;
std::vector<T> h,dep;
std::vector<bool> vis;
T inf=std::numeric_limits<T>::max()>>1;
Dinic(int _n) : n(_n),head(n+1,-1) {}
void add_edge(int u,int v,T cap,T cost=0) {
e.push_back({v,head[u],cap,cost});
head[u]=e.size()-1;
e.push_back({u,head[v],0,-cost});
head[v]=e.size()-1;
}
// Johnson algorithm
void spfa(int s) {
fill(h.begin(),h.end(),inf);
std::queue<int> q;
h[s]=0;
q.push(0);
vis[s]=true;
while(!q.empty()) {
int u=q.front();
q.pop();
vis[u]=false;
for(int i=head[u];~i;i=e[i].nxt) {
int v=e[i].to;
if(e[i].cap>0&&h[v]>h[u]+e[i].cost) {
h[v]=h[u]+e[i].cost;
if(!vis[v]) {
vis[v]=true;
q.push(v);
}
}
}
}
}
bool dij(int s,int t) {
fill(dep.begin(),dep.end(),inf);
fill(vis.begin(),vis.end(),false);
std::priority_queue<std::pair<T,int>,std::vector<std::pair<T,int>>,std::greater<std::pair<T,int>>> pq;
dep[s]=0;
pq.push({0,s});
while(!pq.empty()) {
int u=pq.top().second;
pq.pop();
if(vis[u]) continue;
vis[u]=true;
for(int i=head[u];~i;i=e[i].nxt) if(e[i].cap>0){
int v=e[i].to;
auto newdep=dep[u]+e[i].cost+h[u]-h[v];
if(dep[v]>newdep) {
dep[v]=newdep;
pq.push({dep[v],v});
}
}
}
return dep[t]!=inf;
}
T dfs(int u,int t,T flow) {
if(u==t||!flow) return flow;
T rest=flow;
vis[u]=true;
for(int i=now[u];~i&&rest;i=e[i].nxt) {
now[u]=i;
int v=e[i].to;
if(!vis[v]&&dep[v]==dep[u]+e[i].cost+h[u]-h[v]&&e[i].cap>0) {
T delta=dfs(v,t,std::min(rest,e[i].cap));
if(!delta) continue;
e[i].cap-=delta;
e[i^1].cap+=delta;
rest-=delta;
}
}
vis[u]=false;
return flow-rest;
}
// flag 表示初始图中是否可能存在负权边,如果存在的话需要先Johnson算法求出h函数
auto MCMF(int s,int t,int flag=0) {
h.assign(n+1,0); vis.assign(n+1,false); dep.resize(n+1);
T flow=0,cost=0;
if(flag) spfa(s);
while(dij(s,t)) {
std::fill(vis.begin(),vis.end(),false);
now=head;
T delta=0,tmp;
while(tmp=dfs(s,t,inf))
delta+=tmp;
for(int i=0;i<=n;i++)
h[i]+=dep[i];
flow+=delta,cost+=h[t]*delta;
}
return std::make_pair(flow,cost);
}
void resetflow(T x=0) {
for(auto &it:e)
it.flow=x;
}
};
namespace IO
{
char iobuf[1<<25],*p1=iobuf,*p2=iobuf;
#define getchar() (p1==p2&&(p2=(p1=iobuf)+fread(iobuf,1,1<<21,stdin),p1==p2)?EOF:*p1++)
void read(){} template <typename T,typename... other>
inline void read(T &f,other &...y)
{
f=0;T fu=1;char c=getchar();
while(c<'0'||c>'9') {if(c=='-'){fu=-1;}c=getchar();}
while(c>='0'&&c<='9') {f=(f<<3)+(f<<1)+(c&15);c=getchar();}
f*=fu;
read(y...);
}
template <typename T>
void print(T x,char c=0)
{
if(x<0) putchar('-'),x=-x;
if(x<10) putchar(x+48);
else print(x/10),putchar(x%10+48);
if(c) putchar(c);
}
inline void reads(std::string &f)
{
std::string str="";char ch=getchar();
while(ch<'!'||ch>'~') ch=getchar();
while((ch>='!')&&(ch<= '~')) str+=ch,ch=getchar();
f=str;
}
void prints(std::string s)
{
for(int i=0;s[i];++i)
putchar(s[i]);
}
#ifndef endl
#define endl '\n'
#endif
struct Fastiostream {
friend Fastiostream &operator>>(Fastiostream &in,std::string &s) {reads(s); return in;}
friend Fastiostream &operator>>(Fastiostream &in,auto &x) {read(x); return in;}
friend Fastiostream &operator<<(Fastiostream &out,const char c) {putchar(c); return out;}
friend Fastiostream &operator<<(Fastiostream &out,const char *c) {while(*c!=0) putchar(*(c++)); return out;}
friend Fastiostream &operator<<(Fastiostream &out,const std::string &s) {prints(s); return out;}
friend Fastiostream &operator<<(Fastiostream &out,const auto &x) {print(x); return out;}
} fio;
}
namespace MCMF {
using i64 = long long;
using cap = i64;
const int N = 1205;
const int M = 120005;
const i64 flow_INF = 1145141919810114514ll;
const i64 cost_offset = 1145141919;
int n, m, s, t;
struct edge {
int from, to, nxt;
cap flow, cost;
bool origin;
} e[M << 1];
int cnt;
int h[N];
int add_edge(int u, int v, cap flow, cap cost, bool directed = true) {
++m;
e[++cnt] = {u, v, h[u], flow, cost, 1};
h[u] = cnt;
e[++cnt] = {v, u, h[v], directed ? 0 : flow, -cost, 0};
h[v] = cnt;
return cnt;
}
int tme;
int vis[N], fa[N], fe[N], circle[N], mark[N];
cap pi[N];
void dfs(int u, int fi) {
fa[u] = e[fi].from, fe[u] = fi;
mark[u] = 1;
for (int i = h[u]; i; i = e[i].nxt) {
int v = e[i].to;
if (e[i].origin && !mark[v])
dfs(v, i);
}
}
cap phi(int u) {
if (mark[u] == tme)
return pi[u];
mark[u] = tme, pi[u] = phi(fa[u]) + e[fe[u]].cost;
return pi[u];
}
cap pushflow(int eg) {
int rt = e[eg].from, lca = e[eg].to;
++tme;
int circle_cnt = 0;
while (rt)
mark[rt] = tme, rt = fa[rt];
while (mark[lca] ^ tme)
mark[lca] = tme, lca = fa[lca];
cap minflow = e[eg].flow, p = 2, del_u = 0;
for (int u = e[eg].from; u ^ lca; u = fa[u]) {
circle[++circle_cnt] = fe[u];
if (e[fe[u]].flow < minflow)
minflow = e[fe[u]].flow, del_u = u, p = 0;
}
for (int u = e[eg].to; u ^ lca; u = fa[u]) {
int ne = fe[u] ^ 1;
circle[++circle_cnt] = ne;
if (e[ne].flow < minflow)
minflow = e[ne].flow, del_u = u, p = 1;
}
circle[++circle_cnt] = eg;
cap cost = 0;
for (int i = 1; i <= circle_cnt; ++i) {
cost += e[circle[i]].cost * minflow;
e[circle[i]].flow -= minflow, e[circle[i] ^ 1].flow += minflow;
}
if (p == 2) return cost;
int u = e[eg].from, v = e[eg].to;
if (p == 1) std::swap(u, v);
int last_e = eg ^ p, last_u = v;
while (last_u ^ del_u) {
last_e ^= 1, --mark[u], std::swap(fe[u], last_e);
int nu = fa[u];
fa[u] = last_u, last_u = u, u = nu;
}
return cost;
}
void init_sz(int _n) { n = _n, m = 0, cnt = 1, tme = 1; }
std::pair<cap, cap> solve(int _s, int _t) {
s = _s, t = _t;
add_edge(t, s, flow_INF, -cost_offset);
dfs(t, 0), mark[t] = ++tme;
fa[t] = 0;
cap cost = 0, flow = 0;
bool run = 1;
while (run) {
run = 0;
for (int i = 2; i <= cnt; ++i)
if (e[i].flow && e[i].cost + phi(e[i].from) - phi(e[i].to) < 0)
cost += pushflow(i), run = 1;
}
flow = e[cnt].flow;
return std::make_pair(flow, cost + flow * cost_offset);
}
}
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
int n,m;
IO::fio>>n>>m;
MCMF::init_sz(n);
for(int i=0;i<m;i++) {
int u,v,c,w;
IO::fio>>u>>v>>c>>w;
MCMF::add_edge(u,v,c,w);
}
auto [flow,cost]=MCMF::solve(1,n);
cout<<flow<<" "<<cost<<endl;
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Pretests
Final Tests
Test #1:
score: 10
Accepted
time: 0ms
memory: 5736kb
input:
8 27 2 3 2147483647 100 1 3 1 100 2 4 2147483647 10 1 4 1 10 2 4 2147483647 10 1 4 1 10 2 8 3 0 3 5 2147483647 100 1 5 1 100 3 8 1 0 3 2 2147483647 0 4 5 2147483647 10 1 5 1 10 4 8 1 0 4 2 2147483647 0 5 6 2147483647 1 1 6 1 1 5 6 2147483647 1 1 6 1 1 5 7 2147483647 1 1 7 1 1 5 8 3 0 5 2 2147483647 ...
output:
8 243
result:
ok 2 number(s): "8 243"
Test #2:
score: 10
Accepted
time: 1ms
memory: 5736kb
input:
12 49 2 10 2147483647 5 1 10 1 5 2 5 2147483647 50 1 5 1 50 2 9 2147483647 8 1 9 1 8 2 8 2147483647 47 1 8 1 47 2 11 2147483647 17 1 11 1 17 2 12 5 0 3 12 0 0 3 2 2147483647 0 4 6 2147483647 18 1 6 1 18 4 11 2147483647 12 1 11 1 12 4 9 2147483647 14 1 9 1 14 4 12 3 0 4 2 2147483647 0 5 11 2147483647...
output:
15 436
result:
ok 2 number(s): "15 436"
Test #3:
score: 10
Accepted
time: 1ms
memory: 5752kb
input:
27 169 2 15 2147483647 24 1 15 1 24 2 19 2147483647 96 1 19 1 96 2 12 2147483647 49 1 12 1 49 2 13 2147483647 75 1 13 1 75 2 24 2147483647 2 1 24 1 2 2 27 5 0 3 27 0 0 3 2 2147483647 0 4 11 2147483647 99 1 11 1 99 4 3 2147483647 85 1 3 1 85 4 27 2 0 4 2 2147483647 0 5 27 0 0 5 2 2147483647 0 6 9 214...
output:
60 4338
result:
ok 2 number(s): "60 4338"
Test #4:
score: 10
Accepted
time: 1ms
memory: 5948kb
input:
77 2149 2 42 2147483647 33 1 42 1 33 2 68 2147483647 30 1 68 1 30 2 76 2147483647 13 1 76 1 13 2 51 2147483647 93 1 51 1 93 2 12 2147483647 39 1 12 1 39 2 57 2147483647 74 1 57 1 74 2 70 2147483647 21 1 70 1 21 2 73 2147483647 24 1 73 1 24 2 52 2147483647 54 1 52 1 54 2 15 2147483647 99 1 15 1 99 2 ...
output:
1000 74606
result:
ok 2 number(s): "1000 74606"
Test #5:
score: 10
Accepted
time: 0ms
memory: 5980kb
input:
102 4199 2 48 2147483647 42 1 48 1 42 2 85 2147483647 50 1 85 1 50 2 22 2147483647 83 1 22 1 83 2 95 2147483647 97 1 95 1 97 2 82 2147483647 34 1 82 1 34 2 25 2147483647 72 1 25 1 72 2 4 2147483647 17 1 4 1 17 2 47 2147483647 10 1 47 1 10 2 71 2147483647 12 1 71 1 12 2 68 2147483647 39 1 68 1 39 2 2...
output:
2000 161420
result:
ok 2 number(s): "2000 161420"
Test #6:
score: 10
Accepted
time: 0ms
memory: 7952kb
input:
102 4199 2 79 2147483647 13 1 79 1 13 2 83 2147483647 73 1 83 1 73 2 75 2147483647 90 1 75 1 90 2 30 2147483647 92 1 30 1 92 2 54 2147483647 25 1 54 1 25 2 66 2147483647 53 1 66 1 53 2 52 2147483647 37 1 52 1 37 2 63 2147483647 46 1 63 1 46 2 11 2147483647 20 1 11 1 20 2 55 2147483647 53 1 55 1 53 2...
output:
2000 143072
result:
ok 2 number(s): "2000 143072"
Test #7:
score: 10
Accepted
time: 2ms
memory: 5992kb
input:
102 4199 2 39 2147483647 45 1 39 1 45 2 51 2147483647 11 1 51 1 11 2 86 2147483647 63 1 86 1 63 2 23 2147483647 46 1 23 1 46 2 48 2147483647 63 1 48 1 63 2 87 2147483647 8 1 87 1 8 2 73 2147483647 63 1 73 1 63 2 5 2147483647 52 1 5 1 52 2 80 2147483647 21 1 80 1 21 2 31 2147483647 44 1 31 1 44 2 101...
output:
2000 146132
result:
ok 2 number(s): "2000 146132"
Test #8:
score: 10
Accepted
time: 5ms
memory: 6492kb
input:
302 10599 2 72 2147483647 169 1 72 1 169 2 260 2147483647 165 1 260 1 165 2 12 2147483647 108 1 12 1 108 2 16 2147483647 26 1 16 1 26 2 28 2147483647 148 1 28 1 148 2 7 2147483647 74 1 7 1 74 2 139 2147483647 199 1 139 1 199 2 231 2147483647 9 1 231 1 9 2 287 2147483647 123 1 287 1 123 2 135 2147483...
output:
5000 1106316
result:
ok 2 number(s): "5000 1106316"
Test #9:
score: 10
Accepted
time: 4ms
memory: 6576kb
input:
302 10599 2 222 2147483647 132 1 222 1 132 2 17 2147483647 7 1 17 1 7 2 177 2147483647 253 1 177 1 253 2 90 2147483647 195 1 90 1 195 2 128 2147483647 289 1 128 1 289 2 42 2147483647 193 1 42 1 193 2 213 2147483647 133 1 213 1 133 2 263 2147483647 293 1 263 1 293 2 50 2147483647 155 1 50 1 155 2 228...
output:
5000 1290871
result:
ok 2 number(s): "5000 1290871"
Test #10:
score: 10
Accepted
time: 4ms
memory: 7916kb
input:
302 10599 2 176 2147483647 289 1 176 1 289 2 190 2147483647 99 1 190 1 99 2 10 2147483647 96 1 10 1 96 2 240 2147483647 165 1 240 1 165 2 273 2147483647 205 1 273 1 205 2 248 2147483647 194 1 248 1 194 2 220 2147483647 122 1 220 1 122 2 194 2147483647 167 1 194 1 167 2 8 2147483647 67 1 8 1 67 2 227...
output:
5000 1395897
result:
ok 2 number(s): "5000 1395897"