1 | // -*- C++ -*- |
---|
2 | /* |
---|
3 | preflow_push_max_flow_h |
---|
4 | by jacint. |
---|
5 | Runs a preflow push algorithm with the modification, |
---|
6 | that we do not push on nodes with level at least n. |
---|
7 | Moreover, if a level gets empty, we set all nodes above that |
---|
8 | level to level n. Hence, in the end, we arrive at a maximum preflow |
---|
9 | with value of a max flow value. An empty level gives a minimum cut. |
---|
10 | |
---|
11 | Member functions: |
---|
12 | |
---|
13 | void run() : runs the algorithm |
---|
14 | |
---|
15 | The following functions should be used after run() was already run. |
---|
16 | |
---|
17 | T maxflow() : returns the value of a maximum flow |
---|
18 | |
---|
19 | void mincut(CutMap& M) : sets M to the characteristic vector of a |
---|
20 | minimum cut. M should be a map of bools initialized to false. |
---|
21 | |
---|
22 | */ |
---|
23 | |
---|
24 | #ifndef PREFLOW_PUSH_MAX_FLOW_H |
---|
25 | #define PREFLOW_PUSH_MAX_FLOW_H |
---|
26 | |
---|
27 | #define A 1 |
---|
28 | |
---|
29 | #include <algorithm> |
---|
30 | #include <vector> |
---|
31 | #include <stack> |
---|
32 | |
---|
33 | #include <reverse_bfs.h> |
---|
34 | |
---|
35 | |
---|
36 | namespace marci { |
---|
37 | |
---|
38 | template <typename Graph, typename T, |
---|
39 | typename FlowMap=typename Graph::EdgeMap<T>, typename CapMap=typename Graph::EdgeMap<T>, |
---|
40 | typename IntMap=typename Graph::NodeMap<int>, typename TMap=typename Graph::NodeMap<T> > |
---|
41 | class preflow_push_max_flow { |
---|
42 | |
---|
43 | typedef typename Graph::NodeIt NodeIt; |
---|
44 | typedef typename Graph::EachNodeIt EachNodeIt; |
---|
45 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
46 | typedef typename Graph::InEdgeIt InEdgeIt; |
---|
47 | |
---|
48 | Graph& G; |
---|
49 | NodeIt s; |
---|
50 | NodeIt t; |
---|
51 | IntMap level; |
---|
52 | CapMap& capacity; |
---|
53 | int empty_level; //an empty level in the end of run() |
---|
54 | T value; |
---|
55 | |
---|
56 | public: |
---|
57 | |
---|
58 | preflow_push_max_flow(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity) : |
---|
59 | G(_G), s(_s), t(_t), level(_G), capacity(_capacity) { } |
---|
60 | |
---|
61 | |
---|
62 | /* |
---|
63 | The run() function runs a modified version of the |
---|
64 | highest label preflow-push, which only |
---|
65 | finds a maximum preflow, hence giving the value of a maximum flow. |
---|
66 | */ |
---|
67 | void run() { |
---|
68 | |
---|
69 | int n=G.nodeNum(); |
---|
70 | int b=n-2; |
---|
71 | /* |
---|
72 | b is a bound on the highest level of an active node. |
---|
73 | */ |
---|
74 | |
---|
75 | IntMap level(G,n); |
---|
76 | TMap excess(G); |
---|
77 | FlowMap flow(G,0); |
---|
78 | |
---|
79 | std::vector<int> numb(n); |
---|
80 | /* |
---|
81 | The number of nodes on level i < n. It is |
---|
82 | initialized to n+1, because of the reverse_bfs-part. |
---|
83 | */ |
---|
84 | |
---|
85 | std::vector<std::stack<NodeIt> > stack(n); |
---|
86 | //Stack of the active nodes in level i. |
---|
87 | |
---|
88 | |
---|
89 | /*Reverse_bfs from t, to find the starting level.*/ |
---|
90 | level.set(t,0); |
---|
91 | std::queue<NodeIt> bfs_queue; |
---|
92 | bfs_queue.push(t); |
---|
93 | |
---|
94 | while (!bfs_queue.empty()) { |
---|
95 | |
---|
96 | NodeIt v=bfs_queue.front(); |
---|
97 | bfs_queue.pop(); |
---|
98 | int l=level.get(v)+1; |
---|
99 | |
---|
100 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
---|
101 | NodeIt w=G.tail(e); |
---|
102 | if ( level.get(w) == n ) { |
---|
103 | bfs_queue.push(w); |
---|
104 | ++numb[l]; |
---|
105 | level.set(w, l); |
---|
106 | } |
---|
107 | } |
---|
108 | } |
---|
109 | |
---|
110 | level.set(s,n); |
---|
111 | |
---|
112 | |
---|
113 | |
---|
114 | /* Starting flow. It is everywhere 0 at the moment. */ |
---|
115 | for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) |
---|
116 | { |
---|
117 | if ( capacity.get(e) == 0 ) continue; |
---|
118 | NodeIt w=G.head(e); |
---|
119 | if ( level.get(w) < n ) { |
---|
120 | if ( excess.get(w) == 0 && w!=t ) stack[level.get(w)].push(w); |
---|
121 | flow.set(e, capacity.get(e)); |
---|
122 | excess.set(w, excess.get(w)+capacity.get(e)); |
---|
123 | } |
---|
124 | } |
---|
125 | |
---|
126 | /* |
---|
127 | End of preprocessing |
---|
128 | */ |
---|
129 | |
---|
130 | |
---|
131 | /* |
---|
132 | Push/relabel on the highest level active nodes. |
---|
133 | */ |
---|
134 | /*While there exists an active node.*/ |
---|
135 | while (b) { |
---|
136 | if ( stack[b].empty() ) { |
---|
137 | --b; |
---|
138 | continue; |
---|
139 | } |
---|
140 | |
---|
141 | NodeIt w=stack[b].top(); //w is a highest label active node. |
---|
142 | stack[b].pop(); |
---|
143 | int lev=level.get(w); |
---|
144 | int exc=excess.get(w); |
---|
145 | int newlevel=2*n-2; //In newlevel we bound the next level of w. |
---|
146 | |
---|
147 | // if ( level.get(w) < n ) { //Nem tudom ez mukodik-e |
---|
148 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
---|
149 | |
---|
150 | if ( flow.get(e) == capacity.get(e) ) continue; |
---|
151 | NodeIt v=G.head(e); |
---|
152 | //e=wv |
---|
153 | |
---|
154 | if( lev > level.get(v) ) { |
---|
155 | /*Push is allowed now*/ |
---|
156 | |
---|
157 | if ( excess.get(v)==0 && v != s && v !=t ) |
---|
158 | stack[level.get(v)].push(v); |
---|
159 | /*v becomes active.*/ |
---|
160 | |
---|
161 | int cap=capacity.get(e); |
---|
162 | int flo=flow.get(e); |
---|
163 | int remcap=cap-flo; |
---|
164 | |
---|
165 | if ( remcap >= exc ) { |
---|
166 | /*A nonsaturating push.*/ |
---|
167 | |
---|
168 | flow.set(e, flo+exc); |
---|
169 | excess.set(v, excess.get(v)+exc); |
---|
170 | exc=0; |
---|
171 | break; |
---|
172 | |
---|
173 | } else { |
---|
174 | /*A saturating push.*/ |
---|
175 | |
---|
176 | flow.set(e, cap ); |
---|
177 | excess.set(v, excess.get(v)+remcap); |
---|
178 | exc-=remcap; |
---|
179 | } |
---|
180 | } else if ( newlevel > level.get(v) ) newlevel = level.get(v); |
---|
181 | |
---|
182 | } //for out edges wv |
---|
183 | |
---|
184 | |
---|
185 | if ( exc > 0 ) { |
---|
186 | for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
---|
187 | |
---|
188 | if( flow.get(e) == 0 ) continue; |
---|
189 | NodeIt v=G.tail(e); |
---|
190 | //e=vw |
---|
191 | |
---|
192 | if( lev > level.get(v) ) { |
---|
193 | /*Push is allowed now*/ |
---|
194 | |
---|
195 | if ( excess.get(v)==0 && v != s && v !=t) |
---|
196 | stack[level.get(v)].push(v); |
---|
197 | /*v becomes active.*/ |
---|
198 | |
---|
199 | int flo=flow.get(e); |
---|
200 | |
---|
201 | if ( flo >= exc ) { |
---|
202 | /*A nonsaturating push.*/ |
---|
203 | |
---|
204 | flow.set(e, flo-exc); |
---|
205 | excess.set(v, excess.get(v)+exc); |
---|
206 | exc=0; |
---|
207 | break; |
---|
208 | } else { |
---|
209 | /*A saturating push.*/ |
---|
210 | |
---|
211 | excess.set(v, excess.get(v)+flo); |
---|
212 | exc-=flo; |
---|
213 | flow.set(e,0); |
---|
214 | } |
---|
215 | } else if ( newlevel > level.get(v) ) newlevel = level.get(v); |
---|
216 | |
---|
217 | } //for in edges vw |
---|
218 | |
---|
219 | } // if w still has excess after the out edge for cycle |
---|
220 | |
---|
221 | excess.set(w, exc); |
---|
222 | |
---|
223 | |
---|
224 | /* |
---|
225 | Relabel |
---|
226 | */ |
---|
227 | |
---|
228 | if ( exc > 0 ) { |
---|
229 | //now 'lev' is the old level of w |
---|
230 | level.set(w,++newlevel); |
---|
231 | --numb[lev]; |
---|
232 | |
---|
233 | if ( !numb[lev] && lev < A*n ) { //If the level of w gets empty. |
---|
234 | |
---|
235 | for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid() ; ++v) { |
---|
236 | if (level.get(v) > lev ) level.set(v,n); |
---|
237 | } |
---|
238 | for (int i=lev+1 ; i!=n ; ++i) numb[i]=0; |
---|
239 | if ( newlevel < n ) newlevel=n; |
---|
240 | } else if ( newlevel < n ) { |
---|
241 | ++numb[newlevel]; |
---|
242 | stack[newlevel].push(w); |
---|
243 | b=newlevel; |
---|
244 | } |
---|
245 | } |
---|
246 | |
---|
247 | |
---|
248 | |
---|
249 | } //while(b) |
---|
250 | |
---|
251 | value=excess.get(t); |
---|
252 | /*Max flow value.*/ |
---|
253 | |
---|
254 | |
---|
255 | /* |
---|
256 | We count empty_level. The nodes above this level is a mincut. |
---|
257 | */ |
---|
258 | while(true) { |
---|
259 | if(numb[empty_level]) ++empty_level; |
---|
260 | else break; |
---|
261 | } |
---|
262 | |
---|
263 | } // void run() |
---|
264 | |
---|
265 | |
---|
266 | |
---|
267 | /* |
---|
268 | Returns the maximum value of a flow. |
---|
269 | */ |
---|
270 | |
---|
271 | T maxflow() { |
---|
272 | return value; |
---|
273 | } |
---|
274 | |
---|
275 | |
---|
276 | |
---|
277 | /* |
---|
278 | Returns a minimum cut. |
---|
279 | */ |
---|
280 | template<typename CutMap> |
---|
281 | void mincut(CutMap& M) { |
---|
282 | |
---|
283 | for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid(); ++v) { |
---|
284 | if ( level.get(v) > empty_level ) M.set(v, true); |
---|
285 | } |
---|
286 | } |
---|
287 | |
---|
288 | |
---|
289 | }; |
---|
290 | }//namespace marci |
---|
291 | #endif |
---|
292 | |
---|
293 | |
---|
294 | |
---|
295 | |
---|
296 | |
---|