1 | /* |
---|
2 | preflow_push_max_flow_h |
---|
3 | by jacint. |
---|
4 | Runs a preflow push algorithm with the modification, |
---|
5 | that we do not push on nodes with level at least n. |
---|
6 | Moreover, if a level gets empty, we set all nodes above that |
---|
7 | level to level n. Hence, in the end, we arrive at a maximum preflow |
---|
8 | with value of a max flow value. An empty level gives a minimum cut. |
---|
9 | |
---|
10 | Member functions: |
---|
11 | |
---|
12 | void run() : runs the algorithm |
---|
13 | |
---|
14 | The following functions should be used after run() was already run. |
---|
15 | |
---|
16 | T maxflow() : returns the value of a maximum flow |
---|
17 | |
---|
18 | NodeMap<bool> mincut(): returns a |
---|
19 | characteristic vector of a minimum cut. |
---|
20 | */ |
---|
21 | |
---|
22 | #ifndef PREFLOW_PUSH_MAX_FLOW_H |
---|
23 | #define PREFLOW_PUSH_MAX_FLOW_H |
---|
24 | |
---|
25 | #include <algorithm> |
---|
26 | #include <vector> |
---|
27 | #include <stack> |
---|
28 | |
---|
29 | #include <reverse_bfs.h> |
---|
30 | |
---|
31 | |
---|
32 | namespace marci { |
---|
33 | |
---|
34 | template <typename Graph, typename T> |
---|
35 | class preflow_push_max_flow { |
---|
36 | |
---|
37 | typedef typename Graph::NodeIt NodeIt; |
---|
38 | typedef typename Graph::EachNodeIt EachNodeIt; |
---|
39 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
40 | typedef typename Graph::InEdgeIt InEdgeIt; |
---|
41 | |
---|
42 | Graph& G; |
---|
43 | NodeIt s; |
---|
44 | NodeIt t; |
---|
45 | typename Graph::EdgeMap<T>& capacity; |
---|
46 | T value; |
---|
47 | typename Graph::NodeMap<bool> mincutvector; |
---|
48 | |
---|
49 | |
---|
50 | |
---|
51 | public: |
---|
52 | |
---|
53 | preflow_push_max_flow ( Graph& _G, NodeIt _s, NodeIt _t, |
---|
54 | typename Graph::EdgeMap<T>& _capacity) : |
---|
55 | G(_G), s(_s), t(_t), capacity(_capacity), mincutvector(_G, false) { } |
---|
56 | |
---|
57 | |
---|
58 | /* |
---|
59 | The run() function runs a modified version of the |
---|
60 | highest label preflow-push, which only |
---|
61 | finds a maximum preflow, hence giving the value of a maximum flow. |
---|
62 | */ |
---|
63 | void run() { |
---|
64 | |
---|
65 | typename Graph::EdgeMap<T> flow(G, 0); |
---|
66 | typename Graph::NodeMap<int> level(G); |
---|
67 | typename Graph::NodeMap<T> excess(G); |
---|
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 | In the beginning it is at most n-2. |
---|
74 | */ |
---|
75 | |
---|
76 | std::vector<int> numb(n); //The number of Nodes on level i < n. |
---|
77 | std::vector<std::stack<NodeIt> > stack(2*n-1); |
---|
78 | //Stack of the active Nodes in level i. |
---|
79 | |
---|
80 | /*Reverse_bfs from t, to find the starting level.*/ |
---|
81 | reverse_bfs<Graph> bfs(G, t); |
---|
82 | bfs.run(); |
---|
83 | for(EachNodeIt v=G.template first<EachNodeIt>(); v.valid(); ++v) |
---|
84 | { |
---|
85 | int dist=bfs.dist(v); |
---|
86 | level.set(v, dist); |
---|
87 | ++numb[dist]; |
---|
88 | } |
---|
89 | |
---|
90 | level.set(s,n); |
---|
91 | |
---|
92 | /* Starting flow. It is everywhere 0 at the moment. */ |
---|
93 | for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) |
---|
94 | { |
---|
95 | if ( capacity.get(e) > 0 ) { |
---|
96 | NodeIt w=G.head(e); |
---|
97 | flow.set(e, capacity.get(e)); |
---|
98 | stack[level.get(w)].push(w); |
---|
99 | excess.set(w, excess.get(w)+capacity.get(e)); |
---|
100 | } |
---|
101 | } |
---|
102 | |
---|
103 | /* |
---|
104 | End of preprocessing |
---|
105 | */ |
---|
106 | |
---|
107 | |
---|
108 | |
---|
109 | /* |
---|
110 | Push/relabel on the highest level active Nodes. |
---|
111 | */ |
---|
112 | |
---|
113 | /*While there exists an active Node.*/ |
---|
114 | while (b) { |
---|
115 | |
---|
116 | /*We decrease the bound if there is no active node of level b.*/ |
---|
117 | if (stack[b].empty()) { |
---|
118 | --b; |
---|
119 | } else { |
---|
120 | |
---|
121 | NodeIt w=stack[b].top(); //w is the highest label active Node. |
---|
122 | stack[b].pop(); //We delete w from the stack. |
---|
123 | |
---|
124 | int newlevel=2*n-2; //In newlevel we maintain the next level of w. |
---|
125 | |
---|
126 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
---|
127 | NodeIt v=G.head(e); |
---|
128 | /*e is the Edge wv.*/ |
---|
129 | |
---|
130 | if (flow.get(e)<capacity.get(e)) { |
---|
131 | /*e is an Edge of the residual graph */ |
---|
132 | |
---|
133 | if(level.get(w)==level.get(v)+1) { |
---|
134 | /*Push is allowed now*/ |
---|
135 | |
---|
136 | if (capacity.get(e)-flow.get(e) > excess.get(w)) { |
---|
137 | /*A nonsaturating push.*/ |
---|
138 | |
---|
139 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
---|
140 | /*v becomes active.*/ |
---|
141 | |
---|
142 | flow.set(e, flow.get(e)+excess.get(w)); |
---|
143 | excess.set(v, excess.get(v)+excess.get(w)); |
---|
144 | excess.set(w,0); |
---|
145 | //std::cout << w << " " << v <<" elore elen nonsat pump " << std::endl; |
---|
146 | break; |
---|
147 | } else { |
---|
148 | /*A saturating push.*/ |
---|
149 | |
---|
150 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
---|
151 | /*v becomes active.*/ |
---|
152 | |
---|
153 | excess.set(v, excess.get(v)+capacity.get(e)-flow.get(e)); |
---|
154 | excess.set(w, excess.get(w)-capacity.get(e)+flow.get(e)); |
---|
155 | flow.set(e, capacity.get(e)); |
---|
156 | //std::cout << w <<" " << v <<" elore elen sat pump " << std::endl; |
---|
157 | if (excess.get(w)==0) break; |
---|
158 | /*If w is not active any more, then we go on to the next Node.*/ |
---|
159 | |
---|
160 | } // if (capacity.get(e)-flow.get(e) > excess.get(w)) |
---|
161 | } // if (level.get(w)==level.get(v)+1) |
---|
162 | |
---|
163 | else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);} |
---|
164 | |
---|
165 | } //if (flow.get(e)<capacity.get(e)) |
---|
166 | |
---|
167 | } //for(OutEdgeIt e=G.first_OutEdge(w); e.valid(); ++e) |
---|
168 | |
---|
169 | |
---|
170 | |
---|
171 | for(InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
---|
172 | NodeIt v=G.tail(e); |
---|
173 | /*e is the Edge vw.*/ |
---|
174 | |
---|
175 | if (excess.get(w)==0) break; |
---|
176 | /*It may happen, that w became inactive in the first 'for' cycle.*/ |
---|
177 | |
---|
178 | if(flow.get(e)>0) { |
---|
179 | /*e is an Edge of the residual graph */ |
---|
180 | |
---|
181 | if(level.get(w)==level.get(v)+1) { |
---|
182 | /*Push is allowed now*/ |
---|
183 | |
---|
184 | if (flow.get(e) > excess.get(w)) { |
---|
185 | /*A nonsaturating push.*/ |
---|
186 | |
---|
187 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
---|
188 | /*v becomes active.*/ |
---|
189 | |
---|
190 | flow.set(e, flow.get(e)-excess.get(w)); |
---|
191 | excess.set(v, excess.get(v)+excess.get(w)); |
---|
192 | excess.set(w,0); |
---|
193 | //std::cout << v << " " << w << " vissza elen nonsat pump " << std::endl; |
---|
194 | break; |
---|
195 | } else { |
---|
196 | /*A saturating push.*/ |
---|
197 | |
---|
198 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
---|
199 | /*v becomes active.*/ |
---|
200 | |
---|
201 | flow.set(e,0); |
---|
202 | excess.set(v, excess.get(v)+flow.get(e)); |
---|
203 | excess.set(w, excess.get(w)-flow.get(e)); |
---|
204 | //std::cout << v <<" " << w << " vissza elen sat pump " << std::endl; |
---|
205 | if (excess.get(w)==0) { break;} |
---|
206 | } //if (flow.get(e) > excess.get(v)) |
---|
207 | } //if(level.get(w)==level.get(v)+1) |
---|
208 | |
---|
209 | else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);} |
---|
210 | //std::cout << "Leveldecrease of Node " << w << " to " << newlevel << std::endl; |
---|
211 | |
---|
212 | } //if (flow.get(e)>0) |
---|
213 | |
---|
214 | } //for in-Edge |
---|
215 | |
---|
216 | |
---|
217 | |
---|
218 | |
---|
219 | /* |
---|
220 | Relabel |
---|
221 | */ |
---|
222 | if (excess.get(w)>0) { |
---|
223 | /*Now newlevel <= n*/ |
---|
224 | |
---|
225 | int l=level.get(w); //l is the old level of w. |
---|
226 | --numb[l]; |
---|
227 | |
---|
228 | if (newlevel == n) { |
---|
229 | level.set(w,n); |
---|
230 | |
---|
231 | } else { |
---|
232 | |
---|
233 | if (numb[l]) { |
---|
234 | /*If the level of w remains nonempty.*/ |
---|
235 | |
---|
236 | level.set(w,++newlevel); |
---|
237 | ++numb[newlevel]; |
---|
238 | stack[newlevel].push(w); |
---|
239 | b=newlevel; |
---|
240 | } else { |
---|
241 | /*If the level of w gets empty.*/ |
---|
242 | |
---|
243 | for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid() ; ++v) { |
---|
244 | if (level.get(v) >= l ) { |
---|
245 | level.set(v,n); |
---|
246 | } |
---|
247 | } |
---|
248 | |
---|
249 | for (int i=l+1 ; i!=n ; ++i) numb[i]=0; |
---|
250 | } //if (numb[l]) |
---|
251 | |
---|
252 | } // if (newlevel = n) |
---|
253 | |
---|
254 | } // if (excess.get(w)>0) |
---|
255 | |
---|
256 | |
---|
257 | } //else |
---|
258 | |
---|
259 | } //while(b) |
---|
260 | |
---|
261 | value=excess.get(t); |
---|
262 | /*Max flow value.*/ |
---|
263 | |
---|
264 | |
---|
265 | |
---|
266 | /* |
---|
267 | We find an empty level, e. The Nodes above this level give |
---|
268 | a minimum cut. |
---|
269 | */ |
---|
270 | |
---|
271 | int e=1; |
---|
272 | |
---|
273 | while(e) { |
---|
274 | if(numb[e]) ++e; |
---|
275 | else break; |
---|
276 | } |
---|
277 | for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid(); ++v) { |
---|
278 | if (level.get(v) > e) mincutvector.set(v, true); |
---|
279 | } |
---|
280 | |
---|
281 | |
---|
282 | } // void run() |
---|
283 | |
---|
284 | |
---|
285 | |
---|
286 | /* |
---|
287 | Returns the maximum value of a flow. |
---|
288 | */ |
---|
289 | |
---|
290 | T maxflow() { |
---|
291 | return value; |
---|
292 | } |
---|
293 | |
---|
294 | |
---|
295 | |
---|
296 | /* |
---|
297 | Returns a minimum cut. |
---|
298 | */ |
---|
299 | |
---|
300 | typename Graph::NodeMap<bool> mincut() { |
---|
301 | return mincutvector; |
---|
302 | } |
---|
303 | |
---|
304 | |
---|
305 | }; |
---|
306 | }//namespace marci |
---|
307 | #endif |
---|
308 | |
---|
309 | |
---|
310 | |
---|
311 | |
---|
312 | |
---|