SLIDE 1
Introduction
Edmonds Karp Algorithm
- Dr. Mattox Beckman
Introduction
Edmonds Karp Algorithm Dr. Mattox Beckman University of Illinois at - - PowerPoint PPT Presentation
Edmonds Karp Algorithm Dr. Mattox Beckman University of Illinois at - - PowerPoint PPT Presentation
Introduction Edmonds Karp Algorithm Dr. Mattox Beckman University of Illinois at Urbana-Champaign Department of Computer Science Introduction Objectives Your Objectives: Implement the Edmonds Karp algorithm for Network Flow Introduction
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Introduction
A simple example
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Introduction
A simple example
A B C D 10/0 5/0 5/0 5/0 10/0
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Introduction
A simple example
A B C D 10/5 5/0 5/0 5/5 10/0
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Introduction
A simple example
A B C D 10/5 5/0 5/0 5/5 10/0
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Introduction
A simple example
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Introduction
A simple example
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Introduction
A simple example
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Introduction
A second example
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Introduction
A second example
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Introduction
A second example
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Introduction
A second example
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Introduction
A second example
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Introduction
Implementation
0 // Stolen from Competitive Programming 3 1 // global variables 2 int res[MAX_V][MAX_V], mf, f, s, t; 3 vi p; // p stores the BFS spanning tree from s 4 5 // traverse BFS spanning tree from s->t 6 void augment(int v, int minEdge) { 7
if (v == s) {
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f = minEdge;
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return;
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} else if (p[v] != -1) {
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augment(p[v], min(minEdge, res[p[v]][v]));
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res[p[v]][v] -= f;
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res[v][p[v]] += f;
14 } }
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Introduction
Implementation, 2
0 mf = 0; 1 while (1) {// O(VE^2) (actually O(V^3 E) Edmonds Karp’s algorithm 2
f = 0;
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vi dist(MAX_V, INF); dist[s] = 0; queue<int> q; q.push(s);
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p.assign(MAX_V, -1);
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while (!q.empty()) {
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int u = q.front(); q.pop();
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if (u == t) break; // stop when we reach sink t
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for (int v = 0; v < MAX_V; v++)
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if (res[u][v] > 0 && dist[v] == INF)
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dist[v] = dist[u] + 1, q.push(v), p[v] = u; }
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augment(t, INF);
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if (f == 0) break; // we cannot send any more flow
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mf += f;
14 }