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annotate docs/algorithm-edmonds-karp.pseudocode @ 141:acd9073cbbe3

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Make a lexerlist.rst that contains the table of the lexers because it is used at least twice
author Franz Glasner <fzglas.hg@dom66.de>
date Thu, 07 May 2026 10:52:14 +0200
parents 1c1985532139
children
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1c1985532139 A couple of real pseudocode examples.
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1 // -*- coding: utf-8; indent-tabs-mode: nil -*-
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2 \ALGORITHM{Edmonds–Karp} \WITH
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3 \INPUT{
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4 \expr{graph}: \expr{graph[v]} should be the list of edges coming out of vertex \expr{v} in the
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5 original graph and their corresponding constructed reverse edges
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6 which are used for push-back flow.
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7 Each edge should have a capacity \expr{cap}, \expr{flow}, source \expr{s} and sink \expr{t}
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8 as parameters, as well as a pointer to the reverse edge \expr{rev}.
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9 \expr{s}: Source vertex
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10 \expr{t}: Sink vertex}
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11 \OUTPUT{
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12 \expr{flow}: Value of maximum flow)}
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13 \IS
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14 flow := 0
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15 \REPEAT
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16 /* Run a breadth-first search (bfs) to find the shortest s-t path.
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17 We use 'pred' to store the edge taken to get to each vertex,
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18 so we can recover the path afterwards. */
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19 q := queue()
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20 q.push(s)
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21 pred := array(graph.length)
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22 \WHILE not empty(q) and pred[t] = null \DO
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23 cur := q.pop()
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24 \FOR \text{Edge} e in graph[cur] \DO
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25 \IF pred[e.t] = null and e.t != s and e.cap > e.flow \THEN
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26 pred[e.t] := e
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27 q.push(e.t)
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28 \END IF
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29 \END FOR
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30 \END WHILE
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31 \IF not (pred[t] = null) \THEN
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32 /* We found an augmenting path.
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33 See how much flow we can send */
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34 df := ∞
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35 \FOR (e := pred[t]; e != null; e := pred[e.s]) \DO
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36 df := min(df, e.cap - e.flow)
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37 \END FOR
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38 /* And update edges by that amount */
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39 \FOR (e := pred[t]; e != null; e := pred[e.s]) \DO
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40 e.flow := e.flow + df
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41 e.rev.flow := e.rev.flow - df
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42 \END FOR
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43 flow := flow + df
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44 \END IF
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45 \UNTIL pred[t] = null \REM i.e., until no augmenting path was found
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46 \RETURN flow
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47 \END ALGORITHM {Edmonds–Karp}