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comparison docs/algorithm-ford-fulkerson.pseudocode @ 116:9bfd87544902

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Use arrows from Supplemental Arrows-A Unicode block where appropriate: better readability
author Franz Glasner <fzglas.hg@dom66.de>
date Wed, 06 May 2026 10:05:57 +0200
parents 6cebd3e7bc97
children
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115:e1663ac707b0 116:9bfd87544902
1 // -*- coding: utf-8; indent-tabs-mode: nil -*- 1 // -*- coding: utf-8; indent-tabs-mode: nil -*-
2 \ALGORITHM{Ford–Fulkerson} \WITH 2 \ALGORITHM{Ford–Fulkerson} \WITH
3 \INPUTS{Given a network \expr{G = (V, E)} with flow capacity \expr{c}, a source node \expr{s}, and a sink node \expr{t}} 3 \INPUTS{Given a network \expr{G = (V, E)} with flow capacity \expr{c}, a source node \expr{s}, and a sink node \expr{t}}
4 \OUTPUT{Compute a flow \expr{f} from \expr{s} to \expr{t} of maximum value} 4 \OUTPUT{Compute a flow \expr{f} from \expr{s} to \expr{t} of maximum value}
5 \IS 5 \IS
6 \TEXT{1. \expr{f(u, v) <- 0} for all edges \expr{(u, v)} 6 \TEXT{1. \expr{f(u, v) \gets 0} for all edges \expr{(u, v)}
7 7
8 2. While there is a path \expr{p} from \expr{s} to \expr{t} in \expr{G_f}, 8 2. While there is a path \expr{p} from \expr{s} to \expr{t} in \expr{G_f},
9 such that \expr{c_f(u, v) > 0} for all edges \expr{(u, v) ∈ p}: 9 such that \expr{c_f(u, v) > 0} for all edges \expr{(u, v) ∈ p}:
10 10
11 1. Find \expr{c_f(p) = min{c_f(u, v): (u, v) ∈ p\}} 11 1. Find \expr{c_f(p) = min{c_f(u, v): (u, v) ∈ p\}}
12 12
13 2. For each edge \expr{(u, v) ∈ p} 13 2. For each edge \expr{(u, v) ∈ p}
14 14
15 1. \expr{f(u, v) <- f(u, v) + c_f(p)} \rem Send flow along the path 15 1. \expr{f(u, v) \gets f(u, v) + c_f(p)} \rem Send flow along the path
16 16
17 2. \expr{f(v, u) <- f(v, u) - c_f(p)} \rem The flow might be "returned" later 17 2. \expr{f(v, u) \gets f(v, u) - c_f(p)} \rem The flow might be "returned" later
18 } 18 }
19 \END ALGORITHM {Ford–Fulkerson} 19 \END ALGORITHM {Ford–Fulkerson}