Editing Pseudocode (section)

==Mathematical style pseudocode==
In [[numerical computation]], pseudocode often consists of [[mathematical notation]], typically from [[matrix (mathematics)|matrix]] and [[set theory]], mixed with the control structures of a conventional programming language, and perhaps also [[natural language]] descriptions. This is a compact and often informal notation that can be understood by a wide range of mathematically trained people, and is frequently used as a way to describe mathematical [[algorithm]]s. For example, the sum operator ([[capital-sigma notation]]) or the product operator ([[capital-pi notation]]) may represent a for-loop and a selection structure in one expression:
 {{nowrap|Return <math>\sum_{k\in S} x_k</math>}}

Normally non-[[ASCII]] [[typesetting]] is used for the mathematical equations, for example by means of markup languages, such as [[TeX]] or [[MathML]], or proprietary [[formula editor]]s.

Mathematical style pseudocode is sometimes referred to as [[pidgin code]], for example ''pidgin [[ALGOL]]'' (the origin of the concept), ''pidgin [[Fortran]]'', ''pidgin [[BASIC]]'', ''pidgin [[Pascal (programming language)|Pascal]]'', ''pidgin [[C (programming language)|C]]'', and ''pidgin [[Lisp (programming language)|Lisp]]''.

===Common mathematical symbols===
<!-- Copied from Wikipedia:WikiProject_Computer_science/Manual_of_style#Algorithms -->
{| class="wikitable"
! Type of operation || Symbol  || Example
|-
| Assignment || ← or := ||<code>''c'' ← 2π''r''</code>, <code> ''c'' := 2π''r''</code>
|-
| Comparison || =, ≠, <, >, ≤, ≥ ||
|-
| Arithmetic || +, −, ×, /, mod ||
|-
| Floor/ceiling || ⌊, ⌋, ⌈, ⌉ || <code>''a'' ← ⌊''b''⌋ + ⌈''c''⌉</code>
|-
| Logical
| '''and''', '''or'''
| 
|-
| Sums, products
| Σ Π
| <code>''h'' ← Σ<sub>''a''∈''A''</sub> 1/''a''</code>
|}

===Example===
The following is a longer example of mathematical-style pseudocode, for the [[Ford–Fulkerson algorithm]]:
<!-- Same example as in Wikipedia:WikiProject_Computer_science/Manual_of_style#Algorithms -->

 '''algorithm''' ford-fulkerson '''is'''
     '''input:''' Graph ''G'' with flow capacity ''c'', 
            source node ''s'', 
            sink node ''t''
     '''output:''' Flow ''f'' such that ''f'' is maximal from ''s'' to ''t''
 
     ''(Note that f<sub>(u,v)</sub> is the flow from node u to node v, and c<sub>(u,v)</sub> is the flow capacity from node u to node v)''
 
     '''for each''' edge (''u'', ''v'') '''in''' ''G''<sub>''E''</sub> '''do'''
         ''f''<sub>(''u'', ''v'')</sub> ← 0
         ''f''<sub>(''v'', ''u'')</sub> ← 0
 
     '''while''' there exists a path ''p'' from ''s'' to ''t'' '''in''' the residual network ''G''<sub>''f''</sub> '''do'''
         let ''c''<sub>''f''</sub> be the flow capacity of the residual network ''G''<sub>''f''</sub>
         ''c''<sub>''f''</sub>(''p'') ← min{''c''<sub>''f''</sub>(''u'', ''v'') | (''u'', ''v'') '''in''' ''p''}
         '''for each''' edge (''u'', ''v'') '''in''' ''p'' '''do'''
             ''f''<sub>(''u'', ''v'')</sub> ←  ''f''<sub>(''u'', ''v'')</sub> + ''c''<sub>''f''</sub>(''p'')
             ''f''<sub>(''v'', ''u'')</sub> ← −''f''<sub>(''u'', ''v'')</sub>
 
     '''return''' ''f''