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<div style="font-size: 1.8em;font-weight:bold;text-align: center;margin:0.2em 0 1em 0">Bubble Sort</div> <div style="font-size: 1.2em; margin:.5em 0 1em 0; text-align:center">whatever</div>

...tions <math>|S|-i+1,\dots,|S|</math> are placed at their ocrrect positions in sorting order. '''Abstract view:''' Step-by-step, move the maximum element seen so far to the position <math>|S| - i + 1

<div style="font-size: 1.8em;font-weight:bold;text-align: center;margin:0.2em 0 1em 0">Selection Sort</div> <div style="font-size: 1.2em; margin:.5em 0 1em 0; text-align:center">whatever</div>

* [[Matchings in graphs#Cardinality-maximal matching|Maximum matching problem]] * [[Max-Flow Problems]]

# In a '''proper set''' (or '''set''', for short), each element occurs at most o ...ltiplicity''' of an element in a multiset is the number of its occurrences in that multiset.

# A '''start node''' <math>s\in V</math>. ...nodes of <math>G</math> that can be reached from <math>s</math> via paths in <math>G</math>.

# A specific '''maximum span of keys''' <math>S\in\mathbb{N}</math>. # An array <math>A</math> with index set <math>\{0,\ldots,S-1\}</math> and [[Sets and sequences|sets]] of keys as components,

'''Implementation:''' If <math>S[l+i-1] > S[l+i]</math>, swap <math>S[l+i-1]</math> and <math>S[l+i]</math>. ...math> is at least as large as all elements at positions <math>l+1,\dots,l+i-1</math> and should thus stay at position <math>l+i</math>.

{{#ev:youtube|https://www.youtube.com/watch?v=j-r4YOPFp7E|500|right||frame}} ## a specific '''maximum number of items''' <math>N_\text{max}\in\mathbb{N}</math>, which is constant throughout the object's lifetime.

'''Algorithmic problem:''' [[One-dimensional string matching]] ..., <math>R</math> contains the start indexes in the range <math>S[1],...,S[i-m+1]</math>.

'''Auxiliary data:''' Five index pointers, <math>m_1,m_2,i_1,i_2,i_3 \in \mathbb N.</math> ...>S</math> and are, hence, constant throughout the loop. More specifically, in <math>S</math> there are

...is assumed. An arc <math>(v,w)</math> preceding an arc <math>(v,w')</math> in this ordering is called '''lexicographically smaller''' than <math>(v,w)</m ...he lexicographically ''smallest'' path from <math>v\in V</math> to <math>w\in V</math> is well defined and unique.