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Recursing - Biological and Cognitive Sciences - Lecture Notes, Study notes of Biogenetics and Computers

During the course work of the Biological and Cognitive Sciences, we study many important concept of the cognitive sciences, the key points are:Recursing, Algorithm Requires, Divide-And-Conquer, Smaller Problems, Larger Problem, Finding, Definition, Recursive Algorithm, Maximum Element, Array

Typology: Study notes

2012/2013

Uploaded on 04/29/2013

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Divide a big problem into two or more smaller
problems.
Solve the smaller problems.
Combine the results into one larger problem.
Very often, a computer algorithm requires some form of
divide-and-conquer
Divide-and-conquer
Recursing Page 1
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Divide a big problem into two or more smaller

problems.

Solve the smaller problems.

Combine the results into one larger problem.

Very often, a computer algorithm requires some form of

divide-and-conquer

Divide-and-conquer

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Recursive definition => recursive algorithm

If an array has one element, its maximum is that element,

split the array in half, and

compute the maximum for each half, and

take the maximum of those two.

else

Recursive definition of maximum element:

Example: Finding the maximum

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sub maxer { my $thing = shift; my $length = @$thing; if ($length == 1) { # one thing is its own max! return $thing->[0]; } else { # split into two arrays! my $size = @$thing; my $mid = int($size/2); my $bot = [@$thing[0..$mid-1]]; my $top = [@$thing[$mid..$size-1]]; my $sbot = &maxer($bot); my $stop = &maxer($top); if ($sbot<$stop) { return $stop; } else { return $sbot; } } } Pasted from Finding the maximum Docsity.com

At each step, the array gets 1/2 as large.

But we have to do the thing for both halves.

We're going to do O(n) comparisons at each level.

There are O(log n) levels

Thus the algorithm is O(n log n) in time.

Runtime for maxer

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one root 0 or more children each child is the root of a tree. N-ary tree:

A recursive structure

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A key idea: if a structure is recursive, then so is the

algorithm that works on it.

Algorithms on recursive structures

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$company->{foo}->{bar} is the children of bar, that must be a child of foo. Docsity.com