Lec 13 Oct 17

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• Lec 13
  Oct 17
• cell arrays
• structures
• advanced recursive programs

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• Cell arrays
• suppose we want to represent a collection of
  sets such as
• 1, 2, 4, 3, 4, 6, 7, 8
• Each set can be represented by vector
• 1, 2, 4, 3, 4, 6, 7, 8
• gtgt A 1, 2, 4, 3, 4, 6, 7, 8
• A becomes 1, 2, 4, 3, 4, 6, 7, 8

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Cell arrays
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Cell array examples
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Cell operations
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Generating all subsets of a given set Given a
set, like 1, 3, 4, the subsets are
1 3 4 1 3 1
4 3 4 1 3 4 We want to write a program to
generate all the subsets of a given collection

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Idea behind algorithm recursion This is a
problem for which non-recursive solutions are
significantly harder than recursive
solutions. Idea input array is a of length
n. Recursively find all subsets of a(2n) Then
add a(1) to each of the subsets. Combine the two
collections.
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• Since we need to represent a collection of sets,
  we have two choices
• use of cell arrays
• use of two-dimensional arrays
• The latter is not suitable for this problem since
  the sizes of the subsets are not the same
• We need a function insert that inserts a given
  number into all the sets of a given collection.

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Example showing how insert works
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Code for insert
function out insert(i, lst) inserts i into
each membet of lst for j 1length(lst)
outj i, lstj end
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Code for subsets function L subsets(lst)
generates all subsets of lst if length(lst) 0
L elseif length(lst) 1 L
lst(1), else L1 subsets(lst(2end))
L2 insert(lst(1), L1) L L1,
L2 end
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Printing the contents of a cell array function
setprint(cellset) prints every member of the
cell in one line assume cellset is a collection
of sets of integers for k1length(cellset)
aprint(cellsetk) fprintf('\n') end function
aprint(r) for j 1length(r) fprintf('d',
r(j)) fprintf(' ') end fprintf('\n')
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Generating all permutations of a given
set Example set 1 3 4 Permutations 1 3
4 1 4 3 3 1 4 3 4 1 4 1 3 4 3 1