L16.%20Cell%20Arrays - PowerPoint PPT Presentation

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L16.%20Cell%20Arrays

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L16. Cell Arrays Set-Up Subscripting Nested Loops String Manipulations – PowerPoint PPT presentation

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Title: L16.%20Cell%20Arrays


1
L16. Cell Arrays
  • Set-Up
  • Subscripting
  • Nested Loops
  • String Manipulations

2
A Small Cell Array
C Alabama,New York,Utah
C
3
Syntax
Entries Separated by Commas
C Alabama,New York,Utah
Curly Brackets
4
Synonym
C Alabama,New York,Utah
C cell(1,3) C1 Alabama C2 New
York C3 Utah
Application Storing strings
5
Vertical Cell Array Set-up
C AlabamaNew YorkUtah
C cell(3,1) C1 Alabama C2 New
York C3 Utah
Application Storing strings
6
Another Small Cell Array
C 1 2 3,1020, zeros(1,4)
C
7
Syntax
Entries Separated by Commas
C 1 2 3, 1020, zeros(1,4)
Curly Brackets
8
Synonym
C 1 2 3, 1020, zeros(1,4)
C cell(1,3) C1 1 2 3 C2
1020 C3 zeros(1,4)
Application Storing a Set of Arrays
9
Problem Set Up a Card Deck
10
Idea
  • A1 A Hearts
  • A2 2 Hearts
  • A13 K Hearts
  • A14 A Clubs
  • A52 K Diamonds

11
Initializations
  • suit Hearts, Clubs,
  • Spades, Diamonds
  • rank A,2,3,4,5,6,
  • 7,8,9,10,J,Q,K
  • A cell(1,52)

12
Use Concatenation
  • suit Hearts, Clubs,
  • Spades, Diamonds
  • rank A,2,3,4,5,6,
  • 7,8,9,10,J,Q,K
  • A16 rank3 suit2

A16 3 Clubs
13
Nested Loop to Get allPossible Combinations
  • i is index of next card
  • i 1
  • for k14
  • Set up the cards in suit k
  • for j113
  • Ai rankj ' ' suitk
  • i i1
  • end
  • end

14
Problem Deal a Card Deck
15
Deal a length-12 Card Deck
A
4k-3
E
2,6,10
4k-2
S
3,7,11
4k-1
4k
W
4,8,12
16
  • N cell(1,13) E cell(1,13)
  • S cell(1,13) W cell(1,13)
  • for k113
  • Nk A4k-3
  • Ek A4k-2
  • Sk A4k-1
  • Wk A4k
  • end

17
Problem Shuffle a Card Deck
18
Shuffle a length-12 Card Deck
19
Step 1 Cut the Deck
20
Step 2 Alternate
1 2 3 4 5 6
1 2 3 4 5 6 7 8 9 10 11 12
21
Step 2 Alternate
1 2 3 4 5 6
k -gt 2k-1
1 3 5 7 9 11
22
Step 2 Alternate
1 2 3 4 5 6
k -gt 2k
2 4 6 8 10 12
23
  • function T Shuffle(S)
  • n length(S) m n/2
  • T cell(n,1)
  • Top S(1m) Bot S(m1n)
  • for k1m
  • T2k-1 Topk
  • T2k Botk
  • end

24
8 Shuffles with a Card Deck
  • And you are back where you started.

25
Illustrate with Color
Set up a 52-color spectrum C cell(52,1) for
k152 f (k-1)/51 Ck f 0
1-f end
These are colors
26
Using fill( , , Ck)
8
7
6
5
4
3
2
1
0
27
Problem Build Cell Array of Roman Numerals
28
Idea
  • C1 I
  • C2 II
  • C3 III
  • C2007 MMVII
  • C3999 MMMXMXCIX

29
A Conversion Problem
  • 1904 11000 9100 010 41
  • M CM
    IV
  • MCMIV

30
1
9
0
4
MCMIV
31
1
9
0
4
M CM IV
32
1
9
0
4
M CM IV
M MM MMM
33
1
9
0
4
M CM IV
  • C
  • CC
  • CCC
  • CD
  • D
  • DC
  • DCC
  • DCCC
  • CM

M MM MMM
34
1
9
0
4
M CM IV
  • C
  • CC
  • CCC
  • CD
  • D
  • DC
  • DCC
  • DCCC
  • CM

X XX XXX XL L LX LXX LXXX XC
M MM MMM
35
1
9
0
4
M CM IV
  • C
  • CC
  • CCC
  • CD
  • D
  • DC
  • DCC
  • DCCC
  • CM

X XX XXX XL L LX LXX LXXX XC
I II III IV V VI VII VIII IX
M MM MMM
Concatenate entries from these cell arrays
36
Ones-Place Conversion
function r Ones2R(x) x is an integer that
satisfies 0 lt x lt 9 r is the Roman
numeral with value x. Ones 'I', 'II',
'III', 'IV', 'V', 'VI','VII', 'VIII',
'IX' if x0 r '' else r
Onesx end
37
Tens-Place Conversion
function r Tens2R(x) x is an integer that
satisfies 0 lt x lt 9 r is the Roman
numeral with value 10x. Tens X', XX',
XXX', XL', L', LX',LXX', LXXX',
XC' if x0 r '' else r
Tensx end
38
Hundreds-Place Conversion
function r Hund2R(x) d is an integer that
satisfies 0 lt x lt 9 r is the Roman
numeral with value 100x. Hund C', CC',
CCC', CD', D', DC',DCC', DCCC',
CM' if x0 r '' else r
Hundx end
39
Thousands-Place Conversion
function r Thou2R(x) d is an integer that
satisfies 0 lt x lt3 r is the Roman
numeral with value 1000x. Thou M', MM',
MMM' if x0 r '' else r
Thoux end
40
Back to Our Problem
  • C1 I
  • C2 II
  • C3 III
  • C2007 MMVII
  • C3999 MMMXMXCIX

41
Generate 1,,3999
  • a b c d

0 lt a lt 3 0 lt b lt 9 0 lt c lt 9 0 lt d lt 9
42
This Prints 0,,3999
  • for a 03
  • for b 09
  • for c 09
  • for d 09
  • n a1000 b100 c10 d
  • end
  • end
  • end
  • end

43
  • n a1000 b100 c10 d
  • if n gt 0
  • Cn Thou(a) Hund(b)
  • Tens(c) Ones(d)
  • end

44
Reverse Problem
  • Given Roman Numeral, compute its value.
  • Assume cell array C(3999,1) available
  • C1 I
  • C3999 MMMCMXCIX

45
  • function k RN2Int(r)
  • r is a string that represents
  • Roman numeral
  • k is its value
  • C RomanNum
  • k1
  • while strcmp(r,Ck)
  • kk1
  • end
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