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