Computer Science 1620

About This Presentation

Title:

Computer Science 1620

Description:

Computer Science 1620 Multi-Dimensional Arrays – PowerPoint PPT presentation

Number of Views:65

Avg rating:3.0/5.0

Slides: 64

Provided by: Kevi1285

Category:

more less

Transcript and Presenter's Notes

Title: Computer Science 1620

1
Computer Science 1620

Multi-Dimensional Arrays

we used arrays to store a set of data of the same
type
e.g. store the assignment grades for a particular
student
int grades4
store a list of hockey players
player players50
however, sometimes data has more structure than
this

Example Store the assignment grades for
multiple students
essentially a 'table' of information

Mark 2
Mark 1
Mark 3
Mark 4
18 16 9 12 13 15 17 16 14 5 2 10
Student 1
Student 2
Student 3
4

Example Store the assignment grades for 5
different students
Solution 1 Store 5 different arrays

int grades14 int grades24 int
grades34 int grades44 int grades54
5

Example Store the assignment grades for 50
different students
Solution 1 Store 50 different arrays

int grades14 int grades24 int
grades34 int grades44 int grades54 int
grades64 int grades74 int grades84 int
grades94 int grades104 int grades114 int
grades124 int grades134 int
grades144 int grades154 int
grades164 int grades174 int
grades184 int grades194 int
grades204 int grades214 int
grades224 int grades234 int
grades244 int grades254 int
grades264 int grades274 int
grades284 int grades294 int
grades304 int grades314 int
grades324 int grades334 int
grades344 int grades354 int
grades364 int grades734 int
grades384 int grades394 int
grades404 int grades414 int
grades424 int grades434 int
grades444 int grades454 int
grades464 int grades474 int
grades484 int grades494 int grades504
6
Multi-Dimensional Arrays

Solution 2 'flatten' the table into one array

18 16 9 12 13 15 17 16 14 5 2 10
int a 18, 16, 9, 12, 13, 15, 17, 16, 14, 5,
2, 10
7
Multi-Dimensional Arrays

what happens when I want the second mark of the
second student?
we must translate
index in array row ( of columns) column
index in array 1 (4) 1 5

18 16 9 12 13 15 17 16 14 5 2 10
int a 18, 16, 9, 12, 13, 15, 17, 16, 14, 5,
2, 10
8

A Table of Information
what do you notice about this declaration?

grades1, grades2, grades3, grades4, and grades5
all have the same type
an array of 4 integers
Question since they all have the same type, can
I store them all in the same array?
have an array of array of 4 integers?

int grades14 int grades24 int
grades34 int grades44 int grades54
9
2D Arrays

2D Arrays
you can declare an "array of arrays"
this creates 3 arrays, all of length 4
when a 2D array is declared, it is often referred
to using table syntax
each array is often referred to as a row
the number of elements in each row refers to the
number of columns in the structure

int a34
10

Declaring a 2D array
use two subscript notations
first subscript number of rows
second subscript number of columns

3 rows
int a34
4 columns
11

Indexing a 2D array
use the same subscript notation as for a
single-dimensional array
use two!
remember indices always start at 0, not 1

refers to second row
18 16 9 12 13 15 17 16 14 5 2 10
a12 17
refers to third column
12

2D Arrays vs. Multiple Arrays
store the assignment grades for 50 different
students

2D Arrays vs. Multiple Arrays
store the assignment grades for 50 different
students

int grades504
14
Multi-Dimensional Arrays

2D Arrays vs. 1D Arrays
what happens when I want the second mark of the
second student?
we must translate
index in array row ( of columns) column
index in array 1 (4) 1 5

18 16 9 12 13 15 17 16 14 5 2 10
int a 18, 16, 9, 12, 13, 15, 17, 16, 14, 5,
2, 10
15
Multi-Dimensional Arrays

2D Arrays vs. 1D Arrays
what happens when I want the second mark of the
second student?
with a 2D array, each index is separate

18 16 9 12 13 15 17 16 14 5 2 10
int a34 // code for initializing a11
15 // this sets the 2nd student's 2nd mark to 15
16

Initializing a 2D array
2D arrays can be initialized just as a 1D array
can

int one12 18, 16, 9, 12, 13, 15, 17, 16, 14,
5, 2, 10 int two34 18, 16, 9, 12,
13, 15, 17, 16, 14, 5, 2, 10
int one12 18, 16, 9, 12, 13, 15, 17, 16, 14,
5, 2, 10 int two34 18, 16, 9, 12,
13, 15, 17, 16, 14, 5, 2, 10
row 1
row 2
row 3
use braces to separate individual rows
17

Initializing a 2D array
inner braces can be omitted
when inner braces omitted, C fills table one
row at a time, from left to right

int one12 18, 16, 9, 12, 13, 15, 17, 16, 14,
5, 2, 10 int two34 18, 16, 9, 12, 13,
15, 17, 16, 14, 5, 2, 10
18 16 9 12 13 15 17 16 14 5 2 10
18

Initializing a 2D array
the first subscript value can be omitted, just as
with single-dimension arrays
the second subscript value cannot be omitted

int one 18, 16, 9, 12, 13, 15, 17, 16, 14,
5, 2, 10 int two4 18, 16, 9, 12, 13,
15, 17, 16, 14, 5, 2, 10 int three
18, 16, 9, 12, 13, 15, 17, 16, 14, 5, 2, 10

Error! Must include column size.
19

2D arrays and loops
our previous array discussions showed strong
relationship with loops
initialize an index variable to 0
loop up to, but not including, size of array
increment index variable by 1
process array element inside loop

int a5 // some code goes here int
result 0 for (int i 0 i lt 5 i)
result ai return result
20

2D arrays and loops
to process each element in a 2D array, use a
nested loop
outer loop loop through rows
inner loop loop through columns
structure of the loops is exactly the same
initialize an index variable to 0
loop up to, but not including, size of array
increment index variable by 1
process array element inside loop
NOTE this is a guideline, but not the rule

Example given a 2D array, find the sum of all
elements inside the array
solution add each element of the array to an
accumulation variable

int a45 // some code goes here int sum
0 for (int i 0 i lt 4 i) for (int j
0 j lt 5 j) result aij
cout gtgt "Sum " ltlt sum ltlt endl
22

Example given a 2D array, find the sum of all
elements inside the array
solution add each element of the array to an
accumulation variable

int a45 // some code goes here int sum
0 for (int i 0 i lt 4 i) for (int j
0 j lt 5 j) result aij
cout gtgt "Sum " ltlt sum ltlt endl
Outer Loop 1. Initialize i to 0
23

Example given a 2D array, find the sum of all
elements inside the array
solution add each element of the array to an
accumulation variable

int a45 // some code goes here int sum
0 for (int i 0 i lt 4 i) for (int j
0 j lt 5 j) result aij
cout gtgt "Sum " ltlt sum ltlt endl
Outer Loop 2. Loop up to, but not including,
number of rows
24

Example given a 2D array, find the sum of all
elements inside the array
solution add each element of the array to an
accumulation variable

int a45 // some code goes here int sum
0 for (int i 0 i lt 4 i) for (int j
0 j lt 5 j) result aij
cout gtgt "Sum " ltlt sum ltlt endl
Outer Loop 3. Increment index by 1
25

Example given a 2D array, find the sum of all
elements inside the array
solution add each element of the array to an
accumulation variable

int a45 // some code goes here int sum
0 for (int i 0 i lt 4 i) for (int j
0 j lt 5 j) result aij
cout gtgt "Sum " ltlt sum ltlt endl
Each pass through this loop accesses a different
row. Now write an inner loop to process each row.
26

Example given a 2D array, find the sum of all
elements inside the array
solution add each element of the array to an
accumulation variable

int a45 // some code goes here int sum
0 for (int i 0 i lt 4 i) for (int j
0 j lt 5 j) result aij
cout gtgt "Sum " ltlt sum ltlt endl
Inner Loop 1. Initialize j to 0
27

Example given a 2D array, find the sum of all
elements inside the array
solution add each element of the array to an
accumulation variable

int a45 // some code goes here int sum
0 for (int i 0 i lt 4 i) for (int j
0 j lt 5 j) result aij
cout gtgt "Sum " ltlt sum ltlt endl
Inner Loop 2. Loop up to, but not including,
size of row (number of columns)
28

Example given a 2D array, find the sum of all
elements inside the array
solution add each element of the array to an
accumulation variable

int a45 // some code goes here int sum
0 for (int i 0 i lt 4 i) for (int j
0 j lt 5 j) result aij
cout gtgt "Sum " ltlt sum ltlt endl
Inner Loop 3. Increment j by 1
29

Example given a 2D array, find the sum of all
elements inside the array
solution add each element of the array to an
accumulation variable

int a45 // some code goes here int sum
0 for (int i 0 i lt 4 i) for (int j
0 j lt 5 j) sum aij cout
gtgt "Sum " ltlt sum ltlt endl
Add value to accumulation variable (sum).
30

2D Arrays and Information Access
a 2D array affords us the same advantages as any
other table
e.g. How would I find the average grade of the
first student?

sum all elements in first row, divide by 4
18 16 9 12 13 15 17 16 14 5 2 10
31

Find first student's average

int grades34 18, 16, 9, 12,
13, 15, 17, 16,
14, 5, 2, 10 int sum 0 for (int j
0 j lt 4 j) sum grades0j cout
gtgt "First student average " ltlt sum/4.0 ltlt endl
32

2D Arrays and Information Access
a 2D array affords us the same advantages as any
other table
e.g. How would I find the average grade of the
first assignment?

sum all elements in first row, divide by 3
18 16 9 12 13 15 17 16 14 5 2 10
33

Find first student's average

int grades34 18, 16, 9, 12,
13, 15, 17, 16,
14, 5, 2, 10 int sum 0 for (int i
0 i lt 3 i) sum gradesi0 cout
gtgt "First assignment average " ltlt sum/3.0 ltlt
endl
34

2D Arrays as function parameters
just like 1D arrays, 2D arrays can be passed as
function parameters
however, just like in initialization, the column
size of the array MUST BE INCLUDED!

Example given a 2D array, write a function that
returns sum of elements in array

int sumArray(int a45) int sum 0
for (int i 0 i lt 4 i) for (int j 0
j lt 5 j) sum aij
return sum
36

Example given a 2D array, write a function that
returns sum of elements in array

int sumArray(int a5, int size) int sum
0 for (int i 0 i lt size i) for
(int j 0 j lt 5 j) sum aij
return sum
37

Example given a 2D array, write a function that
returns sum of elements in array

int sumArray(int a, int size, int size2)
int sum 0 for (int i 0 i lt size i)
for (int j 0 j lt size2 j)
sum aij return sum
This won't compile!
38

Beyond two dimensions
you can include as many dimensions as you like
int a345
a123 6
Rules
when initializing arrays, the sizes of all
dimensions except the first must be declared
explicitly
int a45 1, 2, 3
when passing a multi-dimensional array as a
parameter, sizes of all dimensions except the
first must be declared!

Example Write a function that takes a 2D array
of integers as a parameter, and prints out the
array in 2D format
put each number in a column of size 5

18 16 9 12 13 15 17 16 14 5 2 10
40
void printArray(int a4, int size) Step
1 Print each row in the matrix, following each
with a new line

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

41
void printArray(int a4, int size) Step
1 For each row in the matrix Step 1.1 Print out
row Step 1.2 Print new line

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

42
void printArray(int a4, int size) Step
1 For each row in the matrix Step 1.1 Print out
row Step 1.2 Print new line

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

43
void printArray(int a4, int size) for
(int i 0 i lt size i) Step 1.1 Print out
row Step 1.2 Print new line

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

44
void printArray(int a4, int size) for
(int i 0 i lt size i) Step 1.1 Print out
row Step 1.2 Print new line

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

45
void printArray(int a4, int size) for
(int i 0 i lt size i) Step 1.1 for each
column in row Step 1.1.1 print item at
that column Step 1.2 Print new line

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

46
void printArray(int a4, int size) for
(int i 0 i lt size i) Step 1.1 for each
column in row Step 1.1.1 print item at
that column Step 1.2 Print new line

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

47
void printArray(int a4, int size) for
(int i 0 i lt size i) for (int j 0 j lt
4 j) Step 1.1.1 print item at
that column Step 1.2 Print new line

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

48
void printArray(int a4, int size) for
(int i 0 i lt size i) for (int j 0 j lt
4 j) Step 1.1.1 print item at
that column Step 1.2 Print new line

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

49
void printArray(int a4, int size) for
(int i 0 i lt size i) for (int j 0 j lt
4 j) cout ltlt setw(5) ltlt
aij Step 1.2 Print new line

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

50
void printArray(int a4, int size) for
(int i 0 i lt size i) for (int j 0 j lt
4 j) cout ltlt setw(5) ltlt
aij Step 1.2 Print new line

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

51
void printArray(int a4, int size) for
(int i 0 i lt size i) for (int j 0 j lt
4 j) cout ltlt setw(5) ltlt
aij cout ltlt endl

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

Example 2 Write an add function for a 2D array,
that adds the two arrays component by component
(assume arrays are same size)

1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 18 19 20 21 22 23 24
14 16 18 20 22 24 26 28 30 32 34 36

53
void add(int size, int a4, int b4, int
c4) Step 1 Add each item from a and b,
place result in C

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

54
void add(int size, int a4, int b4, int
c4) Step 1 Add each corresponding item
from a and b, place result in c's corresponding
location

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

55
void add(int size, int a4, int b4, int
c4) Step 1 for each corresponding item
in a and b Step 1.1 Place the sum of these
items in c's corresponding location

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

56
void add(int size, int a4, int b4, int
c4) Step 1 for each corresponding item
in a and b Step 1.1 Place the sum of these
items in c's corresponding location

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

57
void add(int size, int a4, int b4, int
c4) Step 1 for each row of a (and
b) Step 1.1 for each column of a (and b)
Step 1.1.1 Place the sum of these items in c's
corresponding location

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

58
void add(int size, int a4, int b4, int
c4) Step 1 for each row of a (and
b) Step 1.1 for each column of a (and b)
Step 1.1.1 Place the sum of these items in c's
corresponding location

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

59
void add(int size, int a4, int b4, int
c4) for (int i 0 i lt size i)
Step 1.1 for each column of a (and b) Step
1.1.1 Place the sum of these items in c's
corresponding location

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

60
void add(int size, int a4, int b4, int
c4) for (int i 0 i lt size i)
Step 1.1 for each column of a (and b) Step
1.1.1 Place the sum of these items in c's
corresponding location

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

61
void add(int size, int a4, int b4, int
c4) for (int i 0 i lt size i)
for (int j 0 j lt 4 j) Step 1.1.1
Place the sum of these items in c's corresponding
location

Algorithm
Step 1 Print each row in the matrix, following
each with a new line

62
void add(int size, int a4, int b4, int
c4) for (int i 0 i lt size i)
for (int j 0 j lt 4 j) Step 1.1.1
Place the sum of these items in c's corresponding
location