Sorting Arrays
Chapter 14
1
Agenda
Review of Arrays 
Sorting Arrays
Bubble Sort
Selection Sort
Finding the smallest element in array
Multidimensional arrays
2
Review Arrays
You know how to declare, initialize, process
arrays with loops, and pass them to functions:
float stuff[10]={3, 4, 6, 8, 2, 1, 0};
for (int k=0; k<9; k++)
stuff[k]=stuff[k+1];
Display(stuff, 10);
3
You can also pass one (or more)
individual cells of an array to a function:
int scores[8]={33, 54, 65, 84, 42, 61, 100, 53};
swap(scores[4], scores[1]);
swap(scores[2], scores[7]);
Notice a
Pattern?
void swap(int& x, int& y)
{ // exchanges the values of x , y:
float temp = x;
x = y;
y = temp;
}
4
A small problem…relates to Lab13 p9-11
How do we read a file into an array?
If we don’t know how many lines are in file
How big an array do we need?
How will we keep track of the size of the data set?
For example, look at scores.txt online
Open your notebooks…this is important!
5
Agenda
Review of Arrays
Sorting Arrays 
Bubble Sort
Selection Sort
Finding the smallest element in array
Multidimensional arrays
6
Sorting Arrays
Computer scientists often need to sort
arrays –Why?
Because it’s easier to find things in the array
when it is sorted
Most data looks better displayed in sorted
form (phone books, employee records,
Lacrosse games)
How can we sort an array? What is the
algorithm? A: There are several!!
7
Bubble Sort
Bubble sort is one of the simplest sorting
algorithms
It proceeds through a sequence of
iterations, each time moving the next
largest item into its correct position
On each iteration, it compares each pair
of consecutive elements, moving the
larger element up
8
Bubble Sort
55
22
99
66
55
9
Bubble Sort
55
22
99
66
> 55 ?
10
Bubble Sort
55
22
99
66
swap
11
Bubble Sort
22
55
99
66
55
12
Bubble Sort
22
55
99
66
> 55 ?
13
Bubble Sort
22
55
99
66
99
14
Bubble Sort
22
55
99
66
> 99 ?
15
Bubble Sort
22
55
99
66
swap
16
Bubble Sort
22
55
66
99
Notice how the data “bubbles up” through
the array moving slowly, one bin at a time
After N-1 “Passes” or “Sweeps”, the final
array is guaranteed to be sorted in
ascending order, no matter what input data
17
Bubble Sort
#include <iostream.h>
void print(float a[], int n); //Prints array a
void sort(float a[], int n);//Sorts array a
void swap(float& , float&);//Swaps a[j] and a[j+1]
void main()
{
float a[] =
{55.5, 22.5, 99.9, 66.6, 44.4, 88.8, 33.3, 77.7};
print(a,8);
sort(a,8);
print(a,8);
}
void print(float a[], int n)
{
for (int i=0; i<n-1; i++)
cout<< a[i] << ", ";
cout << a[n-1] << endl;
}
18
Bubble Sort (contd)
void sort(float a[], int n)
{
for (int i=1; i<n; i++)
for ( int j=0; j<n-1; j++)
if(a[j] > a[j+1]) swap(a[j],a[j+1]);
}
void swap(float& x, float& y)
{
float temp;
temp=y;
y=x;
x=temp;
}
19
Selection Sort
Another way of sorting is the selection sort
The main idea is to keep finding the
smallest (and next smallest) items in the
array
And move them into correct position (swap)
20
Selection Sort
data
0
1
2
3
55
22
99
66
smallest
small_pos
55
0
k
0
55 < smallest?
F
21
Selection Sort
data
0
1
2
3
55
22
99
66
smallest
small_pos
55
0
k
0
22 < smallest?
T
22
Selection Sort
data
0
1
2
3
55
22
99
66
smallest
small_pos
22
1
k
0
22 < smallest?
T
23
Selection Sort
data
0
1
2
3
55
22
99
66
smallest
small_pos
22
1
k
0
99 < smallest?
F
24
Selection Sort
data
0
1
2
3
55
22
99
66
smallest
small_pos
22
1
k
0
66 < smallest?
F
25
Selection Sort—SWAP
data
smallest
22
0
1
2
3
55
22
99
66
small_pos
1
k
0
Swap(data[k], data[small_pos]);
26
Selection Sort—Repeat
0
1
2
3
22
55
99
66
smallest
small_pos
55
1
k
1
55 < smallest ?
F
27
Selection Sort—Finding Smallest
After (SIZE-1) iterations of the above, array is sorted
The heart of this algorithm is finding the smallest element
of the array (and it’s position or index small_pos):
smallest=data[0];
// assume 0th cell
small_pos=0;
// is smallest
for (n=0; n<SIZE; n++) // go thru array
if (data[n]<smallest) // if smaller
{
small_pos=n;
//save position
smallest=data[n];
// and value
}
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Selection Sort—the whole function
void Sort(int data[], int size)
{ int n, k, small_pos, smallest;
for (k=0; k<size-1; k++)
{ smallest=data[k]; // assume kth cell
small_pos=k;
// is smallest
for (n=k; n<SIZE; n++)
if (data[n]<smallest)// if smaller
{
small_pos=n;
//save position
smallest=data[n];
// and value
}
Swap(data[k], data[small_pos]);
}
}
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Agenda
Review of Arrays
Sorting Arrays
Bubble Sort
Selection Sort
Finding the smallest element in array
Multidimensional arrays 
30
Multidimensional Arrays
The arrays we have looked at till now
have been one-dimensional
They are linear (or sequential)
An array of arrays is called a
multidimensional array
A one-dimensional array of onedimensional arrays is called a twodimensional array
31
Multidimensional Arrays
0
1
2
3
4
An array
32
Multidimensional Arrays
0
1
2
3
4
5
COLUMNS
0
1
2
3
ROWS
An array of arrays
33
Multidimensional Array
Simplest way to define a multidimensional array is
int matrix[4][6];
This would create a two-dimensional array
of type int with 4 rows and 6 columns
int matrix[4][6]={0};
34
Multidimensional Arrays
1
2
0
0
0
0
0
2
0
3
0
matrix
0
1
ROWS
0
3
4
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
COLUMNS
An array of arrays
35
Accessing a 2D Array
matrix[2][3]=22;
matrix[0][5]=44;
1
2
0
0
0
0
0
2
0
3
0
matrix
0
1
0
3
4
5
0
0
44
0
0
0
0
0
0
22 0
0
0
0
0
0
0
36
Processing a 2D Array w/Loop
for(k=0; k<6; k++)
matrix[3][k]=k;
1
2
0
0
0
0
0
2
0
3
0
matrix
0
1
0
3
4
5
0
0
44
0
0
0
0
0
0
22 0
0
1
2
3
5
4
37
2D Array Read/Print Example
#include<iostream.h>
void read(int a[][5]); //Read the input into two dimen array a
void print(const int a[][5]);//Print array a
void main()
{ int a[3][5];
read(a);
print(a);
}
void read(int a[][5])
{ cout << "Enter 15 integers, 5 per row:\n";
for (int i=0; i<3; i++)
{
for (int j=0; j<5; j++)
cin >> a[i][j];
}
}
38
2D Array Example (contd)
void print(const int a[][5])
{ for (int i=0; i<3; i++)
{
cout << "Row " << i << ": ";
for (int j=0; j<5; j++)
cout << " " << a[i][j];
cout << endl;
}
}
39
That’s a wrap !
What we learned today:
Sorting Arrays
Bubble Sort
Selection Sort
Multidimensional arrays
40
Go back home proud !
You’re brighter than Ar’ray’ !
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