Lecture 5
Searching and Sorting
Richard Gesick
The focus
Searching - examining the contents
of the array to see if an element
exists within the array
Sorting - rearranging the elements of
the array to be in a particular order
Sorting
There are many ways to order
elements within a collection. There
is typically a trade-off between
complexity of the algorithm and the
performance of the algorithm.
a simple approach to sorting
realize that it is slower than other
methods that are more complex to
code yet more efficient.
Bubble Sort
Repeatedly pair-wise examine
elements and swap them if needed;
this is called a "Bubble sort" since
elements "bubble" to their correct
positions.
Bubble Sort Algorithm
for (int i = 0; i < A.Length - 1; i++)
for (int j = i; j < A.Length; j++)
{
if (A[j] < A[i])
{
int temp = A[j];
A[j] = A[i];
A[i] = temp;
}
}
Selection Sort
The selection sort algorithm
repeatedly finds the smallest
element in the unsorted tail region of
the array and moves it to the front
Sorting an Array of Integers
Array in original order 11 9 17 5 12
Find the smallest and swap it with the first
element
5 9 17 11 12
Find the next smallest. It is already in the
correct place
5 9 17 11 12
Sorting an Array of Integers (2)
Find the next smallest and swap it with the first
element of unsorted portion
5 9 11 17 12
Repeat
5 9 11 12 17
When the unsorted portion is of length 1, we are done
5 9 11 12 17
This algorithm is slow when run on large data sets
Time Taken By Selection Sort on Various Size Arrays
Selection Sort Algorithm
int i = 0;
int j = 0;
for (i = 0; i < B.Length - 1; i++)
{
int minPos = i;
for (j = i + 1; j < B.Length; j++)
{
if (B[j] < B[minPos])
minPos = j;
}
if (i != minPos && minPos < B.Length)
{
int temp = B[minPos];
B[minPos] = B[i];
B[i] = temp;
}
}
Insertion Sort
Consider what you would do to sort a set
of cards. This approach is an insertion sort
- taking a new item and place it correctly
relative to the other items in the "finished"
portion. You continually maintain two sets
- unexamined, unsorted cards and a set of
examined/sorted cards. For each card in
the unexamined set, take it out of that set
and place it correctly relative to the
examined set.
Insertion Sort Algorithm
List<int> inOrder = new List<int>();
foreach (int temp in C)
{
bool added = false;
for (int i = 0; i < inOrder.Count; i++)
{
if (temp < inOrder[i])
{
inOrder.Insert(i, temp);
added = true;
break;
}
}
if (!added)
inOrder.Add(temp);
}
Sorting in a C# Program
The List class contains sort methods
To sort an array of integers
convert to a List and call the sort method
List<int> E=D.ToList<int>();
E.Sort();
Linear Search
Also called sequential search
Examines all values in an array until it finds a
match or reaches the end
Number of visits for a linear search of an array
of n elements
- The average search visits n/2 elements
- The maximum visits is n
A linear search is an O(n) algorithm
Linear Search Algorithm
steps = 0;
foreach (int temp in G)
{
steps++;
if (temp == find)
return true;
}
return false;
Binary Search
Locates a value in a sorted array by determining
whether the value occurs in the first or second half,
then repeating the search in one of the halves
Number of visits to search an sorted array of size n
We visit one element (the middle element) then
search either the left or right subarray
Binary search is a O( log(n) ) algorithm
Binary Search Algorithm
int low=0;
int high= G.Length;
int mid = 0;
while (!found)
{
steps++;
mid = (low + high) / 2;
if (find == G[mid])
return true;
else if (find < G[mid])
high = mid;
else
low = mid;
if (low > high-1 || high < low +1)
return false;
}