Data Structures- Part4 basic sorting algorithms

Data Structures I (CPCS-204)
Week # 4: Sorting Algorithms

Sorting
 Motivation
 Generally, to arrange a list of elements in some order
 List of numbers
 10 20 50 30 40 60 25 (Unsorted list)
 10 20 25 30 40 50 60 (Sorted list, ascending)
 60 50 40 30 25 20 10 (Sorted list, descending)
 List of alphabets
 P A K I S T A N (Unsorted list)
 A A I K N P S T (Sorted list, ascending)
 T S P N K I A A (Sorted list, descending)

Sorting Algorithms
1. Bubble Sort
2. Selection Sort
3. Insertion Sort
4. Quick Sort
5. Merge Sort
There are few more sorting algorithms; you
can find them in a book on data structures
and algorithms (or on the Web)

Bubble Sort Algorithm: Informal
 Repeatedly compare the elements at
consecutive locations in a given list, and do the
following until the elements are in required
order:
 If elements are not in the required order, swap them
(change their position)
 Otherwise do nothing

Bubble Sort in Action: Phase 1
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Bubble Sort Algorithm in Java
void bubbleSort(int List[]){
int temp;
int size = List.length;
for (i = 0; i < size - 1; i++)
for (j = 0; j < size – (i + 1); j++){
if (List[j] > List[j+1]){
temp = List[j];
List[j] = List[j+1];
List[j+1] = temp;
}
}
}
}
Time complexity of the Bubble Sort algorithm is O(n2). Think why?

Selection Sort: Informal
 Suppose we want to sort an array in ascending
order:
 Locate the smallest element in the array; swap it
with element at index 0
 Then, locate the next smallest element in the array;
swap it with element at index 1.
 Continue until all elements are arranged in order

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Selection Sort Algorithm in Java
void selectionSort(int List[]){
int temp, min;
for (i = 0; i < size; i++){
min = i;
for (j = i + 1; j < size; j++){
if (List[j] < List[min]){
min = j;
}
}
temp = List[min];
List[min] = List[i];
List[i] = temp;
}
}
Time complexity of the Selection Sort algorithm is O(n2). Think why?

Bubble Sort vs. Selection Sort
 Selection Sort is more efficient than Bubble Sort,
because of fewer exchanges in the former
 Both Bubble Sort and Selection Sort belong to
the same (quadratic) complexity class (O(n2))
 Bubble Sort may be easy to understand as
compared to Selection Sort – What do you think?

Insertion Sort
Works like someone who
inserts one more card at a time
into a hand of cards that are
already sorted
To insert 12, we need to make
room for it …
6 10 24
36
12
20

21
6 10 24
… by shifting first 36
towards right…
36
12
21
Insertion Sort

… and then shifting 24
towards right
6 10 24 36
12
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Insertion Sort

Once room is available,
insert the element (12 in this
case)
6 10 12
24 36
23
Insertion Sort

Insertion Sort: Informal
 We divide the list into two parts: Sorted and
Unsorted parts
 Initially
o the sorted part contains the first element (at index 0)
o the unsorted part contains the elements from index 1 to N-1
 Then, we move element from index 1 to an appropriate
position in the sorted part, keeping order intact
 Then, we move element from index 2 to an appropriate
position in the sorted part, keeping order intact
...
 Finally, we move element from index N-1 to an
appropriate position in the sorted part, keeping order intact

Insertion Sort Algorithm in Java
void insertionSort(int List[]){
int temp;
for (int i = 1; i < size; i++){
int j = i;
temp = List[i];
while (j > 0 && temp < List[j - 1]){
List[j] = List[j - 1]; // right shifting
j--;
}
List[j] = temp;
}
}
Time complexity of the Insertion Sort algorithm is O(n2). Think why?

Outlook
Next week, we’ll discuss recursion

Data Structures- Part4 basic sorting algorithms

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