Sorting Algorithms

BUBBLE SORT INSERTION SORT SELECTION SORT RADIX SORT

TOPICS TO BE DISCUSSED

BUBBLE SORT If we compare pairs of adjacent elements

and none are out of order, the list is sorted

If any are out of order, we must have to swap them to get an ordered list

Bubble sort will make passes though the list swapping any adjacent elements that are out of order

7 2 8 5 4

2 7 8 5 4

2 7 8 5 4

2 7 5 8 4

2 7 5 4 8

2 7 5 4 8

2 5 7 4 8

2 5 4 7 8

2 7 5 4 8

2 5 4 7 8

2 4 5 7 8

2 5 4 7 8

2 4 5 7 8

2 4 5 7 8

(done)

EXAMPLE OF BUBBLE SORT

ALGORITHM……

STEP 1: Repeat steps 2 and 3 for I=1 to N-1STEP 2: Repeat step 3 for J=1 to N-1STEP 3: [Exchange elements] If A[J]>A[J+1] then TEMP:=[J] A[J]:=A[J+1] A[J+1]:=TEMP [end of if statement] [end of step 2 for statement] [end of step 1 for statement]STEP 4: Exit

INSERTION SORT

ALGORITHM……STEP 1: Repeat step 2 to 4 for I=2 to nSTEP 2: Set temp:=A[I] position:=I-1

STEP 3: [move down 1 position all elements greater than temp]

repeat while temp<A[position] and position>=1 set A[position +1]:=A[position] set position:=position-1 [end of loop]STEP 4: [insert temp at proper position] set A[position+1]:=temp [end of step 1 for loop]STEP 5: [finished] Exit

SELECTION SORT

ALGORITHM……STEP 1: repeat steps 2 to 4 for K=1 to n-1STEP 2: set min:=A[K] position:=K

STEP 3:[make pass and obtain element with smallest value] Repeat for I=K+1 To n if min>A[I] then min:=A[I] and position:=1 [end of if statement] [end of step 3 loop]STEP 4:[exchange elements] if position <> K then temp:=A[k] A[K]:=A[position] A[position]:=temp [end of if statement] [end of step 1 for loop]STEP 5:[finished] exit

RADIX SORT

Assuming decimal elements and 10 buckets, we would put the elements into the bucket associated with its units digit

The buckets are actually queues so the elements are added at the end of the bucket

At the end of the pass, the buckets are combined in increasing order

RADIX SORT EXAMPLE

The unit digit is 0

The unit digit is 1

The unit digit is 2

The unit digit is 3

RADIX SORT EXAMPLE(CONTINUED)The unit digits are already in order

Now start sorting the tens digit

Values in the buckets are now in order

The unit and tens digits are already in order

Now start sorting the hundreds digit

RADIX SORT EXAMPLE(CONTINUED)

THANKS