CS212: Data Structures and Algorithms Sorting Algorithms

Outline Simple Sort Selection Sort Insertion Sort Exchange (Bubble) Sort

Simple Sort – Algorithm Get a list of unsorted numbers Repeat steps 3 through 6 until the unsorted list is empty Compare the unsorted numbers Select the smallest unsorted number Move this number to the sorted list Store a maximum value in the place of the smallest number Stop 3

Simple Sort Unsorted Array Sorted Array 4

Simple Sort Unsorted Array Sorted Array 5

Simple Sort Unsorted Array Sorted Array 6

Simple Sort Unsorted Array Sorted Array 7

Simple Sort Unsorted Array Sorted Array 8

Simple Sort Unsorted Array Sorted Array 9

Simple Sort Unsorted Array Sorted Array 10

Simple Sort Unsorted Array Sorted Array 11

Selection Sort Find minimum element in the list and also the index of the minimum element. Min_Index = 0 for (I = start; I <= end - 1; I++) if (A[ Min_Index] > A[ I]) Min_Index = I; 12

Selection Sort Swap two elements of the list Swap(I, j) { temp = A[ I ] ; A[ I ] = A[ j ]; A[ j ] = temp; } 13

Selection Sort The complete algorithm is: for i ← 1 to n-1 do min j ← i; min x ← A[i] for j ← i + 1 to n do If A[j] < min x then min j ← j min x ← A[j] A[min j] ← A [i] A[i] ← min x 14

Selection Sort Unsorted Array Swap first smallest i.e. 2 with first array location i.e. 7 15

Selection Sort Unsorted Array Swap second smallest i.e. 3 with second array location i.e. 8 16

Selection Sort Unsorted Array Swap third smallest i.e 4 with third array location i.e. 5 17

Selection Sort Unsorted Array Swap fourth smallest i.e. 5 with fourth array location i.e. 7 18

Selection Sort Unsorted Array Swap fifth smallest i.e. 6 with fifth array location i.e. 7 19

Selection Sort Unsorted Array Swap sixth smallest i.e. 7 with sixth array location i.e. 7 20

Selection Sort Sorted Array 21

Insertion Sort – Algorithm Get a list of unsorted numbers Set a marker for the sorted section after the first number in the list Repeat steps 4 through 6 until the unsorted section is empty Select the first unsorted number Swap this number to the left until it arrives at the correct sorted position Advance the marker to the right one position Stop 22

Insertion Sort 23

Insertion Sort 24

Insertion Sort for i ← 2 to n do key ← A[i] j ← i – 1   for i ← 2 to n do key ← A[i] j ← i – 1 while j > 0 and A[j] > key do A[j+1] ← A[j] j ← j – 1 A[j+1] ← key 25

Insertion Sort ← j After while loop j = 1 so A[2] ← 108 Start sorting... ← j i → 66 108 56 14 89 12 34 108 1 n key After while loop j = 1 so A[2] ← 108 26

Insertion Sort ← j Enter while loop shift up 108 Continue sorting... 66 108 56 14 89 12 34 56 1 n key Enter while loop shift up 108 27

Insertion Sort ← j Shifting i → 66 108 56 14 89 12 34 56 1 n key 66 28

Insertion Sort ← j Renter while loop shift up 66 Continue i → 66 108 14 89 12 34 56 1 n key Renter while loop shift up 66 29

Insertion Sort ← j Shifting i → 66 108 108 14 89 12 34 56 1 n key 66 30

Insertion Sort ← j Exit while loop A[1] ← key Continue sorting... i → 66 66 108 14 89 12 34 56 1 n key Exit while loop A[1] ← key 31

Insertion Sort ← j Insert Key i → 66 66 108 14 89 12 34 56 1 n key 56 32

Insertion Sort ← j Continue sorting... i → 56 66 108 14 89 12 34 14 1 key 33

Insertion Sort ← j Continue sorting... i → 14 56 66 108 89 12 34 89 1 key 34

Insertion Sort Continue sorting... 14 56 66 89 108 12 34 12 14 34 56 35

Exchange (Bubble) Sort for i ← n to 2 do for j ← 1 to i – 1 do if A[j] > A[j + 1] then A[j] ↔ A[j + 1] 36

Exchange (Bubble) Sort Start sorting... ← i j → 66 108 56 14 89 12 34 1 n 37

Exchange (Bubble) Sort Continue sorting... j → ← i 66 108 56 14 89 12 34 1 n 66 56 108 14 89 12 34 So on .. 38

Exchange (Bubble) Sort Continue sorting... ← i j → 66 56 14 89 12 108 34 1 n 66 56 14 89 12 34 108 39

Exchange (Bubble) Sort Continue sorting... j → ← i 66 56 14 89 12 34 108 1 n 40