CS 212 Data Structures and Algorithms Sorting Algorithms

CS 212: Data Structures and Algorithms Sorting Algorithms

Outline Simple Sort Selection Sort Insertion Sort Exchange (Bubble) Sort 2

Simple Sort – Algorithm 1. 2. 3. 4. 5. 6. 7. 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 Sorted Array 21

Insertion Sort – Algorithm 1. 2. 3. 4. 5. 6. 7. 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 while j > 0 and A[j] > key do A[j+1] ← A[j] j ← j – 1 A[j+1] ← key 25

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

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

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

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

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

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

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

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

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

Insertion Sort Continue sorting. . . 14 56 66 89 108 12 34 12 14 34 56 66 89 108 1 n 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 1 108 56 14 89 12 34 n 37

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

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

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