Data Structures : Sorting

0 1 2 3 4 5 23 78 45 8 32 56 i=0 min=23 for (i=0;i<n;i++) j=1 min=23 minVal=arr[i] j=2 min=23 for (j=i+1;j<n;j++) j=3 min=8 if minVal >arr[j] j=4 min=8 minVal=arr[j] j=5 min=8 8 78 45 23 32 56 i=1 8 23 45 78 32 56

Loop 1 Loop 2 pass 1 23 14 78 45 8 32 56 Original j=1 swap 23 14 14 23 78 45 8 32 56 j=2 no swap 14 23 78 45 8 32 56 j=3 swap 78 45 14 23 45 78 8 32 56 j=4 swap 78 8 14 23 45 8 78 32 56 j=5 swap 78 32 14 23 45 8 32 78 56 j=6 swap 78 56 14 23 45 8 32 56 78 SORTED

23 78 45 8 32 56 Original Insert 78 23 78 45 8 32 56 Pass 1 Insert 45 after 78 before 23 23 45 78 8 32 56 Pass 2 Insert 8 before 23 8 23 45 78 32 56 Pass 3 insert 32 after 45 before 23 8 23 32 45 78 56 Pass 4 Insert 56 after 78 8 23 32 45 56 78 Pass 5 SORTED

Wall 1 j k n place k element in appropriate place by walking back from j

Array to be Sorted 72 62 14 9 30 21 80 25 70 55 Arr Index 0 1 2 3 4 5 6 7 8 9 1st Incre k=5 Walker Current 72 62 14 9 30 21 80 25 70 55 SWAP 21 62 14 9 30 77 80 25 70 55 21 62 14 9 30 77 80 25 70 55 21 62 14 9 30 77 80 25 70 55 Why Insertion Sort ? 21 62 14 9 30 77 80 25 70 55 9 Arr Index 0 1 2 3 4 5 6 7 8 9 arr[1] 1st Incre k=3 Walker Current 21 62 14 9 30 77 80 25 70 55 SWAP 9 62 14 21 30 77 80 25 70 55 SWAP 9 30 14 21 62 77 80 25 70 55 9 9 30 14 21 62 77 80 25 70 55 arr[1] 9 30 14 21 62 77 80 25 70 55 SWAP FALLBACK 9 25 14 21 30 77 80 62 70 55 SWAP 9 25 14 21 30 70 80 62 77 55 SWAP 9 25 14 21 30 70 55 62 77 80 Arr Index 0 1 2 3 4 5 6 7 8 9 1st Incre k=1 Walker Current 9 25 14 21 30 70 55 62 77 80 9 25 14 21 30 70 55 62 77 80 SWAP 9 14 25 21 30 70 55 62 77 80 SWAP 9 14 21 25 30 70 55 62 77 80 9 14 21 25 30 70 55 62 77 80 9 14 21 25 30 70 55 62 77 80 SWAP

9 14 21 25 30 55 70 62 77 80 SWAP 9 14 21 25 30 55 62 70 77 80 9 14 21 25 30 55 62 70 77 80 SORTED

Why Insertion Sort ?? Wall 15 22 36 25 6 arr[1+k] arr[1+2k] arr[1+3k] arr[1+4k] arr[1+5k] Wall 15 22 25 36 6 arr[1+k] arr[1+2k] arr[1+3k] arr[1+4k] arr[1+5k] 25 is placed in the inserted when we consider only our segment

78 21 14 97 87 62 74 85 76 45 84 22 62 21 14 97 87 78 74 85 76 45 84 22 22 21 14 97 87 78 74 85 76 45 84 62 Determine Pivot 22 21 14 97 87 62 74 85 76 45 84 78 array Index 0 1 2 3 4 5 6 7 8 9 10 11 62 21 14 97 87 22 74 85 76 45 84 78 Sort Left:1 Looking for number > than 62 (pivot) Sort Left:2 Sort Left:3 Sort Right :11 Looking for number < than 62 (pivot) Sort Right :10 Sort Right :9 62 21 14 45 87 22 74 85 76 97 84 78 SWAP … Sort Left :4 Sort Right moves to 5 62 21 14 45 22 87 74 85 76 97 84 78 SWAP 0,11 62 22 21 14 45 62 87 74 85 76 97 84 78 Move Pivot Back < 62 >=62 0,3 22 5,11 14 21 22 45 62 84 74 85 76 78 87 97 87 0,1 14 3,3 14 21 22 45 62 76 74 78 84 85

45 1,1 21 5,9 84 5,7 76 14 21 22 45 62 74 76 78 84 85 5,5 74 7,7 78 11,11 85

or number > than 62 (pivot) or number < than 62 (pivot)

Merge i j i 14 20 36 10 12 30 40 44 14 20 aux 10 12 14 Merge Sort 12 30 21 8 6 9 1 7 12 30 21 8 12 30 8 21 6 9 1 7 12 30 21 8 8 12 21 30 1 6 7 9 1 6 7 8 9 12 21 30 Recursive 12 30 21 8 6 9 1 7 Break into 2 array 12 30 21 8 6 9 1 7 Break into 4 arrays 12 30 21 8 6 9 1 7 Break into 8 arrays 12 30 21 8 6 9 1 7 Now each single elemnet array is sorted !!! SO Merge 12 30 8 21 6 9 1 7 Merge Again 8 12 21 30 1 6 7 9

Merge Again 1 6 7 8 9 12 21 30

m m+1 j 36 10 12 30 40 44 6 9 1 7 6 9 1 7 MergeSort(arr,start,end) //if only 1 elemnet if (start==end) return; //divide into two equal parts m=(i+j)/2 mergeSort(arr,start,middle) mergeSort(arr,middle+1,end) merge(arr,start,middle,end)

MergeSort(arr,start,end) //if only 1 element if (start==end) return; //divide into two equal parts m=(i+j)/2 mergeSort(arr,start,middle) mergeSort(arr,middle+1,end) merge(arr,start,middle,end) Let us analyse Recursion in Merge Sort Let us say an array has 8 elements, how many times will MergeSort get called Start End 0 7 0 3 0 1 0 0 1 1 2 3 2 2 3 3 4 7 4 5 4 4 5 5 6 7 6 6 7 7 If 100 the call would be ? 199

Create Heap by using reheapUp Original After Heap 78 32 56 8 23 45 reheapDown 56 32 45 8 23 78 Pass 1 45 32 23 8 56 78 Pass 2 32 8 23 45 56 78 Pass 3 23 8 32 45 56 78 Pass 4 8 23 32 45 56 78 Pass 5 Sorted 8 23 32 45 56 78 Pass 6

111 112 113 114 115 211 311 411 511 611 121 131 141 151 161 Unit Digit 0 1 111 211 311 411 511 611 121 131 141 151 161 2 112 3 113 4 114 5 115 6 …. Ten Digit Ten Digit 0 0 1 111 211 311 411 511 611 112 113 114 115 1 111 112 113 2 121 2 211 3 131 3 311 4 141 4 411 5 151 5 511 6 161 6 611 …. …. SORTED 111 112 113

114 115 121 131 141 151 161 114 115 121 131 141 151 161 211 311 411 511 611

Created by Jibrael Jos to explain Sort to M.Sc/MCA Students Jul-09 Christ College

Data Structures : Sorting

by Jibrael Jos on Mar 16, 2010

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Data Structures : Sorting — Document Transcript