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Used to walk thru sorting. Examples are based on Foruzan and Gilberg book on Data Structures
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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 WalkerCurrent
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]
consider only our segment
25 is placed in the inserted when we
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
Looking for number > than 62 (pivot)
Looking for 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
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