Insertion Sort

1
Insertion Sort

• Input A sequence of n numbers or
• An array A
• e.g. A
• Output A permutation of the input seq. in
• increasing order.
• lengthA n, in the e.g., lengthA6

3
5
1
6
4
2
2
Insertion Sort
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5
1
6
4
2
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Insertion Sort
5
2
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Insertion Sort
5
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Insertion Sort
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6
Insertion Sort
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4
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7
Insertion Sort
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8
Insertion Sort
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Insertion Sort
2
5
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Insertion Sort
2
1
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Insertion Sort
2
1
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Insertion Sort
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5
1
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Insertion Sort
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5
1
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Insertion Sort
2
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4
1
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Insertion Sort
2
5
4
1
16
Insertion Sort
1
5
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2
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Insertion Sort
1
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Insertion Sort
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Insertion Sort
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1
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Insertion Sort
3
1
6
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4
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Insertion Sort
6
1
3
5
4
2
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Insertion Sort
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1
3
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Insertion Sort
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Insertion Sort
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Insertion Sort
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Insertion Sort
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Insertion Sort
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28
Insertion Sort

• Input A sequence of n numbers or
• An array A
• e.g. A
• Output A permutation of input seq.
• lengthA n, in the e.g. lengthA6

3
5
1
6
4
2
29
Insertion Sort

• Insertion-Sort (A)
• 1 for j ? 2 to lengthA
• 2 do key ?Aj
• 3 ? Insert Aj into the sorted
• sequence A1,, j-1
• 4 i ? j-1
• 5 while igt0 and Aigtkey
• 6 do Ai1?Ai
• 7 i? i-1
• 8 Ai1 ?key

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Insertion Sort (j6)
3
1
6
5
4
2
Key
2 do key ?Aj
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Insertion Sort (j6)
3
key
i5
1
6
5
4
2
4 i ? j-1
32
Insertion Sort
3
key
i5
i4
6
1
5
4
2
6
5 while igt0 and Aigtkey
6 do Ai1?Ai
7 i?i-1
33
Insertion Sort
3
key
i4
i3
6
1
5
4
2
6
5
5 while igt0 and Aigtkey
6 do Ai1?Ai
7 i?i-1
34
Insertion Sort
3
key
i3
i2
6
1
5
4
2
5
4
5 while igt0 and Aigtkey
6 do Ai1?Ai
7 i?i-1
35
Insertion Sort
3
key
i2
6
1
4
2
5
4
5 while igt0 and Aigtkey 6
do Ai1?Ai 7
i?i-1
8 Ai1?key
36
Insertion Sort
6
1
5
4
3
2
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39
Insertion Sort
3
key
i4
6
1
5
4
2
6
5 while igt0 and Aigtkey 6
do Ai1?Ai 7
i?i-1
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Insertion Sort
3
key
i4
6
1
5
4
2
6
5 while igt0 and Aigtkey 6
do Ai1?Ai 7
i?i-1
41
Insertion Sort
3
key
i3
6
1
5
4
2
5
5 while igt0 and Aigtkey 6
do Ai1?Ai 7
i?i-1
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Insertion Sort
3
key
i2
6
1
5
4
2
4
5 while igt0 and Aigtkey 6
do Ai1?Ai 7
i?i-1 8 Ai1 ? key
43
Insertion Sort
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1
5
4
3
2
44
Merge Sort
45
Merge
2
7
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4
1
8
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3
1
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8
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46

• Input Two sorted arrays L1,...,n1 and
  R1,..., n2
• Output A permutation A1,, n1n2 of L ? R in
• increasing order.
• i ? 1
• j ? 1
• for k ? 1 to n1n2
• do if Li lt Rj
• then Ak ? Li
• i ? i1
• else Ak ? Rj
• j ? j1

47

• L1,3 and R2,4
• i ? 1
• j ? 1
• for k ? 1 to n1n2
• do if Li lt Ri
• then Ak ? Li
• i ? i1
• else Ak ? Rj
• j ? j1

A
A 1,
A 1,2,
A 1,2,3,
i1
j1
k1
k2
k3
k4
L11lt R12
L23gtR12
L23ltR24
L3?? R24
A11
A33
i2
i3
A22
j2
48
L1,3,1 and R2,4,1

• L1,3 and R2,4
• Ln11Ã 1
• Rn21Ã 1
• i ? 1
• j ? 1
• for k ?1 to n1n2
• do if Lilt Rj
• then Akà Li
• i à i1
• else Akà Rj
• jà j1

A
A 1,
A 1,2,
A 1,2,3,
A 1,2,3,4
i1
j1
k1
k2
k3
k4
L11lt R12
L23gtR12
L23ltR24
L3?gt R24
A11
A33
i2
i3
A22
A44
j2
j3
49

• 7 n/8
• 3 n/4
• 1 n/2

1 2 3 4 5 6 7 8
2 4 5 7
1 3 6 8
2 5
4 7
1 6
3 8
5
7
4
2
1
3
8
6