Radix Sort

Radix SortRadix Sort

CH Gowri KumarCH Gowri Kumar

[email protected]@gmail.com

April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com

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Bucket SortBucket Sort

Given that, we have N integers in the Given that, we have N integers in the range 0 to M-1range 0 to M-1

Maintain an array count of size M, which Maintain an array count of size M, which is initialized to zero. Thus, count has M is initialized to zero. Thus, count has M cells (buckets).cells (buckets).

Read ARead Ai i

Increment count[AIncrement count[Aii] by 1] by 1 After all the input array is read, scan the After all the input array is read, scan the

count array, printing out a representation count array, printing out a representation of sorted list.of sorted list.


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Radix SortRadix Sort

Radix sort is generalization of bucket Radix sort is generalization of bucket sort.sort.

It uses several passes of bucket sortIt uses several passes of bucket sort Perform the bucket sorts by “least Perform the bucket sorts by “least

significant digits”significant digits” First sort by digit in units placeFirst sort by digit in units place Second sort by digit in tens placeSecond sort by digit in tens place Third sort by digit in hundreds placeThird sort by digit in hundreds place …………..


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Pass 364 8 216 512 27 729 0 1 343 125

Let’s sort the following array using radix sort: Let’s sort the following array using radix sort:


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64 8 216 512 27 729 0 1 343 125

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64 8 216 512 27 729 0 1 343 125

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64


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64 8 216 512 27 729 0 1 343 125

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64 8 216 512 27 729 0 1 343 125

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64 8 216 512 27 729 0 1 343 125

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64 8 216 512 27 729 0 1 343 125

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512


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64 8 216 512 27 729 0 1 343 125

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64 8 216 512 27 729 0 1 343 125

8

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27

729


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64 8 216 512 27 729 0 1 343 125

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729

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64 8 216 512 27 729 0 1 343 125

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729

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64 8 216 512 27 729 0 1 343 125

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729

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343


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64 8 216 512 27 729 0 1 343 125

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729

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125


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0 0


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512

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0 0


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512

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0


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512

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729

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125

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512

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729

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0 1

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512

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0 1 512

8

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512

27

729

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125

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0 1 512

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216

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729

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125

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0 1 512 343 64 125 216 27 8 729

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00 1 512 343 64 125 216 27 8 729

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0 1 512 343 64 125 216 27 8 729

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0 0


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0 01 512 343 64 125 216 27 8 729

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0 0


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0 1 512 343 64 125 216 27 8 729

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0 10


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0 1 512 343 64 125 216 27 8 729

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0 10

1 512


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0 1 512 343 64 125 216 27 8 729

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0 10

1 512

4 343


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0 1 512 343 64 125 216 27 8 729

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0 10

1 512

4 343

6 64


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0 1 512 343 64 125 216 27 8 729

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0 10

1 512

4 343

6 64

2 125


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0 1 512 343 64 125 216 27 8 729

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0 10

1 216

4 343

6 64

2 125

512


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0 1 512 343 64 125 216 27 8 729

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0 10

1 216

4 343

6 64

2 27

512

125


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0 1 512 343 64 125 216 27 08 729

3

5

7

8

9

0 10

1 216

4 343

6 64

2 27

512

125


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0 1 512 343 64 125 216 27 8 729

3

5

7

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0 80

1 216

4 343

6 64

2 27

512

125

1


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0 1 512 343 64 125 216 27 8 729

3

5

7

8

9

0 80

1 216

4 343

6 64

2 729

512

125

1

27


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5

7

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0 80

1 216

4 343

6 64

2 729

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125

1

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0 80

1 216

4 343

6 64

2 729

512

125

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27

0 1 8


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1 216

4 343

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2 729

512

125 27

0 1 8

0


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1 216

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6 64

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125 27

0 1 8 512 216

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4 343

6 64

2 729125 27

0 1 8 512 216

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5

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4 343

6 64

2 729125 27

0 1 8 512 216 125 27 729

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4 343

6 64

0 1 8 512 216 125 27 729

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4 343

6 64

0 1 8 512 216 125 27 729 343

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6 64

0 1 8 512 216 125 27 729 343

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6 64

0 1 8 512 216 125 27 729 343 64

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0 1 8 512 216 125 27 729 343 64

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000 1 8 512 216 125 27 729 343 64

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0 1 8 512 216 125 27 729 343 64

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0 001 8 512 216 125 27 729 343 64

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0 1 8 512 216 125 27 729 343 64

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0 1 008 512 216 125 27 729 343 64

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0 1 8 512 216 125 27 729 343 64

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0 1 8 512 216 125 27 729 343 64

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0 80 1

5 512


Pass 1

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0 1 8 512 216 125 27 729 343 64

1

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0 80 1

5 512

2 216


Pass 1

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7

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0 1 8 512 216 125 27 729 343 64

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0 80 1

5 512

2 216

1 125


Pass 1

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0 1 8 512 216 125 027 729 343 64

4

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0 80 1

5 512

2 216

1 125


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0 1 8 512 216 125 27 729 343 64

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0 270 1

5 512

2 216

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0 1 8 512 216 125 27 729 343 64

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0 270 1

5 512

2 216

1 125

8

7 729


Pass 1

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0 1 8 512 216 125 27 729 343 64

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0 270 1

5 512

2 216

1 125

8

7 729

3 343


Pass 1

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8

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0 1 8 512 216 125 27 729 343 064

4

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0 270 1

5 512

2 216

1 125

8

7 729

3 343


Pass 1

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9

0 1 8 512 216 125 27 729 343 64

4

6

0 640 1

5 512

2 216

1 125

8

7 729

3 343

27


Pass 1

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8

9

4

6

0 640 1

5 512

2 216

1 125

8

7 729

3 343

27


Pass 1

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8

9

4

6

0 640 1

5 512

2 216

1 125

8

7 729

3 343

27

0 1 8 27 64


Pass 1

Pass 2

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8

9

4

6

5 512

2 216

1 125

7 729

3 343

0 1 8 27 64

0


Pass 1

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8

9

4

6

5 512

2 216

1 125

7 729

3 343

0 1 8 27 64 125

0


Pass 1

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8

9

4

6

5 512

2 216

7 729

3 343

0 1 8 27 64 125

0

1


Pass 1

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8

9

4

6

5 512

2 216

7 729

3 343

0 1 8 27 64 125 216

0

1


Pass 1

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8

9

4

6

5 512

7 729

3 343

0 1 8 27 64 125 216

0

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Pass 1

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5 512

7 729

3 343

0 1 8 27 64 125 216 343

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Pass 1

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5 512

7 729

0 1 8 27 64 125 216 343

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Pass 1

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5 512

7 729

0 1 8 27 64 125 216 343 512

0

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Pass 1

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7 729

0 1 8 27 64 125 216 343 512

0

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Pass 1

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4

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7 729

0 1 8 27 64 125 216 343 512 729

0

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0 1 8 27 64 125 216 343 512 729

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The EndThe End

Radix Sort

Education

Transcript of Radix Sort