radix sort

Radix SortRadix Sort

CH Gowri KumarCH Gowri Kumar

gkumar007@gmail.comgkumar007@gmail.com

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

Pass 1

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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

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

64 8 216 512 27 729 0 1 343 125

Pass 1

Pass 2

Pass 3

Pass 1

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Pass 3

Pass 1

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Pass 3

Pass 1

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Pass 1

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0 1 512

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Pass 3

0 1 512

Pass 1

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Pass 3Pass 2Pass 2

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Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

00 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 01 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 08 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

0 1 512 343 64 125 216 27 8 729

Pass 1

Pass 2

Pass 3

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Pass 3

Pass 1

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Pass 3

125 27

Pass 1

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Pass 3

125 27

0 1 8 512 216

Pass 1

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Pass 3

2 729125 27

0 1 8 512 216

Pass 1

Pass 2

Pass 3

2 729125 27

0 1 8 512 216 125 27 729

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729 343

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729 343

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729 343 64

Pass 1

Pass 2

Pass 3Pass 3Pass 3

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729 343 64

Pass 1

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Pass 3

000 1 8 512 216 125 27 729 343 64

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729 343 64

Pass 1

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0 001 8 512 216 125 27 729 343 64

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729 343 64

Pass 1

Pass 2

Pass 3

0 1 008 512 216 125 27 729 343 64

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729 343 64

0 80 1

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729 343 64

0 80 1

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729 343 64

0 80 1

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729 343 64

0 80 1

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729 343 64

0 80 1

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729 343 64

0 80 1

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729 343 64

0 80 1

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 027 729 343 64

0 80 1

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729 343 64

0 270 1

Pass 1

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Pass 3

0 1 8 512 216 125 27 729 343 64

0 270 1

Pass 1

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Pass 3

0 1 8 512 216 125 27 729 343 64

0 270 1

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729 343 64

0 270 1

Pass 1

Pass 2

Pass 3

0 1 8 512 216 125 27 729 343 64

0 270 1

Pass 1

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Pass 3

0 1 8 512 216 125 27 729 343 064

0 270 1

Pass 1

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Pass 3

0 1 8 512 216 125 27 729 343 64

0 640 1

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0 1 8 512 216 125 27 729 343 64

0 640 1

Pass 1

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Pass 3

0 640 1

Pass 1

Pass 2

Pass 3

0 640 1

0 1 8 27 64

Pass 1

Pass 2

Pass 3

0 1 8 27 64

Pass 1

Pass 2

Pass 3

0 1 8 27 64 125

Pass 1

Pass 2

Pass 3

0 1 8 27 64 125

Pass 1

Pass 2

Pass 3

0 1 8 27 64 125 216

Pass 1

Pass 2

Pass 3

0 1 8 27 64 125 216

Pass 1

Pass 2

Pass 3

0 1 8 27 64 125 216 343

Pass 1

Pass 2

Pass 3

0 1 8 27 64 125 216 343

Pass 1

Pass 2

Pass 3

0 1 8 27 64 125 216 343 512

Pass 1

Pass 2

Pass 3

0 1 8 27 64 125 216 343 512

Pass 1

Pass 2

Pass 3

0 1 8 27 64 125 216 343 512 729

Pass 1

Pass 2

Pass 3

0 1 8 27 64 125 216 343 512 729

Pass 1

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The EndThe End

radix sort

radix sort radix sort

generalization of bucket

passes of bucket sort

count array

array count of size

bucket sorts

following array

input array

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