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.
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
Pass 2
Pass 3
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 …………..
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
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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:
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
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Pass 3Pass 1Pass 1
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0
1
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
0
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
0
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
0
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64
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
8
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0
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64 8 216 512 27 729 0 1 343 125
8
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0
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64 8 216 512 27 729 0 1 343 125
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
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216
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
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27
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
8
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64 8 216 512 27 729 0 1 343 125
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64
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216
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729
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343
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0 0
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64
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216
512
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729
1
343
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0 0
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64
0
8
216
512
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729
1
343
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0
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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64
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8
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512
27
729
343
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1 1
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1
8
216
512
27
729
343
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1 1
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1
8
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512
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729
343
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512
8
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512
27
729
343
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512
8
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729
343
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
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0 1 512 343 64 125 216 27 8 729
0
1
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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00 1 512 343 64 125 216 27 8 729
0
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
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0 1 512 343 64 125 216 27 8 729
1
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0 0
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
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0 01 512 343 64 125 216 27 8 729
1
2
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0 0
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512 343 64 125 216 27 8 729
1
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512 343 64 125 216 27 8 729
1
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512 343 64 125 216 27 8 729
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0 10
1 512
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512 343 64 125 216 27 8 729
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1 512
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512 343 64 125 216 27 8 729
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1 512
4 343
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512 343 64 125 216 27 8 729
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1 512
4 343
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512 343 64 125 216 27 8 729
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1 512
4 343
6 64
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512 343 64 125 216 27 8 729
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1 512
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512 343 64 125 216 27 8 729
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1 512
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6 64
2 125
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512 343 64 125 216 27 8 729
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1 512
4 343
6 64
2 125
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512 343 64 125 216 27 8 729
3
5
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1 216
4 343
6 64
2 125
512
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512 343 64 125 216 27 8 729
3
5
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0 10
1 216
4 343
6 64
2 125
512
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512 343 64 125 216 27 8 729
3
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0 10
1 216
4 343
6 64
2 27
512
125
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
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0 1 512 343 64 125 216 27 08 729
3
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1 216
4 343
6 64
2 27
512
125
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
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0 1 512 343 64 125 216 27 8 729
3
5
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0 80
1 216
4 343
6 64
2 27
512
125
1
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512 343 64 125 216 27 8 729
3
5
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0 80
1 216
4 343
6 64
2 27
512
125
1
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
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0 1 512 343 64 125 216 27 8 729
3
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0 80
1 216
4 343
6 64
2 729
512
125
1
27
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 512 343 64 125 216 27 8 729
3
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0 80
1 216
4 343
6 64
2 729
512
125
1
27
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 80
1 216
4 343
6 64
2 729
512
125
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27
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 80
1 216
4 343
6 64
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512
125
1
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0 1 8
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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1 216
4 343
6 64
2 729
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125 27
0 1 8
0
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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1 216
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6 64
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125 27
0 1 8 512 216
0
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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4 343
6 64
2 729125 27
0 1 8 512 216
0
1
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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4 343
6 64
2 729125 27
0 1 8 512 216 125 27 729
0
1
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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4 343
6 64
0 1 8 512 216 125 27 729
0
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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4 343
6 64
0 1 8 512 216 125 27 729 343
0
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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6 64
0 1 8 512 216 125 27 729 343
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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6 64
0 1 8 512 216 125 27 729 343 64
0
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 8 512 216 125 27 729 343 64
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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000 1 8 512 216 125 27 729 343 64
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 8 512 216 125 27 729 343 64
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0 0
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 001 8 512 216 125 27 729 343 64
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0 0
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 8 512 216 125 27 729 343 64
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 008 512 216 125 27 729 343 64
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 8 512 216 125 27 729 343 64
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 8 512 216 125 27 729 343 64
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 8 512 216 125 27 729 343 64
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0 80 1
5 512
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 8 512 216 125 27 729 343 64
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0 80 1
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 8 512 216 125 27 729 343 64
1
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0 80 1
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 8 512 216 125 27 729 343 64
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 8 512 216 125 27 729 343 64
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 8 512 216 125 027 729 343 64
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0 80 1
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2 216
1 125
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 8 512 216 125 27 729 343 64
4
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0 270 1
5 512
2 216
1 125
8
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 8 512 216 125 27 729 343 64
4
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0 270 1
5 512
2 216
1 125
8
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 8 512 216 125 27 729 343 64
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0 270 1
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2 216
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8
7 729
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 8 512 216 125 27 729 343 64
4
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0 270 1
5 512
2 216
1 125
8
7 729
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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0 1 8 512 216 125 27 729 343 64
4
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0 270 1
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8
7 729
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April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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8
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0 1 8 512 216 125 27 729 343 064
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0 270 1
5 512
2 216
1 125
8
7 729
3 343
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
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8
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0 1 8 512 216 125 27 729 343 64
4
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0 640 1
5 512
2 216
1 125
8
7 729
3 343
27
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
Pass 2
Pass 3
8
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
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
Pass 2
Pass 3
8
9
4
6
0 640 1
5 512
2 216
1 125
8
7 729
3 343
27
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
Pass 2
Pass 3
8
9
4
6
0 640 1
5 512
2 216
1 125
8
7 729
3 343
27
0 1 8 27 64
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
Pass 2
Pass 3
8
9
4
6
5 512
2 216
1 125
7 729
3 343
0 1 8 27 64
0
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
Pass 2
Pass 3
8
9
4
6
5 512
2 216
1 125
7 729
3 343
0 1 8 27 64 125
0
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
Pass 2
Pass 3
8
9
4
6
5 512
2 216
7 729
3 343
0 1 8 27 64 125
0
1
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
Pass 2
Pass 3
8
9
4
6
5 512
2 216
7 729
3 343
0 1 8 27 64 125 216
0
1
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
Pass 2
Pass 3
8
9
4
6
5 512
7 729
3 343
0 1 8 27 64 125 216
0
1
2
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
Pass 2
Pass 3
8
9
4
6
5 512
7 729
3 343
0 1 8 27 64 125 216 343
0
1
2
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
Pass 2
Pass 3
8
9
4
6
5 512
7 729
0 1 8 27 64 125 216 343
0
1
2
3
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
Pass 2
Pass 3
8
9
4
6
5 512
7 729
0 1 8 27 64 125 216 343 512
0
1
2
3
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
Pass 2
Pass 3
8
9
4
6
7 729
0 1 8 27 64 125 216 343 512
0
1
2
3
5
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
Pass 2
Pass 3
8
9
4
6
7 729
0 1 8 27 64 125 216 343 512 729
0
1
2
3
5
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
Pass 2
Pass 3
8
9
4
6
0 1 8 27 64 125 216 343 512 729
0
1
2
3
5
7
April 12, 2023April 12, 2023 www.gowrikumar.comwww.gowrikumar.com
Pass 1
Pass 2
Pass 3
The EndThe End