Consider the array:

42 88 4 889 9 72 4561 34

If these items are sorted into ascending order by the LSD Radix Sort algoirthm, what is the resulting sequence of items?

(enter each number, separated by a comma; do not use any spaces or quotation marks)

Question

Consider the array:

42	88	4	889	9	72	4561	34

If these items are sorted into ascending order by the LSD Radix Sort algoirthm, what is the resulting sequence of items?

(enter each number, separated by a comma; do not use any spaces or quotation marks)

BlackTom AI · Accepted Answer

Here is how LSD radix sort would process the numbers step by step, using base 10 and stable counting sorts by each digit from least significant to most significant.

Initial sequence: 42, 88, 4, 889, 9, 72, 4561, 34

First pass (units digit): sort by the ones place (0-9), keeping the relative order of numbers with the same units digit.
- 42 -> 2
- 88 -> 8
- 4 -> 4
- 889 -> 9
- 9 -> 9
- 72 -> 2
- 4561 -> 1
- 34 -> 4
Grouping by units digit while preserving order within each group yields: 4561 (1), 42 then 72 (2), 4 then 34 (4), 88 (8), 889 then 9 (9).
Result after pass 1: 4561, 42, 72, 4, 34, 88, 889, 9

Second pass (tens digit): sort by the tens place, using 0 for numbers with no tens, preserving order within equal tens digits.
- 4561 -> tens = 6
- 42 -> tens = 4
- 72 -> tens = 7
- 4 -> tens = 0
- 34 -> tens = 3
- 88 -> tens = 8
- 889 -> tens = 8
- 9 -> tens = 0
Grouping by tens digit: 0: 4, 9; 3: 34; 4: 42; 6: 4561; 7: 72; 8: 88, 889.
Result after pass 2: 4, 9, 34, 42, 4561, 72, 88, 889

Third pass (hundreds digit): sort by the hundreds place (0 for numbers with fewer than 3 digits).
- 4 -> hundreds = 0
- 9 -> hundreds = 0
- 34 -> hundreds = 0
- 42 -> hundreds = 0
- 4561 -> hundreds = 5
- 72 -> hundreds = 0
- 88 -> hundreds = 0
- 889 -> hundreds = 8
Grouping by hundreds digit: 0: 4, 9, 34, 42, 72, 88; 5: 4561; 8: 889.
Result after pass 3: 4, 9, 34, 42, 72, 88, 4561, 889

Fourth pass (thousands digit): sort by the thousands place (0 for numbers with fewer than 4 digits).
- 4, 9, 34, 42, 72, 88, 889 -> thousands = 0
- 4561 -> thousands = 4
Grouping: 0: 4, 9, 34, 42, 72, 88, 889; 4: 4561.
Result after pass 4: 4, 9, 34, 42, 72, 88, 889, 4561

Since all numbers are now in their final increasing order, the LSD radix sort yields the sequence above when read left to right.

XLMC0202501 Topic 24 Quiz

Consider the array: 42 88 4 889 9 72 4561 34 If these items are sorted into ascending order by the LSD Radix Sort algoirthm, what is the resulting sequence of items? (enter each number, separated by a comma; do not use any spaces or quotation marks)

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