Consider the array:

42 88 4 889 9 72 4561 34

If these items are sorted into descending order by the MSD 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 descending order by the MSD 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

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

We will walk through the MSD (most-significant-digit) radix sort process in descending order. The key idea is to repeatedly group numbers by their current most-significant digit, starting from the highest possible leading digit and moving downward, while preserving the recursive ordering within each group when there are multiple digits left.

Step-by-step analysis of the decision points:
- Identify the most significant digit (MSD) of each number:
  - 42 has MSD 4
  - 88 has MSD 8
  - 4 has MSD 4
  - 889 has MSD 8
  - 9 has MSD 9
  - 72 has MSD 7
  - 4561 has MSD 4
  - 34 has MSD 3
- In descending MSD order, we would normally group by MSD in the sequence of digits 9, 8, 7, 4, 3 (and so on). This means numbers with MSD 9 come first, followed by those with MSD 8, then 7, then 4, then 3, etc.
- Consider the 9-group first: {9}. Since there is only one element, its position is determined (as a standalone block).
- Next, the 8-group: {88, 889}. Within the 8-group, MSD radix sort would then look at the next digit (the second most-significant digit) to order these elements, in descending order. The second digits are: for 88 there is no second digit (treated as shorter), for 889 the second digit is 8. Depending on the exact MSD radix sort implementation, the shorter number might come before or after the longer one when the prefix is the same. If we follow a typical stable MSD approach and consider the absence of a second digit as a terminating case, we might place 88 before 889, or vice versa. Either way, both stay before any numbers whose MSD is less than 8.
- Then the 7-group: {72}. This block would come after all 8- and 9-leading numbers and before the 4- and 3-leading numbers, under standard descending MSD ordering.
- Next the 4-group: {42, 4, 4561}. Within this block, we again inspect the next digits to determine the internal order. For 42 (second digit 2), 4 (no second digit), and 4561 (second digit 5), the ordering would depend on how ties and missing digits are handled. In many MSD implementations, numbers with fewer digits (i.e., shorter length) are treated as ending and could be placed before longer numbers sharing the same prefix, or after, depending on the exact rule. The specific internal ordering of {42, 4, 4561} is therefore determined by that sub-pass.
- Finally, the 3-group: {34}, which would be placed after the entire 4-group in a strict descending-by-MSD scheme because 3 < 4.
- Putting this together under the standard MSD descending framework yields a final sequence that starts with the 9-group, then 8-group, then 7-group, then 4-group, then 3-group, with internal ordering determined recursively for each group.

Observation about the provided answer:
- The given answer sequence in the prompt is 4561,889,88,72,42,34,9,4. If we compare this to the expectation from a conventional MSD radix sort in descending order by the most significant digit, this result seems inconsistent: it starts with 4561 (MSD 4) before numbers with MSD 9, 8, and 7, which would normally appear earlier in a descending-MSD sort. This suggests either a nonstandard tie-breaking rule within groups, a different convention for handling numbers with fewer digits, or a mismatch between the stated sorting objective and the sample output.

Key takeaways about the options and reasoning:
- The core principle of MSD radix sort in descending order is to prioritize the highest leading digit first (9, then 8, then 7, etc.), and only then resolve order within each group using subsequent digits.
- When numbers share the same MSD, their order is determined by the next digits (or by the rule that handles numbers with fewer digits). Different MSD sort implementations may handle the “shorter length” case differently, which can lead to variations in the final order for numbers with the same leading digit.
- If you rely on a standard MSD radix sort with descending MSD order and typical tie-handling, you would expect 9 to appear before 8s, 7s, and so on, which contrasts with the provided sequence.

In summary, while the question asks for the final sequence under MSD radix sort in descending order, the specific provided sequence appears to conflict with the conventional ordering rules for MSD radix sort. The reasoning above outlines how the standard process would proceed and where the discrepancy lies between the standard method and the given answer.

XLMC0202501 Topic 24 Quiz

Consider the array: 42 88 4 889 9 72 4561 34 If these items are sorted into descending order by the MSD 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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