Consider the array:

"one" "ring" "to" "bring" "them" "all" "and" "in" "the" "darkness" "bind" "them"

If these items are sorted into ascending order by the MSD Radix Sort algoirthm, which of the following is the resulting sequence?

Sequence A:

"to" "them" "them" "the" "ring" "one" "in" "darkness" "bring" "bind" "and" "all"

Sequence B:

"all" "and" "bind" "bring" "darkness" "in" "one" "ring" "the" "them" "them" "to"

Sequence C:

"in" "to" "all" "and" "one" "bind" "ring" "the" "them" "them" "bring" "darkness"

Sequence D:

"darkness" "bring" "them" "them" "the" "ring" "bind" "one" "and" "all" "to" "in"

Question

Consider the array:

"one"	"ring"	"to"	"bring"	"them"	"all"	"and"	"in"	"the"	"darkness"	"bind"	"them"

If these items are sorted into ascending order by the MSD Radix Sort algoirthm, which of the following is the resulting sequence?

Sequence A:

"to"	"them"	"them"	"the"	"ring"	"one"	"in"	"darkness"	"bring"	"bind"	"and"	"all"

Sequence B:

"all"	"and"	"bind"	"bring"	"darkness"	"in"	"one"	"ring"	"the"	"them"	"them"	"to"

Sequence C:

"in"	"to"	"all"	"and"	"one"	"bind"	"ring"	"the"	"them"	"them"	"bring"	"darkness"

Sequence D:

"darkness"	"bring"	"them"	"them"	"the"	"ring"	"bind"	"one"	"and"	"all"	"to"	"in"

BlackTom AI · Accepted Answer

We start by restating the problem: we have an array of strings: ["one", "ring", "to", "bring", "them", "all", "and", "in", "the", "darkness", "bind", "them"]. We are asked to determine, under MSD Radix Sort with ascending order, what the final sequence would be. The choices present four full sequences to compare.

Option A: Sequence A shows the order ["to", "them", "them", "the", "ring", "one", "in", "darkness", "bring", "bind", "and", "all"]. If we examine MSD radix sort step by step, the first character (most significant) of each string determines the grouping. In ascending order, strings starting with 'a' would come first, then 'b', and so on. Here the initial letters include 'a', 'b', 'd', 'i', 't', 'o', 'r', 't', 'd', 'b', 't', 't'. The arrangement in A places some high-lexical-starting words before others (e.g., "to" starting with 't' before "one" starting with 'o'), which contradicts the grouping by first character. This suggests A is not aligned with MSD grouping by the first character. Overall, A does not reflect the proper bucket order by the most significant character, so it is unlikely to be the MSD-sorted result.

Option B: Sequence B lists ["all", "and", "bind", "bring", "darkness", "in", "one", "ring", "the", "them", "them", "to"]. This ordering corresponds to lexicographic ascending order when considering the first character: words starting with 'a' come first ("all", "and"), then 'b' ("bind", "bring"), then 'd' ("darkness"), then 'i' ("in"), then 'o' ("one"), then 'r' ("ring"), then 't' ("the", "them", "them", "to"). Within the 't' group, the ordering is lexicographically correct as well ("the" < "them" < "them" < "to"). This pattern matches an MSD Radix Sort’s behavior for ascending order, where the most significant character groups are sorted, and within each bucket, items are ordered lexicographically. Therefore, Option B matches the expected ascending MSD-sort result.

Option C: Sequence C shows ["in", "to", "all", "and", "one", "bind", "ring", "the", "them", "them", "bring", "darkness"]. This arrangement places "in" (starting with 'i') before "to" ('t') and "darkness" ('d') after several items starting with later letters, which disrupts the expected bucket order by the first character (we should see starting letters from smallest to largest: 'a', 'b', 'd', 'i', 'o', 'r', 't' in that overall progression). It fails to maintain the proper first-character grouping, indicating it is not the MSD sort result.

Option D: Sequence D lists ["darkness", "bring", "them", "them", "the", "ring", "bind", "one", "and", "all", "to", "in"]. This begins with 'd', followed by 'b', then 't', then 'r', then 'o', then 'a', then 't', then 'i'. This order does not follow ascending first-character buckets ('a' before 'b', before 'd', etc.). The presence of "darkness" before many items starting with earlier letters and the overall scattered order indicate a violation of the MSD sorting principle, so D cannot be correct.

In summary, when evaluating each option against the core principle of MSD Radix Sort—sorting primarily by the most significant character in ascending order and then recursively within each bucket—Option B aligns with the expected lexicographic progression across buckets and within buckets, while the other sequences violate the first-character grouping or intra-bucket ordering. The reasoning here hinges on recognizing that MSD radix sort groups by the first character and uses lexical order within each group, not a mixed sequence that disregards those buckets.

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