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Assume radix sort has sorted integers by absolute value to produce the array (-12, 23, -42, 73, -78), and is about to build the negative and non-negative buckets to complete the sort.

What integers will be placed into the negative bucket?

Question

zyBooks_18

Assume radix sort has sorted integers by absolute value to produce the array (-12, 23, -42, 73, -78), and is about to build the negative and non-negative buckets to complete the sort.

What integers will be placed into the negative bucket?

BlackTom AI · Accepted Answer

To determine which integers go into the negative bucket, we need to recall how radix sort by absolute value would partition numbers before placing them into sign-based buckets.

First, list the given numbers with their signs and absolute values in the order provided: -12 (abs 12), 23 (abs 23), -42 (abs 42), 73 (abs 73), -78 (abs 78).

Next, understand the negative bucket should contain all numbers that are negative, regardless of their absolute values, since the negative bucket is intended for negative numbers before the final concatenation with non-negative numbers.

Now evaluate each option:
- Option 1: -42, 73, -78
  This set includes two negative numbers (-42, -78) correctly but omits -12 and erroneously places 73 (a non-negative) in the negative bucket. Since -12 is missing and 73 is included, this option is incorrect.
- Option 2: -12, 23
  This option contains -12 correctly, but it includes 23, which is non-negative, and omits -42 and -78. Therefore, it does not accurately represent all and only the negative numbers.
- Option 3: -12, -42, -78
  This option lists all and only the negative numbers from the list: -12, -42, and -78. It excludes the positive numbers 23 and 73 and captures every negative value present in the input.

Based on these checks, only the third option matches the expected negative bucket composition for this set of numbers when sorting by absolute value and partitioning by sign. The first two options either misplace a positive number into the negative bucket or omit one or more negative numbers, leading to incorrect partitioning.

zyBooks_18 Assume radix sort has sorted integers by absolute value to produce the array (-12, 23, -42, 73, -78), and is about to build the negative and non-negative buckets to complete the sort. What integers will be placed into the negative bucket?

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