Suppose you are Radix-sorting N numbers with D digits, using B buckets. What's the best description of the runtime of Radix sort? OO(ND+BD) O(N+B+D) O(N log N) O(N?) O(ND) O(N) O(NDB) Now suppose the numbers are all 64-bit integers. What's the best description of the runtime of Radix sort? O(N log N) O(N?) O(ND+BD) OO(N+B+D) O(N) OO(NDB) OO(ND)

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**Radix Sort Runtime Analysis**

When sorting \( N \) numbers with \( D \) digits using \( B \) buckets, the runtime of the Radix sort can be described as follows:

1. \( O(ND + BD) \)
2. \( O(N + B + D) \)
3. \( O(N \log N) \)
4. \( O(N^2) \)
5. \( O(ND) \)
6. \( O(N) \)
7. \( O(NDB) \)

**Special Case: 64-bit Integers**

For numbers that are all 64-bit integers, the best description of the runtime of Radix sort is:

1. \( O(N \log N) \)
2. \( O(N^2) \)
3. \( O(ND + BD) \)
4. \( O(N + B + D) \)
5. \( O(N) \)
6. \( O(NDB) \)
7. \( O(ND) \)

Explore how the complexity changes with the number of digits and buckets used in sorting, and understand the efficiency of Radix sort for different data sets.
Transcribed Image Text:**Radix Sort Runtime Analysis** When sorting \( N \) numbers with \( D \) digits using \( B \) buckets, the runtime of the Radix sort can be described as follows: 1. \( O(ND + BD) \) 2. \( O(N + B + D) \) 3. \( O(N \log N) \) 4. \( O(N^2) \) 5. \( O(ND) \) 6. \( O(N) \) 7. \( O(NDB) \) **Special Case: 64-bit Integers** For numbers that are all 64-bit integers, the best description of the runtime of Radix sort is: 1. \( O(N \log N) \) 2. \( O(N^2) \) 3. \( O(ND + BD) \) 4. \( O(N + B + D) \) 5. \( O(N) \) 6. \( O(NDB) \) 7. \( O(ND) \) Explore how the complexity changes with the number of digits and buckets used in sorting, and understand the efficiency of Radix sort for different data sets.
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