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If we use Radix Sort to sort n integers in the range (nk/2,nk], for some k>0 which is independent of n, the time taken would be?
- a)Θ(n)
- b)Θ(kn)
- c)Θ(nlogn)
- d)Θ(n2)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If we use Radix Sort to sort n integers in the range (nk/2,nk], for so...
Radix sort time complexity = O(wn)
for n keys of word size= w
⇒w = log(nk)
O(wn)=O(klogn.n)
⇒ kO(nlogn)
for n keys of word size= w
⇒w = log(nk)
O(wn)=O(klogn.n)
⇒ kO(nlogn)
Most Upvoted Answer
If we use Radix Sort to sort n integers in the range (nk/2,nk], for so...
Radix sort time complexity = O(wn)
for n keys of word size= w
⇒w = log(nk)
O(wn)=O(klogn.n)
⇒ kO(nlogn)
for n keys of word size= w
⇒w = log(nk)
O(wn)=O(klogn.n)
⇒ kO(nlogn)
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Community Answer
If we use Radix Sort to sort n integers in the range (nk/2,nk], for so...
Explanation:
Radix Sort:
- Radix Sort is a non-comparative integer sorting algorithm that sorts data with integer keys by grouping keys by individual digits which share the same significant position and value.
- It processes the digits one at a time, starting from the least significant digit to the most significant digit.
Time Complexity of Radix Sort:
- The time complexity of Radix Sort is O(nk) for n keys which are integers of k bits.
- When sorting n integers in the range (nk/2, nk], for some k > 0, the time complexity would be O(nlogn).
- This is because the range of integers is nk/2 to nk, which is essentially nlogn. This means that the integers are in the range of O(nlogn) bits.
Explanation of Option 'C' (Theta(nlogn)):
- The time complexity of Radix Sort for n integers in the range (nk/2, nk] is O(nlogn).
- This is because the range of integers falls within the O(nlogn) range due to the constraint k > 0.
- Therefore, the correct answer is option 'C' which states that the time taken would be Theta(nlogn).
Radix Sort:
- Radix Sort is a non-comparative integer sorting algorithm that sorts data with integer keys by grouping keys by individual digits which share the same significant position and value.
- It processes the digits one at a time, starting from the least significant digit to the most significant digit.
Time Complexity of Radix Sort:
- The time complexity of Radix Sort is O(nk) for n keys which are integers of k bits.
- When sorting n integers in the range (nk/2, nk], for some k > 0, the time complexity would be O(nlogn).
- This is because the range of integers is nk/2 to nk, which is essentially nlogn. This means that the integers are in the range of O(nlogn) bits.
Explanation of Option 'C' (Theta(nlogn)):
- The time complexity of Radix Sort for n integers in the range (nk/2, nk] is O(nlogn).
- This is because the range of integers falls within the O(nlogn) range due to the constraint k > 0.
- Therefore, the correct answer is option 'C' which states that the time taken would be Theta(nlogn).
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