Consider a following algorithm and answer the questions below. ALGORITHM(X) INPUT: Integer X OUTPUT: Integer count 1 count = 0 2 conver X to bit string S 3 while S# 0 (A) 14 count = count + 1 5 S=SA (S - 1) 6 return count What is the time complexity of this algorithm in Theta(0) notation where the size of bit string S is n? Justify your answer. • Suppose that the following loop is inserted in (A). Does it affect the complexity? If so, find the complexity in Theta(0) notation. Justify your answer. for i = 0 to S.length - 1

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Consider the following algorithm and answer the questions below.

**ALGORITHM(X)**

- **INPUT:** Integer \(X\)
- **OUTPUT:** Integer count

1. \( \text{count} = 0 \)
2. Convert \( X \) to bit string \( S \)
3. **while** \( S \neq 0 \)
   - (A)
4. \( \text{count} = \text{count} + 1 \)
5. \( S = S \land (S - 1) \)
6. **return** count

---

- **Q1:** What is the time complexity of this algorithm in Theta (Θ) notation where the size of bit string \( S \) is \( n \)? Justify your answer.
  
- **Q2:** Suppose that the following loop is inserted in (A). Does it affect the complexity? If so, find the complexity in Theta (Θ) notation. Justify your answer.

  ```
  for i = 0 to S.length - 1
      print S[i]
      i = i + 1
  ```

- **Q3:** What is the return value when \( X \) is 79?
Transcribed Image Text:Consider the following algorithm and answer the questions below. **ALGORITHM(X)** - **INPUT:** Integer \(X\) - **OUTPUT:** Integer count 1. \( \text{count} = 0 \) 2. Convert \( X \) to bit string \( S \) 3. **while** \( S \neq 0 \) - (A) 4. \( \text{count} = \text{count} + 1 \) 5. \( S = S \land (S - 1) \) 6. **return** count --- - **Q1:** What is the time complexity of this algorithm in Theta (Θ) notation where the size of bit string \( S \) is \( n \)? Justify your answer. - **Q2:** Suppose that the following loop is inserted in (A). Does it affect the complexity? If so, find the complexity in Theta (Θ) notation. Justify your answer. ``` for i = 0 to S.length - 1 print S[i] i = i + 1 ``` - **Q3:** What is the return value when \( X \) is 79?
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