(b) 1: function Func(A[],n) 2: X = 0 3: for i = 1 to √n] do m = Random(²) for j = 1 to m² do for k=1 toj do 4: 5: 6: 7: 8: 9: 10: x = x+im- jk end for end for end for
(b) 1: function Func(A[],n) 2: X = 0 3: for i = 1 to √n] do m = Random(²) for j = 1 to m² do for k=1 toj do 4: 5: 6: 7: 8: 9: 10: x = x+im- jk end for end for end for
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Question
Determine the expected case running time of the algorithm. Fully justify your solution.
Determine the best case running time of the algorithm and state what condition must be true for
it to occur. No justification is needed!
Determine the worst case running time of the algorithm and state what condition must be true for
it to occur. No justification is needed!
![Certainly! Below is the transcription of the code presented in the image:
---
### Function Definition
**Function** `Func(A[], n)`
1. Initialize `x = 0`
2. **For** `i` from `1` to `floor(sqrt(n))` **do**
3.   Set `m = Random(i^2)`
4.   **For** `j` from `1` to `m^2` **do**
5.    **For** `k` from `1` to `j` **do**
6.     Update `x = x + im - jk`
7.    **End For**
8.   **End For**
9. **End For**
10. **Return** `x`
**End Function**
---
**Explanation:**
This pseudocode describes a function `Func` that takes an array `A[]` and an integer `n` as inputs and computes a value `x`. The function initializes `x` to zero and iterates over three nested loops, modifying `x` with each iteration:
1. The outer loop iterates over `i` from `1` to the floor value of the square root of `n`.
2. Within this loop, `m` is randomly assigned a value based on the square of `i`.
3. A second loop iterates `j` from `1` to `m^2`.
4. A third nested loop runs `k` from `1` to `j`.
5. Inside the innermost loop, the value of `x` is updated by adding the product of `i` and `m` and subtracting the product of `j` and `k`.
Finally, the function returns the computed value `x`.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F330cf313-caca-43c7-afc0-d8b8f359cc96%2Fc4e763b4-b44a-41ad-abf1-a0ada576d2a8%2F3a6jy9x_processed.png&w=3840&q=75)
Transcribed Image Text:Certainly! Below is the transcription of the code presented in the image:
---
### Function Definition
**Function** `Func(A[], n)`
1. Initialize `x = 0`
2. **For** `i` from `1` to `floor(sqrt(n))` **do**
3.   Set `m = Random(i^2)`
4.   **For** `j` from `1` to `m^2` **do**
5.    **For** `k` from `1` to `j` **do**
6.     Update `x = x + im - jk`
7.    **End For**
8.   **End For**
9. **End For**
10. **Return** `x`
**End Function**
---
**Explanation:**
This pseudocode describes a function `Func` that takes an array `A[]` and an integer `n` as inputs and computes a value `x`. The function initializes `x` to zero and iterates over three nested loops, modifying `x` with each iteration:
1. The outer loop iterates over `i` from `1` to the floor value of the square root of `n`.
2. Within this loop, `m` is randomly assigned a value based on the square of `i`.
3. A second loop iterates `j` from `1` to `m^2`.
4. A third nested loop runs `k` from `1` to `j`.
5. Inside the innermost loop, the value of `x` is updated by adding the product of `i` and `m` and subtracting the product of `j` and `k`.
Finally, the function returns the computed value `x`.
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