Part II While HeapSort (as we saw in Studio 6) is more amenable than MergeSort to an in-place implementation, MergeSort has its own advantages. For this problem, suppose you want to perform MergeSort on a really huge array A. The array is so big that it doesn't fit in your computer's memory and has to be stored in the cloud. More specifically, assume that our computer has enough memory to hold 36 elements, for some constant b, but A has size n much greater than b. We can call read (X, i, B) to read a chunk of b elements from an array X (in the cloud) starting at index i into a local array B. Similarly, we can call write (C, X, i) to write a chunk of b elements stored in local array C to a cloud array X starting at index i. Here's a proposed (incomplete!) implementation of the merge operation that merges cloud arrays X and Y into cloud array Z. The code uses local arrays A, B, and C, each of size b, to cache X, Y, and Z. For simplicity, we assume that the input arrays X and Y have sizes a multiple of b, and that reading past the end of either X or Y returns values oo as in the studio. "mod" is the integer modulo operator (% in Java). MERGE(X, Y, Z) i +0 j+0 k 0 READ(X, 0, A) READ(Y, 0, B) while A[i mod b] <∞ or Blj mod b] <∞ do u ← A[i mod b] v← B[j mod b] C[k mod b]= min(u, v) if u
Part II While HeapSort (as we saw in Studio 6) is more amenable than MergeSort to an in-place implementation, MergeSort has its own advantages. For this problem, suppose you want to perform MergeSort on a really huge array A. The array is so big that it doesn't fit in your computer's memory and has to be stored in the cloud. More specifically, assume that our computer has enough memory to hold 36 elements, for some constant b, but A has size n much greater than b. We can call read (X, i, B) to read a chunk of b elements from an array X (in the cloud) starting at index i into a local array B. Similarly, we can call write (C, X, i) to write a chunk of b elements stored in local array C to a cloud array X starting at index i. Here's a proposed (incomplete!) implementation of the merge operation that merges cloud arrays X and Y into cloud array Z. The code uses local arrays A, B, and C, each of size b, to cache X, Y, and Z. For simplicity, we assume that the input arrays X and Y have sizes a multiple of b, and that reading past the end of either X or Y returns values oo as in the studio. "mod" is the integer modulo operator (% in Java). MERGE(X, Y, Z) i +0 j+0 k 0 READ(X, 0, A) READ(Y, 0, B) while A[i mod b] <∞ or Blj mod b] <∞ do u ← A[i mod b] v← B[j mod b] C[k mod b]= min(u, v) if u
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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11, 12, 13
![**Part II**
While HeapSort (as we saw in Studio 6) is more amenable than MergeSort to an in-place implementation, MergeSort has its own advantages. For this problem, suppose you want to perform MergeSort on a really huge array A. The array is so big that it doesn’t fit in your computer’s memory and has to be stored in the cloud.
More specifically, assume that our computer has enough memory to hold 3b elements, for some constant b, but A has size n much greater than b. We can call `read(X, i, B)` to read a chunk of b elements from an array X (in the cloud) starting at index i into a local array B. Similarly, we can call `write(C, X, i)` to write a chunk of b elements stored in local array C to a cloud array X starting at index i.
Here’s a proposed (incomplete!) implementation of the merge operation that merges cloud arrays X and Y into cloud array Z. The code uses local arrays A, B, and C, each of size b, to cache X, Y, and Z. For simplicity, we assume that the input arrays X and Y have sizes a multiple of b, and that reading past the end of either X or Y returns values ∞ as in the studio. “mod” is the integer modulo operator (% in Java).
```plaintext
Merge(X, Y, Z)
i <- 0
j <- 0
k <- 0
READ(X, 0, A)
READ(Y, 0, B)
while A[i mod b] < ∞ or B[j mod b] < ∞ do
u <- A[i mod b]
v <- B[j mod b]
C[k mod b] = min(u, v)
if u < v
BLOCK1
else
BLOCK2
k <- k + 1
if k mod b = 0
WRITE(C, Z, k - b)
```
**Exercises:**
10. **Supply blocks of pseudocode** to replace the lines “BLOCK1” and “BLOCK2” to complete the implementation of the merge operation. Consider which parts of the regular merge algorithm are missing, and when/how to fetch more data from the cloud.
11. **Exactly how many times** must the merge function call each of `read`](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92856043-199e-49b6-95ce-27336f8d0cbd%2F9917d41b-eb73-4ca3-b8e9-98f6e858f942%2Fdxye3rf_processed.png&w=3840&q=75)
Transcribed Image Text:**Part II**
While HeapSort (as we saw in Studio 6) is more amenable than MergeSort to an in-place implementation, MergeSort has its own advantages. For this problem, suppose you want to perform MergeSort on a really huge array A. The array is so big that it doesn’t fit in your computer’s memory and has to be stored in the cloud.
More specifically, assume that our computer has enough memory to hold 3b elements, for some constant b, but A has size n much greater than b. We can call `read(X, i, B)` to read a chunk of b elements from an array X (in the cloud) starting at index i into a local array B. Similarly, we can call `write(C, X, i)` to write a chunk of b elements stored in local array C to a cloud array X starting at index i.
Here’s a proposed (incomplete!) implementation of the merge operation that merges cloud arrays X and Y into cloud array Z. The code uses local arrays A, B, and C, each of size b, to cache X, Y, and Z. For simplicity, we assume that the input arrays X and Y have sizes a multiple of b, and that reading past the end of either X or Y returns values ∞ as in the studio. “mod” is the integer modulo operator (% in Java).
```plaintext
Merge(X, Y, Z)
i <- 0
j <- 0
k <- 0
READ(X, 0, A)
READ(Y, 0, B)
while A[i mod b] < ∞ or B[j mod b] < ∞ do
u <- A[i mod b]
v <- B[j mod b]
C[k mod b] = min(u, v)
if u < v
BLOCK1
else
BLOCK2
k <- k + 1
if k mod b = 0
WRITE(C, Z, k - b)
```
**Exercises:**
10. **Supply blocks of pseudocode** to replace the lines “BLOCK1” and “BLOCK2” to complete the implementation of the merge operation. Consider which parts of the regular merge algorithm are missing, and when/how to fetch more data from the cloud.
11. **Exactly how many times** must the merge function call each of `read`
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