Explain why this loop invariant has the inductive property
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
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Explain why this loop invariant has the inductive property
![1 For all i,k let V[i,k] = W[i,k] and back [i,k] = i.
2 For all i let V[i,i] = 0.
3 j = 0;
4 // loop invariant holds here
5 while(j < n)
6 {
7
// if the loop invariant holds here
8
j++;
9
for all i and k // really two nested loops
10
{
11
temp =
V[i,j]+V[j,k];
12
if (temp < V[i,k])
13
{
14
V[i,k] = temp;
15
back [i,k]
back [j,k] ;
%3D
16
}
17
}
18
// then the loop invariant holds here
19 }
20
// the loop invariant holds here and j = n, hence V[i,k] is the shortest path from i to k.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8286f434-a784-4f79-abd3-62efd8f21fc9%2F418a5c85-aa4e-4c82-b7da-e1dd59181bfe%2Fbk22ulg_processed.png&w=3840&q=75)
Transcribed Image Text:1 For all i,k let V[i,k] = W[i,k] and back [i,k] = i.
2 For all i let V[i,i] = 0.
3 j = 0;
4 // loop invariant holds here
5 while(j < n)
6 {
7
// if the loop invariant holds here
8
j++;
9
for all i and k // really two nested loops
10
{
11
temp =
V[i,j]+V[j,k];
12
if (temp < V[i,k])
13
{
14
V[i,k] = temp;
15
back [i,k]
back [j,k] ;
%3D
16
}
17
}
18
// then the loop invariant holds here
19 }
20
// the loop invariant holds here and j = n, hence V[i,k] is the shortest path from i to k.
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