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Explain why this loop invariant has the inductive property

Explain why this loop invariant has the inductive property

Computer Networking: A Top-Down Approach (7th Edition)
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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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.
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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