Can anyone help me to understand the concept of loop invariants? I know it is a constant property throughout the iterations of a loop. However, there are so many unchanged properties through the iteration of a loop. How can I identify the correct loop invariants? What are the necessary steps to finish this kind of question?

Please show me your solution step-by-step, thanks.

2. Identify the loop invariant for the following algorithms. (a) function Sum(A) answer=0; n=length(A); for i=l to n answer += A[i] end return answer end (b) function Reverse (A) n=length(A) i=ceiling (n/2) j=ceiling (n/2) + (n+1) mod 2 while i >0 and ja tmp=A[i] A[i]=A[j] Aj]=tmp i=i-1 j=j+1 end end (c) Assume that A is sorted such that the largest value is at A[n]. Assume A contains the value target. function Search (A, target) //returns the index of the value target left=1 right=length(A) while left target right=m-1 else return m end end end