GATE CSE 1987 | Question: 7a

Question

List the invariant assertions at points $A, B, C, D$ and $E$ in program given below:

Program division (input, output)
Const 
    dividend = 81; 
    divisor = 9;
Var  remainder, quotient:interger
begin 
    (*(dividend >= 0) AND (divisor > 0)*)  
    remainder := dividend;  
    quotient := 0;  
    (*A*)
While (remainder >= 0) do
begin (*B*)
    quotient := quotient + 1;
    remainder := remainder - divisor;
    (*C*)
end;  
    (*D*)
    quotient := quotient - 1;
    remainder := remainder + divisor;  
    (*E*)
end

Comments

Easy to understand resource:

https://www.cs.miami.edu/home/burt/learning/Math120.1/Notes/LoopInvar.html

Answer 1

A: remainder >= 0 and quotient = 9;

B: remainder >= 0 and quotient  <= divident/divisor

C: quotient - 1 <= divident/divisor

D: remainder < 0 and quotient - 1 = $\lfloor$ divident/divisor $\rfloor$

E: divident = divisor * quotient + remainder

PS: To be fixed.

Comments

@Arjun Sir what is meant by invariant assertions and how did you get this answer? 

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@Arjun sir, does this answer need any update?