[mind_21]

hat will be the correct Loop invariant "I" for this Program
P =n >= 1
private static final long f i b ( int n ) {
long fib1 , fib 2 ;
int fib 3 = n − 1 ;
fib 1 = fib2 = 1 ;
while ( fib3 > 0 && fib3−− > 0) / / fib3 goes t o 0
fib2 = fib1 + ( fib1 = fib2 ) ;
System .out.println ( fib3 ) ;
return fib1 ;

Q = fib1 = F(n)

i have 3 possibility
I=fib3 = fib1 + fib2
I=fib1 + fib2 = F(n) ^ n − 1 >=fib3 >=−1
or
I=fib2 = fib1 + fib2 ^ 0 <= fib3 <= n




please i really need help on this subject , please

[mojo666]

I'm not sure what the loop invariant is in this case, however I do know that all of your statements are incorrect. An invariant can never be false.

1) I = fib3 = fib1 + fib2

fib3 is rarely if ever equal to fib1 + fib2. This statement is usually false.

2)I=fib1 + fib2 = F(n) ^ n − 1 >=fib3 >=−1

Where did the "F(n) ^ n − 1" come from? Anyways, fib1+fib2 is usually smaller than fib3 in the first few iterations, thus this statement can be false.

3) I=fib2 = fib1 + fib2 ^ 0 <= fib3 <= n

Again, not sure where the "fib1 + fib2 ^ 0" came from. fib3 is going to be 0 at the end of the loop. fib2 will never be smaller than 1. thus at the end of the loop "fib2<=fib3" is false.