Problem 1 (Preserving Invariants). For each of the following loop invariants, determine whether or not the loop invariant is true every time, and justify your answer.
(a)
i=0
j=0
while ( j < 10000):
#LI : 2 * i == j
i = i+2
j = j+4
(b)
i=4
j=2
while ( j < 10000):
#LI : 2 * i == j
i = i+2
j = j+4
(c)
k=0
i=0
while (k <= 10000):
#LI : i == k
k = k + 1
i = i + 2
(d)
n = . . . some positive number . . .
i=0
while ( i < n ) :
# LI : i <= n
i = i + 2
(e)
n = . . . some positive number . . .
i=0
while ( i < n ) :
# LI : i <= n
i = i + 1
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Problem 1 (Preserving Invariants)a) The loop invariant is true every iteration of the loop.
i will have values 0, 2, 4, 6, 8, 10, …
j will have values 0, 4, 8, 12, 16, 20, …
It is always true that j is equal to 2 * i
b) The loop invariant is false from the start.
i will have values 4, 6, 8, 10, 12, 14, …...
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