For this pseudocode present a loop invariant and prove it, n >= 0. i <= 0;...
For this pseudocode present a loop invariant and prove it, n >= 0.
i <= 0;
s <=2;
while i < n do
i <= i + 1
s <= s * s
Homework Answers
The best loop invariant for this while loop is n-i > 0. Because the loop executes when the value of i is less than n. It terminates once when the i value becomes equal to n.
For example, if n = 5. i = 0 starts with 0.
Iteration 1 : n > i , i = 0, 5 - 0 > 0
Iteration 2 : n > i , i = 1, 5 - 1 > 0
Iteration 3 : n > i , i = 2, 5 - 2 > 0
Iteration 4 : n > i , i = 3, 5 - 3 > 0
Iteration 5 : n > i , i = 4, 5 - 4 > 0
Iteration 6 : n > i , i = 5, 5 - 5 = 0 --> Loop terminates.
From iteration 1 to 5 the loop invariant n - i > 0 holds.
**Comment for any further queries.
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For this pseudocode present a loop invariant and prove it, n
>= 0.
i <= 0;...
(a) Prove the following loop invariant by induction on the number of loop iterations: Loop Invariant:...
(a) Prove the following loop invariant by induction on the
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of the for loop, total = a1 + a2 + · · · + ak and L contains
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To prove the correctness of the following: # pre: int >= 1 fac = 1 i...
To prove the correctness of the following:
# pre: int >= 1
fac = 1
i = n
while i>0:
fac = fac*i
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which loop invariant do we need?
(Hint, you will need two statements that are both
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Please provide both full statements as well as which
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(a) Prove the following loop invariant by induction on the
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of the for loop, total = a1 + a2 + · · · + ak and L contains
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(b) Use the loop invariant to prove that the algorithm is
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while i>0:
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which loop invariant do we need?
(Hint, you will need two statements that are both
true. One about fac and one about i)
Please provide both full statements as well as which
loop invariant is needed in a full proof.
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