Part B: Problem 4: Describe specific loop invariant(s) for proving correct- ness for each of the following algorithms. You do not have to prove that the algorithms are correct: (a) def find_min(A): min =A[0] for i in range(1, len(A)): if min > A[i]: min =A[i] return min (b) def find max(A): for i in range(0, len(A)): isMax = True for j in range(0, len (A)): if A[j] A[i]: isMax = False if isMax: return A[i] (c) def even numbers (A): E = [] for i in range(0, len (A)): if A[i] % 2 0: return E E.append(A[i]) (d) def double_array(A): for i in range(0, len(A)): A[i] =A[i] ✶ 2 return A (e) def dot product (A, B): sum = 0.0 for i in range(0, min(len(A), len(B))): sum sum + A[i]*B[i] return sum
Part B: Problem 4: Describe specific loop invariant(s) for proving correct- ness for each of the following algorithms. You do not have to prove that the algorithms are correct: (a) def find_min(A): min =A[0] for i in range(1, len(A)): if min > A[i]: min =A[i] return min (b) def find max(A): for i in range(0, len(A)): isMax = True for j in range(0, len (A)): if A[j] A[i]: isMax = False if isMax: return A[i] (c) def even numbers (A): E = [] for i in range(0, len (A)): if A[i] % 2 0: return E E.append(A[i]) (d) def double_array(A): for i in range(0, len(A)): A[i] =A[i] ✶ 2 return A (e) def dot product (A, B): sum = 0.0 for i in range(0, min(len(A), len(B))): sum sum + A[i]*B[i] return sum
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![Part B: Problem 4: Describe specific loop invariant(s) for proving correct-
ness for each of the following algorithms. You do not have to prove that the
algorithms are correct:
(a) def find_min(A):
min =A[0]
for i in range(1, len(A)):
if min > A[i]:
min =A[i]
return min
(b) def find max(A):
for i in range(0, len(A)):
isMax = True
for j in range(0, len (A)):
if A[j]
A[i]:
isMax = False
if isMax:
return A[i]
(c) def even numbers (A):
E = []
for i in range(0, len (A)):
if A[i] % 2 0:
return E
E.append(A[i])
(d) def double_array(A):
for i in range(0, len(A)):
A[i] =A[i] ✶ 2
return A
(e) def dot product (A, B):
sum = 0.0
for i in range(0, min(len(A), len(B))):
sum sum + A[i]*B[i]
return sum](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F484188b8-fc12-4b00-9063-5f4fd5fd3e65%2Fa5287db2-1b03-4ca1-8ef6-edd28d715c29%2F1ywof6d_processed.png&w=3840&q=75)
Transcribed Image Text:Part B: Problem 4: Describe specific loop invariant(s) for proving correct-
ness for each of the following algorithms. You do not have to prove that the
algorithms are correct:
(a) def find_min(A):
min =A[0]
for i in range(1, len(A)):
if min > A[i]:
min =A[i]
return min
(b) def find max(A):
for i in range(0, len(A)):
isMax = True
for j in range(0, len (A)):
if A[j]
A[i]:
isMax = False
if isMax:
return A[i]
(c) def even numbers (A):
E = []
for i in range(0, len (A)):
if A[i] % 2 0:
return E
E.append(A[i])
(d) def double_array(A):
for i in range(0, len(A)):
A[i] =A[i] ✶ 2
return A
(e) def dot product (A, B):
sum = 0.0
for i in range(0, min(len(A), len(B))):
sum sum + A[i]*B[i]
return sum
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