Question

We are given four items, namely A, B, C, and D. Their corresponding unit profits are p_A, p_B, p_C, and p_D. The following shows five transactions with these items. Each row corresponds to a transaction where a non-negative integer shown in the row corresponds to the total number of occurrences of the correspondence item present in the transaction.

T	A	B	C	D
t1	0	0	3	2
t2	3	4	0	0
t3	0	0	1	3
t4	1	0	3	5
t5	6	0	0	0

• The frequency of an itemset in a row is defined to be the minimum of the number of occurrences of      all items in the itemset. For example, itemset {C, D} in the first row has frequency equals 2. But, itemset {C, D} in the third row has frequency as 1.
• The frequency of an itemset in the dataset is defined to be the sum of the frequencies of the itemset in all rows in the dataset. For example, itemset {C, D} has frequency 2+0+1+3+0=6.

Let f be a function defined on an itemset s (f will be specified later). One example of this functions is

f (s) = i∈s p_i. In this example, if s = {C, D}, then f (s) = p_C+ p_D.

• The profit of an itemset s in the dataset is defined to be the product of the frequency of this itemset in the dataset and f (s). For example, itemset {C, D} has profit 6 × f ({C, D}).

Answer the following question based on the above problem setting.

Assume f (s) = i∈s p_i. Suppose that we know p_A= 5, p_B= 10, p_C= 6, and p_D= 4. We want to find all itemsets with profit at least 50. Can the Apriori Algorithm be adapted to find these itemsets? If yes, please write down the pseudo-code and illustrate it with the above example. If no, please explain why. In this case, please also design an algorithm for this problem and write down the pseudo-code.

Answer 1

class compare():

def __init__(self):
self.dic = {}
self.flis = {}
def adding2(self,x,y):
#print("a")
checks = self.dic.get(x)
if checks is not None:
#print("checks")
for check in checks:
#print(check[0])
#print(x,y)
#print(check[0])
if y == check[0]:
break
else:
if check[0]==checks[len(checks)-1][0]:
if x>y:
self.dic[x].append((y,True))
checkys = self.dic.get(y)
if checkys is not None:
for checky in checkys:
if x == checky[0]:
break
else:
if checky[0]==checkys[len(checkys)-1][0]:

self.dic[y].append((x,False))
else:
self.dic[y]=[]
self.dic[y].append((x,False))

else:

self.dic[x].append((y,False))
checkys = self.dic.get(y)
if checkys is not None:
for checky in checkys:
if x == checky[0]:
break
else:
if checky[0]==checkys[len(checkys)-1][0]:
self.dic[y].append((x,True))
else:
self.dic[y]=[]
self.dic[y].append((x,True))

break
  
else:
self.dic[x]=[]
#print("c")
if x>y:
self.dic[x].append((y,True))
checkys = self.dic.get(y)
if checkys is not None:
for checky in checkys:
if x == checky[0]:
break
else:
if checky[0]==checkys[len(checkys)-1][0]:
self.dic[y].append((x,False))
else:
self.dic[y]=[]
self.dic[y].append((x,False))

else:
self.dic[x].append((y,False))
checkys = self.dic.get(y)
if checkys is not None:
for checky in checkys:
if x == checky[0]:
break
else:
if checky[0]==checkys[len(checkys)-1][0]:
self.dic[y].append((x,True))
else:
self.dic[y]=[]
self.dic[y].append((x,True))

def myfunc(self,x,y):
self.adding2(x,y)

def arrfunc(self,nums):
self.lis= nums
i = len(nums)
  
  

# print(3>0)
for x in range(0,i):
for y in range(x,i):
#print(nums[x],nums[y])
#if nums[x]!=nums[y]:
#print(nums[x],nums[y])
self.myfunc( nums[x],nums[y])

#print(self.dic)
for x in self.dic:
count=1
res = self.dic.get(x)
for ress in res:
if ress[1] is True:
count=count+1
self.flis[x]=count
#print(self.dic)
print(self.flis)

if __name__ == "__main__":
obj = compare()
lis = [60,51,87,40]
obj.arrfunc(lis)