Upload the solutions to Lesson 11.

Author: Mickey0521

11-Sieve_cckao.pdf

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+# you can write to stdout for debugging purposes, e.g.
+# print("this is a debug message")
+
+import math
+
+def solution(A):
+
+    # count the elements of A (by using dictionary)
+    my_dictionary_1 = {}
+    for item in A:
+        if item not in my_dictionary_1:
+            my_dictionary_1[item] = 1
+        else:
+            my_dictionary_1[item] += 1
+    # print(my_dictionary_1)
+    
+    # count the number of non-divisors (into dictionary_2)
+    my_dictionary_2 = {}
+    for item in my_dictionary_1:
+        num_divisor = 0
+        item_sqrt = math.floor(math.sqrt(item))
+        # print( str(item) + ' , ' + str(item_sqrt) )
+        for i in range(1, item_sqrt+1, 1):
+            if (item % i ==0):
+                another_divisor = item / i 
+                
+                if i in my_dictionary_1:
+                    num_divisor = num_divisor + my_dictionary_1[i] 
+                
+                if another_divisor != i:
+                    if another_divisor in my_dictionary_1:
+                        num_divisor = num_divisor + my_dictionary_1[another_divisor]
+                
+        num_non_divisor = len(A) - num_divisor
+        my_dictionary_2[item] = num_non_divisor
+    # print(my_dictionary_2)
+    
+    # put the number of non-divisors into an 'array' (by using list)
+    array_non_divisor = []
+    for i in range( len(A) ):
+        array_non_divisor.append( my_dictionary_2[A[i]] )
+    
+    return array_non_divisor

CountNonDivisible.py

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+# you can write to stdout for debugging purposes, e.g.
+# print("this is a debug message")
+
+import math
+
+def solution(N, P, Q):
+    # write your code in Python 3.6
+    
+    # 1
+    # find primes: use 'Sieve of Eratosthenes'
+    prime_list_boolean = [True] * (N+1) # note: plus one for "0"
+    prime_list_boolean[0] = False   
+    prime_list_boolean[1] = False
+    for i in range( 2, math.floor(math.sqrt(N))+1 ):
+        if prime_list_boolean[i] == True:
+            j = i + i
+            for not_prime in range( j, N+1, i ):
+                prime_list_boolean[not_prime] = False
+    
+    # 2
+    # append 'prime' to list
+    prime_list = []
+    for index in range( N+1 ):
+        if prime_list_boolean[index] == True:
+            prime_list.append(index)
+    # print(prime_list)
+    
+    # 3
+    # find semi-primes
+    semiprime_list_boolean = [False] * (N+1) # note: plus one for "0"
+    for i in range( len(prime_list) ):
+        for j in range(i, len(prime_list), 1):
+            semiprime_temp = prime_list[i] * prime_list[j] 
+            if semiprime_temp > N:
+                break
+            else:
+                semiprime_list_boolean[semiprime_temp] = True
+
+    # 4
+    # count the number of semi-primes
+    count_semiprime_list = [0] * (N+1)
+    num_semiprime_so_far = 0
+    for i in range(N+1):
+        if semiprime_list_boolean[i]==True:
+            num_semiprime_so_far += 1
+        count_semiprime_list[i] = num_semiprime_so_far
+    #print(count_semiprime_list)
+    
+    # 5
+    # return answers to all the queries
+    answer_list = [0] * len(P)
+    for i in range( len(P) ):
+        begin_value = P[i]
+        end_value = Q[i]
+        #print(count_semiprime_list[end_value])
+        #print(count_semiprime_list[begin_value])
+        # be very careful about the 'begin_value' (not included)
+        answer_list[i] = count_semiprime_list[end_value] - count_semiprime_list[ (begin_value-1) ]
+    #print(answer_list)
+    
+    return answer_list

CountSemiprimes_high_performance.py

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+# you can write to stdout for debugging purposes, e.g.
+# print("this is a debug message")
+
+import math
+
+def solution(N, P, Q):
+    # write your code in Python 3.6
+    
+    # 1
+    # find primes: use 'Sieve of Eratosthenes'
+    prime_list = []
+    # put all values
+    # be careful about the range
+    for index in range( 2, N+1 ):
+        prime_list.append(index)
+    #print(prime_list)
+
+    # 2
+    # remove 'not prime'
+    # be careful about the range
+    for item in range( 2, math.floor(math.sqrt(N))+1 ):
+        not_prime_first = item + item
+        for not_prime in range( not_prime_first, N+1, item ):
+            if not_prime in prime_list:
+                prime_list.remove(not_prime)
+    #print(prime_list)
+
+    # 3
+    # find semi-primes
+    semiprime_list = []
+    for i in range( len(prime_list) ):
+        for j in range( i, len(prime_list) ):
+            semiprime = prime_list[i] * prime_list[j] 
+            if semiprime <= N:
+                semiprime_list.append(semiprime)
+    semiprime_list.sort()
+    #print(semiprime_list)
+    
+    # 4
+    # count the number of semi-primes
+    count_semiprime_list = [0] * (N+1)
+    num_semiprime_so_far = 0
+    for i in range(N+1):
+        if i in semiprime_list:
+            num_semiprime_so_far += 1
+        count_semiprime_list[i] = num_semiprime_so_far
+    #print(count_semiprime_list)
+    
+    # 5
+    # return answers to all the queries
+    answer_list = [0] * len(P)
+    for i in range( len(P) ):
+        begin_value = P[i]
+        end_value = Q[i]
+        #print(count_semiprime_list[end_value])
+        #print(count_semiprime_list[begin_value])
+        # be very careful about the 'begin_value' (not included)
+        answer_list[i] = count_semiprime_list[end_value] - count_semiprime_list[ (begin_value-1) ]
+    #print(answer_list)
+    
+    return answer_list