Question

Among the above gropus, only groups 1,2 and 3 are valid groups, whereas group 4 is invalid because it consists of only 2 members.

hence, the output is 3.

Answer 1

# Python3 Program to Count groups
# of size 2 or 3 that have sum
# as multiple of 3
 
# Returns count of all possible
# groups that can be formed
# from elements of a[].


def findgroups(arr, n):
 


    # Create an array C[3] to store


    # counts of elements with 


    # remainder 0, 1 and 2. c[i] 


    # would store count of elements 


    # with remainder i


    c = [0, 0, 0]
 


    # To store the result


    res = 0
 


    # Count elements with remainder 


    # 0, 1 and 2


    for i in range(0, n):


        c[arr[i] % 3] += 1
 


    # Case 3.a: Count groups of size


    # 2 from 0 remainder elements


    res += ((c[0] * (c[0] - 1)) >> 1)
 


    # Case 3.b: Count groups of size


    # 2 with one element with 1


    # remainder and other with 2 remainder


    res += c[1] * c[2]
 


    # Case 4.a: Count groups of size


    # 3 with all 0 remainder elements


    res += (c[0] * (c[0] - 1) * (c[0] - 2)) / 6
 


    # Case 4.b: Count groups of size 3


    # with all 1 remainder elements


    res += (c[1] * (c[1] - 1) * (c[1] - 2)) / 6
 


    # Case 4.c: Count groups of size 3 


    # with all 2 remainder elements


    res += ((c[2] * (c[2] - 1) * (c[2] - 2)) / 6)
 


    # Case 4.c: Count groups of size 3


    # with different remainders


    res += c[0] * c[1] * c[2]
 


    # Return total count stored in res


    return res
 
# Driver program


arr = [3, 6, 7, 2, 9]


n = len(arr)
 


print ("Required number of groups are",


               int(findgroups(arr, n)))