Python Program to Get Sum of cubes of alternate even numbers in an array

Given an array, write a program to find the sum of cubes of alternative even numbers in an array.

Examples:

Input : arr = {1, 2, 3, 4, 5, 6}
Output : Even elements in given array are
2,4,6
Sum of cube of alternate even numbers are 2**3+6**3 = 224

Input : arr = {1,3,5,8,10,9,11,12,1,14}
Output : Even elements in given array are
8,10,12,14
Sum of cube of alternate even numbers are 8**3+12**3=2240

Method 1: Using Iterative method

• Start traversing the array from left to right.
• Maintain a result variable.
• Maintain a Boolean variable to check whether the current element should be added to the result or not.
• If the current element is even and it is an alternate element then find the cube of that element and add to the result.
• Finally, print the result.

Below is the implementation of the above approach

Python3

# Python program to find out
# Sum of cubes of alternate
# even numbers in an array

# Function to find result


def sumOfCubeofAlt(arr):
    n = len(arr)
# Maintain a Boolean variable to check whether current
# element should be added to result or not.
    isAlt = True
    result = 0
    for i in range(n):
        if arr[i] % 2 == 0:
            # If the current element is
            # even and it is alternate

            # element then find the cube of
            # that element and add to the result.
            if isAlt:
                result += int(arr[i]**3)
                isAlt = False
            else:
                isAlt = True
    return result


print(sumOfCubeofAlt([1, 2, 3, 4, 5, 6]))

Output

224

Complexity Analysis:

Time complexity: O(n)
Auxiliary Space: O(1)

Method 2: Using Recursive method

• We can implement the above approach using recursion by passing 4 parameters to the recursive function. The array itself, the index variable( to know where the array is traversed), a Boolean variable to check whether the current element should be added to the result or not, and the result variable to store the final result ( Cube of alternate even numbers).
• The base case is to check whether the index is reached at the end of an array or not.
• If the index is reached to end then stop calling the function and return the result.

Below is the implementation of the above approach

Python3

# Python program to find out
# Sum of cubes of alternate
# even numbers in an array

# Recursive Function to find result


def sumOfCubeofAlt(arr, index, isAlt, ans):
    # Base case, when index reached the
    # end of array then stop calling function.
    if index >= len(arr):
        return ans
    if arr[index] % 2 == 0:
        # If the current element is even and it is alternate
        # element then find the cube of that element and add to the result.
        if isAlt:
            ans += int(arr[index]**3)
            isAlt = False
        else:
            isAlt = True
    return sumOfCubeofAlt(arr, index+1, isAlt, ans)


# isAlt a Boolean variable to check whether current
# element should be added to result or not.
print(sumOfCubeofAlt([1, 2, 3, 4, 5, 6], 0, True, 0))

Output

224

Complexity Analysis:

Time complexity: O(n)
Auxiliary Space: O(n) for recursion call stack.

Method  3:Using range() function

We first get all the even numbers of the list. Then we find sum of cubes of alternate numbers of the above even numbers list

Python3

# Python program to find out
# Sum of cubes of alternate
# even numbers in an array

# Function to find result


def sumOfCubeofAlt(arr):
    result = 0
    evenList = []
    # Getting even numbers from the array
    for i in arr:
        if(i % 2 == 0):
            evenList.append(i)
    n = len(evenList)
    # Getting the cubes of alternate even numbers
    for i in range(0, n, 2):
        result += int(evenList[i]**3)

    return result


print(sumOfCubeofAlt([1, 2, 3, 4, 5, 6]))

Output

224

Time Complexity: O(n)
Auxiliary Space: O(n)

Method #4 : Using filter() and math.pow() methods

Python3

# Python program to find out
# Sum of cubes of alternate
# even numbers in an array
def sumOfCubeofAlt(arr):
    x=list(filter(lambda x: x % 2 == 0, arr))
    res=0
    for i in range(0,len(x)):
        if i%2==0:
            import math
            res+=math.pow(x[i],3)
    return int(res)

print(sumOfCubeofAlt([1, 2, 3, 4, 5, 6]))

Output

224

Time Complexity : O(N)
Auxiliary Space : O(N)

Using list comprehension in python:

Approach:

In this approach, we will use list comprehension to get a list of even elements and a list of even elements with even indices. We will then calculate the sum of cubes of the even elements with even indices using another list comprehension.

Define a function named sum_of_cubes that takes an array arr as an argument.
Use list comprehension to create a list called even_nums that contains all even numbers in the array arr.
Use list comprehension to create another list called even_nums_even_index that contains all even numbers from the list even_nums that have an even index.
Calculate the sum of cubes of the numbers in the list even_nums_even_index using another list comprehension.
Return the sum of cubes from step 4.

Python3

def sum_of_cubes(arr):
    even_nums = [x for x in arr if x % 2 == 0]
    even_nums_even_index = [even_nums[i] for i in range(len(even_nums)) if i % 2 == 0]
    return sum([x**3 for x in even_nums_even_index])

arr1 = [1, 2, 3, 4, 5, 6]
arr2 = [1, 3, 5, 8, 10, 9, 11, 12, 1, 14]

print("Even elements in the first array are:", [x for x in arr1 if x % 2 == 0])
print("Sum of cube of alternate even numbers in the first array is:", sum_of_cubes(arr1))

print("Even elements in the second array are:", [x for x in arr2 if x % 2 == 0])
print("Sum of cube of alternate even numbers in the second array is:", sum_of_cubes(arr2))

Output

Even elements in the first array are: [2, 4, 6]
Sum of cube of alternate even numbers in the first array is: 224
Even elements in the second array are: [8, 10, 12, 14]
Sum of cube of alternate even numbers in the second array is: 2240

Time complexity: O(n)
Space complexity: O(n)