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 resultdef 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 resultprint(sumOfCubeofAlt([1, 2, 3, 4, 5, 6])) |
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 resultdef 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)) |
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 resultdef 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 resultprint(sumOfCubeofAlt([1, 2, 3, 4, 5, 6])) |
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 arraydef 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])) |
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)) |
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)
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